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Information theoretical action selection

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Information theoretical action selection

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Content Information Theoretical Action Selection
by
Christian Potthast
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements of the Degree
DOCTOR OF PHILOSOPHY
(Computer Science)
Committee:
Prof. Gaurav S. Sukhatme (Chair) Computer Science
Prof. Stefan Schaal Computer Science
Prof. Sandeep K. Gupta Electrical Engineering
August, 2016
Copyright 2016 Christian Potthast
Dedicated to my family
ii
Acknowledgements
First of all, I would like to thank my Ph.D. advisor Professor Gaurav Sukhatme for his
guidance and supported during my time at USC. I especially thank Gaurav for giving me
the freedom and condence to pursue my own ideas. Diving into the large eld of robotics
was not easy if you can do whatever you want and need to somehow narrow it down, but
it was immensely rewarding once you have found your passion and see ideas come to life
on a robot. I could not have asked for a better advisor during this journey.
A special thanks also to all of my thesis proposal and defense committee members.
Professor Stefan Schaal, Professor Fei Sha, Professor Hao Li and Professor Sandeep Gupta,
thank you for all your support and guidance.
My rst research experience, involving robots, was at the Technical University of
Munich during my time as a Computer Science Diplom student. During this time, I
worked in the group of Professor Michael Beetz under the direct supervision of Alexandra
Kirsch, Armin Mller and Radu Bogdan Rusu. It was a great experience and laid the
foundation to where I am now.
While still at the Technical University of Munich I spent over a year at the Georgia
Institute of Technology, working with Professor Frank Dellaert. A very special thanks to
Frank for giving me the opportunity and chance to work and learn from him. No doubt,
without Frank I would have never made the decision of pursuing my Doctoral degree in
the USA. During my time at GT I met some great people that all helped me in one way
or the other with OCaml, SLAM, graph optimization and ease my way into the American
way of life. To just name a view, Professor Henrik Christensen, Richard Roberts, Minxuan
Sun, Michael Kaess, Sang Min Oh, Carlos Nieto, Alireza Fathi, Grant Schinlder, Kai Ni
and Matthias Grundmann.
Besides working as a researcher at USC I was also fortunate to have spent time at
two companies. My rst internship was at Willow Garage, the creator of the PR2 robot.
Here, I was again fortunate to be able to work with Radu Bogdan Rusu who gave me
great ideas toward my thesis research work. During long nights and on the weekend I
shared my oce with Koen Buys, Bernhard Zeisl and Ryohei Ueda, thanks for the great
time. My second internship was at the Toyota InfoTechnology Center. Here, I would like
to thank Eric Martinson and Akin Sisbot for their guidance and support. With my oce
mate Young-Ho Kim I had great conversations and good times with our daily raid of the
company fruit platter.
During my time as a graduate student, but especially in my very early years I had
great support from labmates. Jonathan Kelly, Sameera Poduri, Karthik Dantu and Ryan
Neal Smith, were great mentors and I am fortunate to have had them when I started.
Great help also came from Geo Hollinger, J org M uller and Andreas Breitenmoser. A
iii
special big thanks to J org and Andreas, who were instrumental in helping me build a
quadrotor platform and with my research during the nal years of my thesis work.
During the days and sometimes during the nights I spent my time with my RESL peers
in the lab or out in Los Angeles. Together we shared many ups and downs and I would like
to thank everyone for many memorable moments. Thank you, Jon Binney, Jnaneshwar Das,
Arvind Pereira, Hordur Heidarsson, Megha Gupta, Harshvardhan Vathsangam, Stephanie
Kemna, Max P
ueger, David Inkyu Kim, Karol Hausman, Artem Molchanov, James
Preiss, Oliver Kroemer and Lantao Liu. I would also like to thank Carl Oberg for his help
and advice in equipping robots with sensors, helping with experimental setups and many
interesting conversations.
I would also like to thank all the people from the Interaction Lab, CLMC, and ACT
lab. You all made the time at USC unforgettable. Thank you, Ross Mead, Aaron St.
Clair, David Feil-Seifer, Elizabeth Cha, Vince Enachescu, Bharath Sankaran, Harry Su,
Mrinal Kalakrishnan, Peter Pastor, Ludovic Righetti, Jeannette Bohg, Wolfgang H onig. I
want to especially thank Franziska Meier for all her help and motivation throughout the
years!
Finally, I would like to thank my parents Dr. Michael Potthast and Constanze Klimt
as well as my brother Andreas Potthast for their unconditional support throughout the
years. They always believed in me and encouraged me to nd and go my own way. I am
also very thankful that my grandpa Professor Dr. Dr. med. Ferdinant Klimt was still able
to see me succeed in receiving my doctoral degree.
This has been an amazing journey and I am very fortunate and honored to have been
able to pursue my PhD at USC. I would do it all over again!
iv
Table of Contents
1 Introduction 1
1.1 Contributions and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Background 7
2.1 Random Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Information Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Joint Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Conditional Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.4 Mutual Information: . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.5 Relative Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Probabilistic Next Best View Estimation 12
3.1 Next Best View estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.1 Observation Probability . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.2 Posterior Occupancy Probabilities . . . . . . . . . . . . . . . . . . . . 22
3.2 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 System Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 Point Cloud Registration . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.3 Occupancy Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.4 Markov Random Field . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Real Robot Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3.2 Simulated Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.3 Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 Active Multi-View Object Recognition and Online Feature Selection 44
4.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.1 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1.2 Sequential Bayesian Recognition . . . . . . . . . . . . . . . . . . . . . 49
4.1.3 Observation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
v
4.1.4 HMM State Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Action Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1 Expected Loss of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.2 Mutual Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.3 Jerey's Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.4 Convergence and Stopping Criterion . . . . . . . . . . . . . . . . . . . 57
4.3 Feature Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.1 Feature Selection by Expected Loss of Entropy . . . . . . . . . . . . 58
4.3.2 Feature Selection by Mutual Information . . . . . . . . . . . . . . . . 59
4.4 Viewpoint Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4.1 Viewpoint Selection by Expected Loss of Entropy . . . . . . . . . . . 60
4.4.2 Viewpoint Selection by Mutual Information . . . . . . . . . . . . . . 60
4.4.3 Viewpoint Selection by Jerey's Divergence . . . . . . . . . . . . . . 61
4.4.4 Stopping Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.5.1 RGB-D Object Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.5.2 HMM State Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5.3 Simple Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5.4 RGB-D Kernel Descriptors . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5.5 Online Feature Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.5.6 Multi-View Object Recognition . . . . . . . . . . . . . . . . . . . . . . 68
4.5.7 Quadcopter Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.5.8 Object Change Detection . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Online Trajectory Optimization to Improve Object Recognition 84
5.1 Trajectory Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.1.1 Stochastic Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.1.2 Trajectory Updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2 Cost Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.1 Obstacle Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2.2 Center Object in Camera View . . . . . . . . . . . . . . . . . . . . . . 90
5.2.3 Recognition Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.2.4 Information Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3 Object Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3.1 Sequential Bayesian Recognition . . . . . . . . . . . . . . . . . . . . . 91
5.3.2 Observation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.3 HMM State Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.4.1 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.4.2 Quadrotor results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
vi
6 Conclusions 107
References 109
vii
List of Figures
1.1 In the future we will have a variety of dierent robots inhabiting our home
with us. We might have robots in our home that help us clean, cook, do
our laundry and even be our personal butler. . . . . . . . . . . . . . . . . . 2
1.2 A typical sequential action selection process, consisting of three modules:
Action Set, Select Action and Action Execution. First, a subset of possible
actions is dened. Next, we evaluate the utility of all actions in the action
set. Finally, we execute the action with the highest utility. This process
repeats until we terminate given a termination criteria. . . . . . . . . . . . 3
2.1 Spatial relationships between various entropy measures. . . . . . . . . . . 8
2.2 Entropy H(X), measures the uncertainty in a random variable. We are
most uncertain about the outcome if both values are equally likely. . . . . 9
3.1 The point cloud is represented as an occupancy grid. Blue cells are
occupied space, white cells represent free space and yellow cells unknown
space. Unknown space is estimated using a ray traversal algorithm shown
in (a). To estimate the information gain of a potential next position we
reason over the unknown space, as shown in (b). However objects which
have not been seen yet (shaded square) lead to wrong estimations. . . . . 16
3.2 The estimation process modeled as a Hidden Markov Model. The obser-
vation state x
m
is estimated from state x
m−1
given all prior occupancy
probabilities up to o
m−2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 The gure shows the change in observation probability when applied to
our model. The upper half of the picture shows the evolution of the
observation probability when traversing the cells in a ray. The lower part
of the gure show the states of the cell in the ray. . . . . . . . . . . . . . 20
3.4 In this gure we can see virtual scenes corresponding to the cases presented
in Fig. 3.3 and Fig. 3.5. The blue circle on the left of all gures is the
current sensor location, the arrow represents one ray shot into the grid
to a target cell and the dashed white cells represent the cells penetrated
by the ray. Green cells are free, red are occupied, and yellow cells are
unobserved. In 3.4a only free cells are penetrated, in 3.4b only occupied
cells, in 3.4c only unobserved cells and in 3.4d a mix of all are possible
states are penetrated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
viii
3.5 The occupancy probability is shown for each cell in a ray. The upper
half of the picture shows the evolution of the occupancy probability when
traversing the cells in a ray. The lower part of the gure show the states
of the cell in the ray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.6 In (a) and (c) we can see missing data of the box and a cylinder. This
missing measurements lead to holes in the objects. The result of the MRF
approach can be seen in (b) and (d) where the red cells are the cells set
to occupied after convergence of the MRF. . . . . . . . . . . . . . . . . . . 27
3.7 The experimental platform (PR2 Willow Garage). In this paper, we use
the tilting Hokuyo UTM-30LX laser scanner, mounted above the shoulder
and an RGBD sensor mounted on the head, for data acquisition. (Image,
courtesy of Willow Garage) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.8 PR2 robot acquiring data from a table top. The robot is able to position
itself anywhere around the table. . . . . . . . . . . . . . . . . . . . . . . . . 30
3.9 In the images (a)-(d) we show the experimental test scenarios for the
detailed exploration. The table top scenes have dierent number of object
simulating dierent level of clutter. . . . . . . . . . . . . . . . . . . . . . . . 32
3.10 In the graphs (a)-(d) we compare the simple approach which is drawn as
blue line with our proposed method drawn in red and a random approach
in green. We can see that our method drawn in red decreases the number
of unobserved cells faster, which is the eect of choosing NBV positions
more optimal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.11 In the graphs (a)-(d) we show the absolute prediction error over the
number of scans. The error is computed by taking the absolute error
between the predicted information gain and the actual number of seen
cells after a scan is taken. The green line in the graph represents the
simple method while the blue line shows the prediction error of our method. 34
3.12 The gure shows, from left to right, the reduction in unobserved cells after
estimating the NBV position and acquiring new measurements. With
each new observation more information about the environment is revealed,
resulting i a reduction in unobserved (yellow) space. . . . . . . . . . . . . 36
3.13 The gure shows a small oce environment with dierent levels of clutter.
For each environment we start the robot at ve dierent initial starting
locations, depicted as blue circles. . . . . . . . . . . . . . . . . . . . . . . . . 37
3.14 The gure shows a large oce environment, with dierent levels of clutter.
For each environment we start the robot at ve dierent initial starting
locations, depicted as blue circles. . . . . . . . . . . . . . . . . . . . . . . . . 38
3.15 The gure shows the average performance for the small oce environment
Fig. 3.13 of our approach compared to the simple greedy, Latombe, Ya-
mauchi and random. The observability parameter for our approach is set
to a= 0:999 and a= 0:9999. We can see that our approach is on par with
all the other approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
ix
3.16 The gure shows the average performance for the large oce environment
Fig. 3.14. Our approach is at least as good as the other tested approaches.
The observability parameter is set to a= 0:9999. . . . . . . . . . . . . . . . 40
4.1 System overview of the active multi-view object recognition framework.
After each observation, the HMM updates the recognition state, upon
which a new feature (inner loop) or a new viewpoint (outer loop) is selected.
The feature type that is selected rst at any new location is pre-dened.
The iterative processes terminate when the stopping criteria are met. . . 49
4.2 HMM for sequential Bayesian recognition. Given a sequence of observed
features f
1∶t
and executed actions a
1∶t
, we reason about the hidden recog-
nition state of an object at time t, o
t
= {c
t
;
t
}, including its object class
c
t
=c
k
and object pose
t
=
q
. . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Experimental setup. (a): Each object is placed on a turntable that rotates
around the z-axis (yaw rotation) of the world coordinate frame. Object
data is recorded from three dierent viewing angles of 30
○
, 45
○
and 60
○
per viewing direction. (b): Viewing directions denote directions in the x-y
plane of the coordinate frame from which the object can be observed. The
plane is subdivided into bins of 45
○
around the object. Observations of the
object from the same bin will lead to similar estimations of the object's
pose. (c): In multi-view object recognition, a sequence of viewpoints can
be planned in dierent ways. The shown path (red) results from the simple
heuristic \motion along a star pattern", which assumes that the viewpoint
opposite the current viewing direction yields the most information and
thus is the one to visit next. . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4 Simple features|Performance and cost of dierent feature combinations
in single-view object recognition. The recognition accuracies are displayed
as red bars (left side scale, in %). The average cost of computing the
feature combinations per object is shown in log scale as blue bars (right
side scale, in seconds). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
x
4.5 Shown is our custom quadcopter platform. The platform is build upon a
glass ber 330mm mini quad frame. In the middle of the frame we have
built a superstructure that houses the sensors (e.g. IMU) and processing
unit. As the onboard computer we are using a Hardkernel Odroid U3,
which is a 1.7 GHz Cortex-A9 Quad-core processor with 2 GByte RAM.
The onboard computer is used as the
ight control hardware, running the

ight control stack for tasks like attitude estimation, stabilization and
waypoint execution. The custom platform allows for a variable motor and
battery size, enabling to trade-o between
ight-time and payload. In the
current conguration, as shown in the picture, the quadcopter is equipped
with an ASUS Xtion RGB-D camera, used for data collection. In the
above described conguration the platform has a
ight-time of about 13
minutes. To accurately estimate the position of the quadcopter indoors
we use a VICON motion capture system. . . . . . . . . . . . . . . . . . . . 73
4.6 Quadcopter experiment and test setup. The quadcopter robot, equipped
with a RGB-D camera, collects multiple views of a target object (e.g., a
cereal box) in an active object recognition task. . . . . . . . . . . . . . . . 74
5.1 Our quadrotor platform taking an observation of a target object we want
to recognize. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2 Smoothed optimized trajectory around an object we want to identify. . . 88
5.3 Simulation Experiment 1 { In this experiment the vehicle follows the
initial trajectory shown as green dots. The vehicles goal is to follow
the trajectory and recognize 5 objects depicted as circles with green/red
boxes. The green/red boxes show the possible observation angles, once an
observation has been taken from a certain angle the box is marked as red
and no other observation is taken with similar angle. . . . . . . . . . . . . 97
5.4 Simulation Experiment 1 { In this experiment the vehicle follows the
online optimized trajectory. The red dots show the initial trajectory while
the green dots show the optimized trajectory given the initial waypoints.
The new trajectory enables the vehicle to more reliable recognize the 5
objects depicted as circles with green/red boxes. The green/red boxes
show the possible observation angles, once an observation has been taken
from a certain angle the box is marked as red and no other observation is
taken with similar angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.5 Simulation Experiment 2 { In this experiment the vehicle follows the
initial trajectory shown as green dots. The vehicles goal is to follow
the trajectory and recognize 7 objects depicted as circles with green/red
boxes. The green/red boxes show the possible observation angles, once an
observation has been taken from a certain angle the box is marked as red
and no other observation is taken with similar angle. . . . . . . . . . . . . 99
xi
5.6 Simulation Experiment 2 { In this experiment the vehicle follows the
online optimized trajectory. The red dots show the initial trajectory while
the green dots show the optimized trajectory given the initial waypoints.
The new trajectory enables the vehicle to more reliable recognize the 7
objects depicted as circles with green/red boxes. The green/red boxes
show the possible observation angles, once an observation has been taken
from a certain angle the box is marked as red and no other observation is
taken with similar angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.7 Simulation Experiment 3 { In this experiment the vehicle follows the
initial trajectory shown as green dots. The vehicles goal is to follow the
trajectory and recognize 10 objects depicted as circles with green/red
boxes. The green/red boxes show the possible observation angles, once an
observation has been taken from a certain angle the box is marked as red
and no other observation is taken with similar angle. . . . . . . . . . . . . 101
5.8 Simulation Experiment 3 { In this experiment the vehicle follows the
online optimized trajectory. The red dots show the initial trajectory while
the green dots show the optimized trajectory given the initial waypoints.
The new trajectory enables the vehicle to more reliable recognize the 10
objects depicted as circles with green/red boxes. The green/red boxes
show the possible observation angles, once an observation has been taken
from a certain angle the box is marked as red and no other observation is
taken with similar angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.9 From top left to bottom right we show in order how the quadrotor captures
information about the target objects along the optimized trajectory. . . . 104
5.10 Quadrotor results { Optimized trajectory of the quadrotor, 4 objects are
being recognized. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
xii
Abstract
For robots to one day become fully autonomous and assist us in our daily lives, they
need to be able to self reliantly acquire information about their environment. Challenges
arise from the limited energy budget to operate the robot, occlusion from the environment,
and uncertainty in data captured by noisy sensors. To cope with such challenges, the
robot needs to be able to rely on a system that enables it to capture information eciently
while respecting constraints. Furthermore, information acquisition should be reactive to
sensor measurements, incorporate uncertainty and tradeo information gain with energy
usage. In this thesis we study such systems using information theoretical measures to
formulate as general and versatile a framework as possible. Specically, we examine the
task of dening objective functions that enable us to tradeo information with acquisition
cost, enabling the robot to gather as much useful information as possible, but at the same
time keep energy consumption to a minimum. We address this challenge for a variety of
dierent tasks.
First, we examine the problem of 3D data acquisition, which is of outmost importance
to a robotic system since the robot needs to know the environment it is operating in. We
present an information gain-based variant of the next best view problem for an occluded
environment. The developed framework enables the robot to quickly acquire information
by sequentially choosing next observation positions that maximize information. Next, we
look at adaptive action selection in the context of object recognition on robots with limited
operating capabilities. We propose an information-theoretic framework that combines and
unies two common techniques: view planning for resolving ambiguities and occlusions
and online feature selection for reducing computational costs. Concretely, this framework
adaptively chooses two strategies: utilize simple-to-compute features that are the most
informative for the recognition task or move to new viewpoints that optimally reduce
the expected uncertainties on the identity of the object. Lastly, we present an online
trajectory optimization approach that improves object recognition performance. With
the idea in mind that the robot needs to make progress towards a goal, a cost function is
formulated that allows the robot to improve recognition performance, maneuver safely
through the environment and reduce information acquisition cost, while simultaneously
moving towards the goal point. Through extensive experiments, in simulation and on real
robotic systems, this thesis shows the usefulness of adaptive action selection. We have
studied adaptive action selection on two concrete problems, but the use case and need for
such an approach can be found in many other applications.
xiii
Chapter 1
Introduction
Currently, the use of autonomously operating robots in our daily live is still minimal. The
few existing exceptions are robots that either operate in very controlled environments or
are used for highly specialized tasks. We can think of endless applications and scenarios in
which robots can enrich and ease our life, with the holy grail being a multi-purpose robot
that can assist us in many dierent aspects of our life (Fig. 1.1). For autonomous operation,
such robots need to understand the environment they operate in by acquiring information
about its surrounding. In order to acquire information the robot needs to utilize its various
sensors and process the sensor measurements to build an internal representation of the
world it operates in. However, due to occlusions one observation is oftentimes not sucient
to fully capture the environment. To overcome this problem the robot needs to execute
an action, this could be moving to another observation location, to be able to capture
previous unseen parts of the environment and gain new information.
In general, the more information a robot has about its environment the more robustly
and eciently it can execute tasks. Thus, ideally the robot would collect as much
information as possible, however this is often not possible because of resource or time
constraints. For instance, mobile robots are often underpowered and need to be frugal
with resources for computation, reasoning and moving to new positions. In settings like
this, we want to keep the cost to a minimum, while at the same time acquire as much
useful information as possible. Unfortunately, most environments a robot operates in
are unknown to the robot, either it has never been observed before or the environment
has changed compared to last time the robot has observed it. This has the consequence
that we can not optimally precompute the actions necessary for the robot to acquire all
information needed to complete a task. Instead, the robot needs to make decision online
on how and what information needs to be capture or computed.
1
Figure 1.1: In the future we will have a variety of dierent robots inhabiting our home
with us. We might have robots in our home that help us clean, cook, do our laundry and
even be our personal butler.
2
Adaptive action selection is an appealing paradigm to overcome these challenges by
trading off between the cost ( con1putation, movement, etc.) and acquiring ne\v useful
inforn1ation. Action selection is t he process of selecting "what to do next " in unpredictable
environments in real time, given an objective function that evaluates individual actions
for their ut ility. It enables exploratory reactions to unforeseen events or scenes, and offers
greater flexibility in actively seeking t he most useful information for various infonnation
acquisition tasks. The general idea is for the sensors to be controlled such t hat only
data with high information content is collected, and adapted dynanlically to t he robot 's
knowledge (i.e., belief state about the world) as a result of running inference on previously
acquired informat ion.
Action Selection
T he process of selecting online "what to do next" in unpredictable environments.
A typical sequential action selection process, sho\vn in F ig. 1.2, consisting of three
1nodules: ACTION SET, SELECT ACTION and ACTION EXECUTION. The nlain problen1 of
t he action selection process is complexity. Each considered action involves co1nputations.
Since all co1nputations take time, processing resources and require n1e1nory, t he robot can
not possibly evaluate every action iinaginable. Consequently, the robot must constrain
its search to a subset of possible actions. T his subset of a ll possible actions is defined
in the ACTION SET. To find t he best action of the set each individual action needs to
be evaluated for its utility given a defined objective function. Intuitively, the objective
function ranks t he individual actions for t heir usefulness. Co1nn1only, t he action \V it h t he
llighest utility is picked as t he next action. Finally, we execute this action and either repeat
the previous described process or tenninate the process detennined by a termination
criteria.
Termi nate
Action Set Select Action
I
Execute
Objective function
Figure 1.2: A typical sequential action selection process, consisting of three nlodules:
Action Set, Select Action and Action Execution. F irst, a subset of possible actions is
defined. Next, we evaluate t he utility of all actions in the action set. Finally, we execute t he
action wit h the highest utility. Tllis process repeats until we terminate given a tennination
criteria.
3
Concretely, the value of an action is estimated by the objective function and can be
evaluated in many dierent ways, for example using a heuristic or information theoretical
(Shannon, 1948) approach. Information theoretic approaches are popular in robotics,
because it is based on probability theory and statistics. Using probabilistic models in
robotic applications has tremendous advantages, since we can directly model the uncertainty
in data captured by noisy sensors. There are many sources that introduce uncertainty,
measurement noise is the most common one and in general dealt with by formulating
an observation model. Others are much harder to deal with like uncertainty stemming
from incomplete information. Both and many more can be modeled using probabilistic
models, which me frequently use throughout this work. Consequently, using a formalism
that can incorporate probabilistic estimations into our world belief state is of utmost
value. Evaluating actions with information theoretic formulations allows us to do exactly
that, quantifying actions in terms of information gain and uncertainty reduction given our
current belief state.
Given the advantages of probabilistic reasoning in robotics and the ability to incorporate
uncertainties into information theoretic quantities, we present in this work how they can
be utilized for robotic applications. We have applied this for two important problems in
robotics, Autonomous 3D data acquisition and Object recognition.
Autonomous 3D data acquisition and reconstruction of dense geometry of full environ-
ments or single objects is an often required task for robots. For this task, a substantial
diculty, and of most importance, is both the selection of viewpoints for data acquisition
and the successful execution of subsequent tasks like reconstruction or object manipulation.
Many algorithms have been developed to make this process autonomous and ecient for
2d (H. H. Gonzalez-Banos & Latombe, 2002) as well as 3D (Krainin, Curless, & Fox, 2011)
environments. In general, the estimation of such viewpoints is known as the Next Best
View (NBV) problem, rst discussed in (Connolly, 1985). Next Best View approaches seek
a single additional sensor placement or viewpoint given a heuristic or reward function.
Since sensing actions are time consuming, one seeks a sequence of viewpoints which observe
the environment in the minimum number of actions. Evaluating the utility of potential
viewpoints is not easy, since it involves the prediction of the potential knowledge gain about
the world. This is especially dicult in cluttered environments, because they introduce
many visibility constraints due to occlusions. As a result, the diculty of making accurate
predictions of the knowledge gain is increased. In (Potthast & Sukhatme, 2014) we present
an approach that incorporates prior knowledge about the environment to better estimate
information gain in cluttered environments. Thus, more optimal observation positions are
chosen which in turn reduces the number of actions needed
With 3D data acquisition only considering the sensor placement and their information
gain, we next also consider the cost of processing the raw sensor data. In recent work
(Potthast, Breitenmoser, Sha, & Sukhatme, 2015), we have proposed an adaptive action
selection framework for object recognition on robots with limited operating capabilities in
terms of energy. Energy is not just spent on viewpoint planning and motion of the robot,
but also on processing of the raw sensor data into representative features. Conventional
4
approaches for object recognition are tour de force, relying almost exclusively on complex
statistical models for classication and heavy engineering of computationally-intensive
features (Bo, Ren, & Fox, 2011; Lowe, 2004). In stark contrast, our work hinges on
the following intuition: how to reduce overall costs for recognition by relying on very
simple features extracted at multiple views in lieu of complex features extracted at a single
view?. Specically, we describe an information-theoretic framework that unies these
two strategies: view planning for moving robots to the optimal view points and dynamic
feature selection for extracting simple yet informative features. However, unlike standard
feature selection, these two strategies are symbiotic in our algorithm. The selected features
at any given time depend on the past trajectory of the view points while simultaneously
aecting the future view point(s).
So far, the developed frameworks for both 3D data acquisition as well as for object
recognition assumes information collection only when a next best observation position is
reached. This means the robot is estimating a new observation location, moves to the
next location and takes an observation. In practice, however this is highly inecient since
data could potentially, depending on the sensor, be collected while the robot is moving
to a new observation location. To address this problem we present an online trajectory
optimization approach that allows the robot to alter its trajectory such that the most useful
information is collected while in motion. In this work, we formulate an objective function
that optimizes a trajectory such that object recognition performance is improved. Inspired
by prior work (Kalakrishnan, Chitta, Theodorou, Pastor, & Schaal, 2011), we formulate
the optimization as a derivative-free stochastic optimization, allowing us to express the
cost function in an arbitrary way. The cost function is dened such that information
acquisition of target objects is improved, while simultaneously moving towards the goal
point. We show the evaluation of our approach on a quadrotor platform in simulation as
well as on a real robot. The results show that by using an online optimization approach
recognition accuracy is greatly improved, but more importantly the optimized trajectory
reduces the uncertainty of the object posterior class distribution greatly. Hence, verifying
that the optimized trajectory collects more valuable information.
5
1.1 Contributions and Outline
The contributions of this thesis are made in the areas of information theoretical action
selection for autonomous data acquisition, object recognition and feature selection as well
as in trajectory optimization for online object recognition.
1. Probabilistic Next Best View Estimation
We formulate an information-theoretic driven next best view framework for automatic
data acquisition in cluttered environments. The key idea is to select new view
points by iteratively estimating the knowledge gain of potential new observation
positions. The approach reasons about the unknown space in cluttered environments
by probabilistically estimating the likelihood of observing the unknown space.
2. Active Multi-View Object Recognition and Online Feature Selection
We present an action selection approach for object recognition. We describe an
information-theoretic framework that combines and unies two common techniques:
view planning for resolving ambiguities and occlusions and dynamic feature selection
for reducing computational costs. Concretely, the algorithm adaptively chooses two
strategies: utilize features that are the most informative to the recognition task, or
move to new viewpoints that optimally reduces the expected uncertainties on the
identity of the object.
3. Online Trajectory Optimization to Improve Object Recognition
We present an online trajectory optimization approach that optimizes a trajectory
such that object recognition performance is improved. Here, a quadrotor is tasked to
follow a given trajectory, but to increase the recognition accuracy of potential target
objects the system is able to alter the trajectory online. In this work we show that
by optimizing the initial trajectory given a cost function, we can increase recognition
accuracy and additionally show that data processing can be reduced by reducing the
number of observations needed for reliable recognition.
The thesis is organized as follows. In Chapter 2, we introduce the information-
theoretical formalism we use throughout this thesis. We choose an information theoretic
approach because it is based on probability theory and statistics, enabling us to incorporate
uncertainty into our selection of next actions. Chapter 3, we present an information-
theoretic driven next best view framework for automatic data acquisition in cluttered
environments. Next, in Chapter 4, an action selection approach for multi-view object
recognition is presented. In Chapter 5 we present an online trajectory optimization
approach that optimizes a trajectory such that object recognition performance is improved.
Finally, in Chapter 6 we summarize the work presented in this thesis.
6
Chapter 2
Background
Throughout this work we will make extensive use of probability theory and information
theory. Due to the nature of noise in sensors used on robots we need to deal with
uncertainty while the robot is operating. Utilizing probabilistic models allows us to deal
with such sensor noise and incorporate uncertainty in our computations. Furthermore,
information theory, which is bases on probability theory and statistics allows us to quantify
information. The most important quantities of information are entropy, the information
in a random variable, and mutual information, the amount of information in common
between two random variables. In the following we will give a short overview of the
most important concepts and mechanism that allow us to quantify information using
probabilistic methods.
2.1 Random Variable
A random variable X ∶
→E is a measurable function from the set of possible outcomes

to some set E. When the range of X is nite or countable innite, the random variable
is called a discrete random variable and its distribution can be described by a probability
mass function which assigns a probability to each value in the range of X. If the range is
uncountable innite then X is called a continuous random variable and takes values in R
d
or in some smooth nite-dimensional manifold.
In this short introduction we will describe the concepts of information theory on the
behavior of large sets of discrete random variables. A discrete random variable X is
completely dened by the set of values is can take,
, which we assume to be a nite set,
and its probability distribution {p(x)}
x∈

. Here, the value p(x) describes the probability
that the random variable X takes the value x. The probability distribution p∶
→ [0; 1]
must satisfy the normalization condition
Q
x∈

p(x)= 1: (2.1)
The expected value of a discrete random variable is the probability-weighted average
of all possible values. In other words, each possible value the random variable can assume
7
is multiplied by its probability of occurring, and the resulting products are summed to
produce the expected value. Formally we can dene the expectation of the random variable
X as follows:
E[X]=
∞
Q
i=1
x
i
p(x
i
): (2.2)
2.2 Information Theory
Information theory often concerns itself with measures of information of the distributions
associated with random variables. Important quantities of information are entropy, a
measure of information in a single random variable, and mutual information, a measure of
information in common between two random variables. The relationships between some of
the information theory measures, dened in the following subsections, are illustrated in
Fig 2.1.
Figure 2.1: Spatial relationships between various entropy measures.
2.2.1 Entropy
Intuitively, the Shannon entropy gives a measure of the uncertainty of the random variable.
It is a measure of surprise when looking at an outcome of the random variable. It
is sometimes called the missing information: the larger the entropy, the less a priori
information one has on the value of the random variable. The Shannon entropy H of a
8
discrete random variableX with possible values {x
1
;:::;x
n
} and probability mass function
P(X) as:
H(X)=E[I(X)]=E[− ln(P(X))]; (2.3)
withE begin the expectation and I the information content of X. In the discrete case the
Entropy can be computed as following:
H(X)=Q
i
p(x
i
)I(x
i
)=−Q
i
p(x
i
) logp(x
i
): (2.4)
In the above formulation we use the logarithm to the base 2, which is well adapted to
digital communication, and the entropy is then expressed in bits.
The entropy is zero if the outcome of the experiment is unambiguous and it reaches
its maximum if all outcomes of the experiment are equally likely as shown in Fig. 2.2.
Furthermore, the H is a strictly concave of X, i.e. for 0<< 1 and a random variable X
and Y
H(X+(1−)Y )≥H(X)+(1−)H(Y ); (2.5)
with equality i = 0, or = 1, or X =Y .`
0 0.5 1
0
0.5
1
Pr(X = 1)
H(X)
Figure 2.2: Entropy H(X), measures the uncertainty in a random variable. We are most
uncertain about the outcome if both values are equally likely.
9
2.2.2 Joint Entropy
The joint entropy of two discrete random variables X andY is merely the entropy of their
pairing: (X;Y ). This implies that if X andY are independent, then their joint entropy is
the sum of their individual entropies.
H(X;Y )=E
X;Y
[− logp(x;y)]=−Q
x;y
p(x;y) logp(x;y): (2.6)
2.2.3 Conditional Entropy
The conditional entropy quanties the amount of randomness in the random variable X
given that the value of another random variableY is known. The entropy ofX conditioned
on Y is written as H(XSY ) and dened as:
H(XSY )=E
Y
[H(XSy)]
=−Q
y∈Y
p(y)Q
x∈X
p(xSy) logp(xSy)
=−Q
x;y
p(x;y) log
p(x;y)
p(y)
:
(2.7)
2.2.4 Mutual Information:
LetX andY be two random variables,
X
(x) and
Y
(y) the marginal probability density
function of X and Y , respectively and
X;Y
(x;y) the joint probability density function of
(X;Y ). Mutual Information expresses the reduction in uncertainty about variable X after
we have observed Y :
I(X;Y )=H(X)+H(Y )−H(X;Y )
=H(X)−H(XSY ):
(2.8)
This means it measures how much knowing one of these variables reduces uncertainty
about the other. From this notation we can write the Mutual Information as
I(X;Y )=Q
X
Q
Y

X;Y
(x;y) log

X;Y
(x;y)

X
(x)
Y
(y)
=KL(P(X;Y )∥P(X)P(Y )):
(2.9)
The mutual information is symmetric ,
I(X;Y )=I(;Y ;X) (2.10)
10
2.2.5 Relative Entropy
The relative entropy or Kullback-Leibler divergence between two probability distributions
P(X) and Q(X) is dened as:
KL(P∥Q)=Q
i
p(x
i
) log
p(x
i
)
q(x
i
)
: (2.11)
The relative entropy is a measure of \distance\ between two probability distributions. The
K-L divergence presents the amount of information lost if samples from the distribution P
are assumed to be samples from Q.
However, KL(P ∥ Q) is not a true \distance\ since it is not symmetric and does
not obey the triangle inequality. We can formulate a symmetric version base of the K-L
divergence, also known as Jerey's Divergence as:
J(p∥q)=KL(p∥q)+KL(q∥p): (2.12)
11
Chapter 3
Probabilistic Next Best View Estimation
Major research areas in computer vision and robotics are autonomous 3D data acquisition
and reconstruction of dense geometry of full environments or single objects. A substantial
diculty, and of most importance, is the selection of viewpoints for data acquisition and
to accomplish subsequent tasks like reconstruction or object manipulation. Oftentimes we
are limited by time, energy, or storage, but also occlusion making it necessary to estimate
appropriate viewpoints for data acquisition. Over the past decade many algorithms have
been developed to make this process autonomous and ecient for 2D (H. H. Gonzalez-
Banos & Latombe, 2002) as well as 3D (Krainin et al., 2011) environments. A widely used
technique for automatic data acquisition and exploration is to iteratively compute and
place the sensor to a new observation position where a new sensing action is performed.
From a pure reconstruction point of view, we face the problem of optimizing view selection
from the set of available views. The data, from which we want to reconstruct, is usually
presented as a video or as individual images, showing the world or object in question
from dierent viewpoints (Haner & Heyden, 2012),(Dunn & Frahm, 2009). From this
data, we want to nd the subset of data that can best and most eciently reconstruct the
environment. In general, the estimation of such viewpoints known as the Next Best View
(NBV) problem, rst discussed in (Connolly, 1985), which seeks a single additional sensor
placement or viewpoint given a heuristic or reward function.
In many cases sensing actions are time consuming, but also an increase in data does not
guarantee a better reconstruction result, one seeks a sequence of viewpoints which observe
the environment in the minimum number of actions or images. How many measurements
are needed to observe the environment depends, in principle on the selected viewpoints
and with that the gain in knowledge about the world. The potential knowledge increase of
new observation positions can be estimated by reasoning about current world information.
In practice however, making precise estimations of the knowledge increase is dicult and
error prone, because the estimation involves predicting the unobserved portions of the
world.
This is especially true in cluttered environments, because they impose many visibility
constraints due to occlusion thereby increasing the diculty of making accurate predictions
of the knowledge gain. Inaccurate estimations lead to over or under prediction of the
12
gained information, hence possibly non-optimal observation positions are chosen. The
more accurate we predict the information gain the fewer observation are necessary to fully
observe the environment.
View planning approaches are used in a variety of dierent research ares. There are
two major surveys of the problem, one describing the sensor planning problem in vision
applications (K. a. Tarabanis, Allen, & Tsai, 1995). The other is a more recent survey
of view planning for 3D object reconstruction and inspection (Scott, Roth, & Rivest,
2003). Of particular relevance to our work are approaches for exploration and automatic
data acquisition using a robotic system. A survey for robot environment mapping and
exploration can be found in (Thrun, 2002). In this brief review of related work, we focus
on dierent approaches to estimate a set of potential new viewing positions as well as
estimating the best position out of this set.
The main dierences between existing approaches are the selection of the potential new
viewing positions and the estimation of the NBV of this set. The earliest NBV estimation
(Connolly, 1985) proposed two approaches to create a complete model of a scene. The
new sensor position is chosen either by simulating viewpoints sampled from the surface of
a sphere and scored by using ray-casting and change estimation in unknown space or by
using a histogram of normals for unexplored octree node faces.
Several methods have been developed which generate the potential viewpoints uniformly
randomly in the workspace. In (N uchter, Surmann, & Hertzberg, 2003) an exploration
algorithm was developed for a robot operating in 2D but acquired environment information
in 3D. Potential new viewing positions are randomly generated on the 2D workspace of
the robot and evaluated for their individual information gain. The potential new viewing
positions are sampled uniformly randomly in a safe region (H. H. Gonzalez-Banos &
Latombe, 2002), which consists of free space bounded by solid curves. To estimate the
NBV position of this sample set a cost function trading o information gain and travel cost
is evaluated and applied to each sample point. Similarly, in (Amigoni & Gallo, 2005) the
potential viewing positions are sampled randomly from a list of line segments bordering
unobserved space. However, compared to (H. H. Gonzalez-Banos & Latombe, 2002)
the utility function which evaluates the viewing position is more complex and takes the
precision of localization into account. This ensures better localization and registration of
the individual measurement. In (Krainin et al., 2011) a probabilistic surface reconstruction
approach is described using a depth cameras and a robotic manipulator holding an object.
New viewing positions are uniformly sampled around the object and the manipulator hand.
Given a current surface reconstruction a metric is formulated to score the potential new
scanning positions in terms of reduction of uncertainty from virtual created depth maps.
Various methods are developed for reconstruction of dense geometry. In (Dunn &
Frahm, 2009) the next best view estimation is used for ecient 3D model creation from
images. The system estimates new viewpoints that best reduces the reconstructed model
uncertainty. (Haner & Heyden, 2012) and (Hornung, Zeng, & Kobbelt, 2008) proposes a
method for 3D reconstruction from a set of unordered images. The goal is to estimate
a subset of images by sequentially estimating new viewpoint and select the best match.
13
Their approach reduces the computation time and increases accuracy of the reconstructed
model. To nd and select new viewpoints the authors in (Pito, 1999) and (Massios &
Fisher, 1998) utilize surface normal information. Specically, (Pito, 1999) introduces
the notion of positional space, which allowed, in combination with a detailed scanner
model, refraining of expensive ray-casting methods for the next best view estimation. In
(Massios & Fisher, 1998) developed a quality constraint which estimated the quality of
seen voxels in the scenes by utilizing the surface normal information. This improves the
overall reconstruction of the measurement since viewpoints are selected which improve
the laser range data quality of the scanned surface. The work of (Haner & Heyden, 2011)
proposes a continuous optimization of method of nding many future next best view
positions to reconstruct the captured environment. The system utilizes a real-time Visual
simultaneous localization and mapping (SLAM) approach to estimate the sensor position
and map the environment.
Camera in hand system used for model building are used by (Trummer, Munkelt, &
Denzler, 2010) and (Wenhardt, Deutsch, Hornegger, Niemann, & Denzler, 2006). Both
methods rely on images and feature tracking for measurement registration and model
reconstruction. In (Trummer et al., 2010) the authors present a combined online approach
of tracking, reconstruction and NBV estimation. In their work the extended e-criterion is
used, which guids the sensor to the next position to minimize the reconstruction uncertainty.
Feature tracking and 3D reconstruction in (Wenhardt et al., 2006) is done using a Kalman
lter. The optimal NBV, which improves the reconstruction accuracy, is estimated by
reducing the uncertainty in the state estimation.
A variety of frontier-based approaches have been developed that generate potential
new viewing positions on the boundary between free and unobserved space. The earliest
(Yamauchi, 1997) uses a probabilistic occupancy grid map to represent and reason about
the environment. Adjacent frontier edge cells are grouped together into frontier regions.
The centroids of these groups form the set of potential new viewing positions. The closest
frontier region position is the NBV position. Frontier regions are also used in (Blaer &
Allen, 2007) to build a detailed 3D outdoor map in a two step process. First a coarse
exploration of the environment is performed by utilizing a 2D map and observability
polygons to compute coverage positions. In the second step a 3D view planner samples
potential view positions which lie on the frontier region. For each of the candidate
viewpoints they count the number of visible cells using a ray-traversal algorithm. In the
work of (Makarenko, Williams, Bourgault, & Durrant-Whyte, 2002) the authors build a
complete framework and estimate the NBV position given localization quality, navigation
cost and information gain. The information gain is computed over the entropy of the
region around potential new NBV positions. (Stachniss & Burgard, 2003) introduces
coverage maps to better represent the environment. They propose dierent methods to
estimate the NBV position including trading of information gain and travel cost. Recent
work by (Holz, Basilico, Amigoni, & Behnke, 2010) suggests improvements for continuous
data acquisition for 2D mapping in conned spaces such as rooms. In their approach a
room will be fully observed before a position with higher information gain is considered
14
as a candidate NBV position. Additionally, due to continuous data acquisition, NBV
positions are constantly evaluated to avoid reaching a position which is already observed.
In (Wettach & Berns, 2010) an exploration algorithm is developed for 3D data acquisition.
Frontier cells, dened as known cells adjacent to unobserved cells, are ranked according
their length of connecting grid cells. A subset of these are then ranked according their
travel cost with the one with the minimal cost is chose as the NBV position.
Our approach is closest to (Krainin et al., 2011), (Blaer & Allen, 2007), (Stachniss &
Burgard, 2003), (Makarenko et al., 2002) and (H. H. Gonzalez-Banos & Latombe, 2002)
in terms of generating a suitable set of potential new viewing positions and evaluating
the information gain. However, in contrast to previous work, we directly reason over the
unknown space itself and estimate the expected knowledge gain from new views of cluttered
environments. Previous proposed methods assume full visibility to the target region or
object, which makes them poorly suited for cluttered environments since unseen objects
in the occluded space lead to overestimation of the reward for potential new observation
positions.
In the following sections, we describe a framework on automatic data acquisition
and view point selection by iteratively estimating the knowledge gain of potential new
observation positions. The information theoretical driven approach reasons about the
unknown space in the cluttered environment by probabilistically estimating the likelihood
of observing the unknown space. Intuitively, given the prior knowledge about the clutter
in the scene, we try to model the fact that the deeper we look into unobserved regions,
the higher the probability of observing an object we have not seen yet.
3.1 Next Best View estimation
In the NBV problem we are given the task to sequentially observe an environment by
moving a sensor to new viewing positions. The process seeks to minimize some aspect
of unobserved space (e.g. its size), though the exact form of the objective function will
govern the precise optimization being sought.
At each stage of the process, unobserved regions of the environment are estimated
using an occupancy grid and a ray-traversal algorithm, shown in Fig. 3.1a. Each cell c
n
in the occupancy gridO is represented by a random variable o
n
∈ [0; 1] with n= 1:::N,
where N is the total number of cells. The occupancy state o
n
= 0 encodes the cell o
n
as free and o
n
= 1 as occupied. In order to estimate the NBV position many popular
approaches (Stachniss & Burgard, 2003), (H. H. Gonzalez-Banos & Latombe, 2002),
(Krainin et al., 2011), (Holz et al., 2010) formulate the problem in information theoretic
terms and evaluate the gain in information of a set of potential new viewing positions
S = {s
1
;s
2
;:::;s
k
;:::;s
K
}. The NBV position ^ s∈S is then estimated by maximizing the
expected information gain:
^ s= arg max
k
E[I(s
k
)] (3.1)
15
(a) (b)
Figure 3.1: The point cloud is represented as an occupancy grid. Blue cells are occupied
space, white cells represent free space and yellow cells unknown space. Unknown space is
estimated using a ray traversal algorithm shown in (a). To estimate the information gain
of a potential next position we reason over the unknown space, as shown in (b). However
objects which have not been seen yet (shaded square) lead to wrong estimations.
One information measure is entropyH, the amount of uncertainty in a discrete random
variable. The entropyH(o) expresses therefore the uncertainty about the state of a cell, in
this setting whether the cell is free or occupied. For every potential new viewing position
s
k
, after integrating new measurements, the probability distribution of the occupancy grid
either stays constant or changes. To measure the change we compute the information
gain (Kullback-Leibler divergence) of the occupancy grid before and after integrating new
measurements from a potential position s
k
. Following the notation of (Thrun, Burgard, &
Fox, 2005), the information gain I over the occupancy probability p(o
n
) of a given cell c
n
is dened as:
I(p(o
n
Ss
k
;z
n;k
))=H(p(o
n
))−H
′
(p(o
n
Ss
k
;z
n;k
)); (3.2)
where p(o
n
Ss
k
;z
n;k
) is the occupancy probability after integrating a new measurement
z
n;k
from location s
k
according to our sensor model and where H
′
(p(o
n
Ss
k
;z
n;k
)) is the
posterior entropy.
To estimate the posterior entropy we need to know what measurements will be measured
if the sensor is placed at a certain position s
k
. However, since this is not possible due
to the unobserved portions in the occupancy grid, we have to integrate over all possible
measurements to compute the expected information gain for a viewpoint s
k
:
E[I(s
k
)]=
S
z
p(zSM;s
k
) Q
o
i
∈C(s
k
;z)
I(p(o
i
Ss
k
;z
i;k
)) dz (3.3)
16
The set C(s
k
;z) denes the cells which are covered by the measurement z in the current
occupancy grid mapM. Solving this integral in closed form is not feasible since we would
have to integrate over all possible measurements.
A common approximation for the expected information gain is obtained by predicting
the measurement z
k
at position s
k
using a ray-traversal algorithm. Typical methods to
approximate the measurement include Markov Monte Carlo Sampling (Thrun et al., 2005)
or assuming the measurement to be the rst occurrence of a cell with high occupancy
probability (Blaer & Allen, 2007), (Stachniss & Burgard, 2003), p(o) > 0:5. The latter
approximation assumes innite visibility until a cell with high occupancy probability is in
line of sight. However, objects which have not yet been observed could potentially block
the view to unobserved cells and therefore limit the actual information gain of a viewing
position s
k
. Thus, this could potentially lead to poor estimates over the unobserved space
and the computed ^ s is not necessarily the optimal choice, illustrated in Fig. 3.1b. The
better we predict the outcome of a potential new observation positions
k
the more accurate
we can choose ^ s.
We propose to approximate the expected information gain by predicting how likely it
is to see a specic cell from a position s
k
. That is, we estimate the probability that cell c
n
is observable from position s
k
. In detail, we dene p(x) to be the observation probability
of a cell c ∈O. Let x
n
∈ [0; 1] be the random variable expressing the observation state,
where x
n
= 0 denotes the cell c
n
is not visible and x
n
= 1 denotes c
n
is visible.
Given the observation probabilities we then estimate the expected information gain by
estimating the posterior entropy over the occupancy state o of cell c, given x:
E[I(p(oSs;x;z))]≃H(p(o))−H
′
(p(oSs;x;z)); (3.4)
where z is the measurement predicted through a ray-traversal algorithm. We will now
describe how the observation probabilities are computed in Section 3.1.1 and how they
are used to estimate the posterior entropy is described in Section 3.1.2. Both of these
subsections end with sample scenarios depicting the estimated distributions.
3.1.1 Observation Probability
In the following, the assignment of the observation probability p(x
n
) is formalized. The
observation probability depends on all cells which lie in line of sight to the target cell
c
n
, estimated by a ray-traversal algorithm. Assume that the ray r to the target cell c
n
penetrates M cells. Then r can be represented as the concatenation of penetrated cells
r =c
1
:::c
m
:::c
M
. We want to estimate the observation probability of the target cell c
n
given the cells in the ray. Intuitively, the observation probability of a cell c
m
∈r depends
on the occupancy probability and the observability probability of the predecessor cell
in the ray, c
m−1
∈r. For instance, if the predecessor cell is highly likely to be occupied,
the observation probability of c
m
should be low. On the other hand, if the previous cell
is likely to be free, chances are c
m
is observable if the previous cell in the ray was also
17
x
0
x
1
x
2
⋯ x
m−1
x
M
o
0
o
1
⋯ o
m−2
o
m−1
Figure 3.2: The estimation process modeled as a Hidden Markov Model. The observation
statex
m
is estimated from state x
m−1
given all prior occupancy probabilities up to o
m−2
.
likely to be observable. Thus we assume the observation probability to be Markovian and
formulate the estimation process as a Hidden Markov Model, depicted in Fig. 3.2.
To estimate the observation state x
m
we need to estimate the probability distribution
associated with the current state conditioned on the measurements up to the state m− 2.
We can write the estimation of the probability distribution as a two step prediction-update
recursion.
The prediction step, predicts the observation probability x
m
from state x
m−1
given all
prior occupancy probabilities up to o
m−2
:
p(x
m
So
0∶m−2
)= Q
xm={0;1}
p(x
m
Sx
m−1
)p(x
m−1
So
0∶m−2
); (3.5)
where p(x
m
Sx
m−1
) is the probability of transitioning from state x
m−1
to x
m
is. The state
transition is the only open parameter in our system and controls the behavior of our
approach, explained in more detail in section (3.1.1). The prior observation probability of
the rst cell in the ray r
1
is set to x
0
= 1:0, stating full observability of the rst cell c
0
∈r.
The update step to the cellc
m
integrates the occupancy state of cellc
m−1
and is dened
as
p(x
m
So
0∶m−1
)=p(o
m−1
Sx
m
)p(x
m
So
0∶m−2
); (3.6)
with as the normalization factor. Furthermore the measurement p(o
m−1
Sx
m
) can be
written in terms of the current occupancy state of cell o
m−1
p(o
m−1
Sx
m
)∝p(x
m
So
m−1
)= 1−p(o
m−1
): (3.7)
Visibility State Transition Probability
The observation probability of a cell depends on the occupancy probabilities of the cells in
the path of the ray cast as well as the state transition probability of the Markov Process.
The transition probability denes the likelihood of state transitions given their probability
values. However, the transition probability also controls the behavior of the Markov process
and with that the resulting observation probability of a cell. Hence, choosing dierent
18
parameters for the state transition probabilities result in dierent visibility assumptions.
This allows us to control the behavior of the observation probability when intersecting
unobserved cells. As a result dierent parameters result in dierent NBV positions.
In the following we dene the desired behavior of how cells in the ray should aect the
target cell observation probability. Depending on the occupancy probability of the cells in
the ray we want the observation probability of the target cell c
n
to change in a certain
way, when observed from a certain position s
n
. If all cells in the ray r are likely to be free,
we want the observation probability of cell c
n
to be high (with high probability the cell
c
n
is observable). If the ray contains a 'likely occupied cell' at position c
m
, we want the
observation probability of the consecutive cellc
m+1
to drop o steeply to a low observation
probability value. Furthermore, we want the observation probability of all consecutive cells
after c
m
to be low and with that assign the target cell c
n
a low observation probability.
If the ray contains consecutive unobserved cells we want the observation probability to
gradually fall. Assume the occupancy probability for the cell {c
0
;c
1
;:::;c
n−1
} is uncertain.
Then we want the observation probability follow the rule:
p(x
1
)>p(x
2
)>⋅⋅⋅>p(x
n−1
)>p(x
n
) (3.8)
The more uncertain cells the ray needs to penetrate, the smaller is the probability of that
target cell c
n
being visible. Intuitively this expresses the fact that the more unobserved
space a ray penetrates to get to cell c
n
, the more likely it is that the ray will be blocked
by an object that has not yet been observed.
To achieve this we make the state transition probabilityp(x
n+1
Sx
n
) to change adaptively
depending on how far into the ray we are. Let the transition matrix be of the form
p(x
n+1
Sx
n
)=
vis ¬vis

vis t 1−t
¬vis 0:1 0:9
: (3.9)
Then the variable t controls how likely it is to stay in the state visible and with that how
likely it is to transition to the state not visible. The farther we get into the ray, the less
likely we want it to be to stay in state visible. Thus we make t dependent on the number
of cells passed N
cells
so far:
t=a
N
cells
; (3.10)
where a controls how steeply the value of t falls o.
Observability Probability Scenarios
Examples of how the observability probability evolves as we pass through the ray can be
seen in Fig. 3.3. In the upper half of Fig. 3.3 we can see the evolution of the observation
probability. This shows how the probability changes when the ray passes through the
19
p(x)
1
0
#1
#2
#3
#4
occupied free
unobserved
∗
Figure 3.3: The gure shows the change in observation probability when applied to our
model. The upper half of the picture shows the evolution of the observation probability
when traversing the cells in a ray. The lower part of the gure show the states of the cell
in the ray.
cells till it hits the target cell. In the lower part of the gure we can see four examples
cases of what cells a ray might contain. Four dierent scenarios are shown, #1 where
the ray-traversal algorithm had determined only free cells, #2 where only occupied cells
where detected, #3 where only unobserved
∗
cells where detected and nally #4 where a
mix of all possible ray measurements where detected. In scenario #1 the observability
probability stays almost constant close to p(x) = 1. This makes sense, since we do not
pass any occupied or unobserved cells. In contrast, scenario #2 shows how p(x) instantly
drops to a value close to p(x)= 0 as soon as the rst occupied cell is passed, and stays
there since all new measurements are also occupied cells. The scenario #3 shows exactly
the behavior that we have previously described. The ray consists of unobserved cells only,
and the farther we get into the ray the more drops the observability probability p(x). The
last scenario #4 depicts the other wished for behavior, that is as soon as an occupied cell
is passed, p(x) drops and stays relatively small after that.
To better illustrate the cases and why the changes in probability occur in Fig. 3.3
and 3.5 a virtual scenes is shown in Fig. 3.4. The sub gures correspond to the cases
displayed in Fig. 3.3 and 3.5 (#1 is 3.4a , #2 is 3.4b, #3 is 3.4c, #4 is 3.4d). Each cell
in the grid is assigned a new observation probability, which depends on the cells traversed
by the ray. The ray (blue error) is shot from the current sensor location (blue circle) to
the target cell, with the white dashed boxes indicating all cell which are penetrated by the
ray. The case #1 shown in Fig. 3.4a shows that the ray only traverses free cells. This
∗
Note, a cell is unobserved if its initial occupancy probability has not changed, meaning no measurement
has been received for this cell yet. See Section 3.2.3 for more details.
20
(a) (b)
(c) (d)
Figure 3.4: In this gure we can see virtual scenes corresponding to the cases presented in
Fig. 3.3 and Fig. 3.5. The blue circle on the left of all gures is the current sensor location,
the arrow represents one ray shot into the grid to a target cell and the dashed white cells
represent the cells penetrated by the ray. Green cells are free, red are occupied, and yellow
cells are unobserved. In 3.4a only free cells are penetrated, in 3.4b only occupied cells, in
3.4c only unobserved cells and in 3.4d a mix of all are possible states are penetrated.
occurs if we have estimated the cells in a previous observation as fee. In case #2 shown
in Fig. 3.4b we traverse only occupied cells. This results when we have observed an
obstacle so the cells occupied by the obstacle are occluded. In Fig. 3.4b which is shown
in case #3 we traverse only unobserved cells. This occurs if the robot is positioned on the
boundary of observed and unobserved space. In this case we have no knowledge about the
environment and the probability behaves as shown in Fig. 3.3. In the last case #4 shown
in Fig. 3.4d we traverse cells with dierent states. As we can see in Fig. 3.4d the ray
rst traverses free cells, followed by an occupied cell, followed by unobserved cell and so
21
on. This occurs if we have partially estimated the probabilities of the cells but some of
them are still unobserved. Since we penetrate an occupied cells, belonging to an observed
object, the target observation probability immediately decreases to zero, since we can not
observe the cell.
3.1.2 Posterior Occupancy Probabilities
So far we have explained how to compute the observability probabilities of cells. Now
we describe how this observability of a cell is used to estimate the posterior occupancy
probability p(o
m
Sx
m
;z
m
). Intuitively, the occupancy probability now depends on two
factors: how visible is cell c
m
, which is captured by the observability state x
m
and what is
the occupancy state of the predecessor cell c
m−1
in the ray r. Thus, we can again use a
Bayes Filter to compute the posterior occupancy probability p(o
m
Sx
m
;z
1∶m
), through a
recursive prediction-update process. The prediction step is given through:
p(o
m
Sx
m
;z
1∶m−1
)= Q
o
m−1
={0;1}
p(o
m
So
m−1
;x
m
)p(o
m−1
Sz
1∶m−1
); (3.11)
where z
1∶m
are again the measurements predicted through the ray-traversal algorithm.
Note, how the transition matrix depends on the visibility state x
m
of the next cell c
m
.
Intuitively, the visibility of a cell c
m−1
should in
uence how certain the transition to the
next state is. We will explain this in more depth in Section 3.1.2. The measurement
update takes the usual form of
p(o
m
Sx
m
;z
1∶m
)=p(z
m
So
m
)p(o
m
Sx
m
;z
1∶m−1
); (3.12)
where normalizes the distribution.
Occupancy State Transition Matrix
The intuition of why the occupancy transition matrix should depend on the obervability of
the cell c
n
becomes clear when we think about what eect the following transition matrix
would have:
p(o
m
So
m−1
)=
occ free

occ 0:5 0:5
free 0:5 0:5
: (3.13)
When using this transition matrix in the prediction step we will get a very uncertain belief
p(o
m
Sx
m
;z
1∶m−1
), even if the current occupancy state distribution p(o
m−1
Sx
m−1
;z
1∶m−1
)
was very certain. We would want this behavior if the observability of cell c
m
is very low,
because we want the occupancy distribution overc
m
to become less certain. Only if cellc
m
can be given a certain measurement update, the occupancy distributions becomes certain
22
again. Thus we dene the transition matrix depending on the observability probability as
follows:
p(o
m
So
m−1
)=
occ free

occ t 1−t
free 1−t t
; (3.14)
where
t= 0:5+
p(x
m
)
2
: (3.15)
Now, if cell c
m
is likely to be visible the transition matrix is closer to the identity
matrix and will not aect the posterior distribution p(o
m
Sx
m
;z
1∶m
) by much. However, if
cellc
m
is likely to be not visible, the transition matrix will result in a less certain posterior
distribution, unless a measurement with high certainty can be integrated.
Occupancy Probability Scenarios
We use the same scenarios from the observability estimation, to depict the behavior of the
occupancy probability in Fig. 3.5 and illustrated as a virtual scene in Fig. 3.4. Again we
can see how the resulting occupancy probabilities follow our intuition. Scenario #1 shows
how the occupancy probability stays close p(o)= 0 as we pass through a ray full of free
cells. Again in contrast, scenario #2 shows the opposite behavior, where the occupancy
probability stays close top(o)= 1 as we pass only occupied cells in the ray. In scenario #3
p(o) converges against the most uncertain state of p(o)= 0:5 when only unobserved cells
are in the ray. Finally, scenario #4 depicts, how the occupancy probability becomes close
to p(o)= 1 as soon as we observe an occupied cell, but then drops again to the uncertain
state of p(o)= 0:5 after that when encountering unobserved cells, and only dropping to
almost p(o)= 0:0 when measurements of free cells come in.
3.2 Preprocessing
In this section we describe the general framework of our approach. First we give an
overview of the system architecture followed by a detailed description of the individual
steps.
3.2.1 System Architecture
Given a new point cloudP , the rst step is to perform the merging of two point clouds by
transforming the new point cloud into the coordinate frame of the previous one. LetP
n−1
denote the point cloud after n− 1 cycles. Given the new point cloudP, we joinP
n−1
with
23
p(o)
1
0
#1
#2
#3
#4
occupied free
unobserved
Figure 3.5: The occupancy probability is shown for each cell in a ray. The upper half of
the picture shows the evolution of the occupancy probability when traversing the cells in
a ray. The lower part of the gure show the states of the cell in the ray.
P to obtainP
n
. To merge two point clouds we need to nd the rigid transformation of
P's coordinate frame toP
n−1
's coordinate frame. This transformation can be calculated
using the current sensor pose and the rst sensor observation pose. Using the current pose
however leads to erroneous transformation matrices, due to inaccuracy in the sensor pose
estimation. To improve the transformation we use an Iterative Closest Point (ICP) based
approach. ICP is initialized with the estimated transformation using the current sensor
pose and iteratively improves this initial transformation using information fromP
n
andP.
This procedure is explained in more detail in section 3.2.2.
For further processing the point cloudP
n
is converted into an occupancy grid. How-
ever, the sparse representation of the point cloud leads to holes in the occupancy grid
representation of the scene. To ll these holes we use a Markov Random Field (MRF) in
combination with iterated conditional modes (ICM) (Bishop, 2006). MRFs are undirected
graphs with every node conditioned only on its neighboring nodes. ICM is a greedy method
to sequentially maximize local conditional probabilities. Eliminating such holes leads to
improved estimation of occluded space when using a ray-traversal algorithm for occlusion
estimation. The MRF model optimization is described in section 3.2.4.
In the next step we estimate the occluded space in the occupancy grid representation by
using a ray-traversal algorithm. This also allows us to update the occupancy probabilities
of every cell in the occupancy grid given our sensor model. The occupancy probability is
either changing to 'likely free' or remains at uncertain. The denition of the occupancy grid
as well as the ray-traversal algorithm used for estimating the occluded space is explained
in section 3.2.3.
24
The nal step is to determine the next best viewing pose by choosing the pose that
yields the highest expected information gain as explained in Section 3.1.
3.2.2 Point Cloud Registration
In practice, estimation of the current sensor pose will become inaccurate over time. When
transforming the point clouds based on erroneous localization, the clouds will be aected
by the same drift.
To deal with this problem we use ICP (Besl & McKay, 1992) to nd the transformation
that minimizes the dierence between two point clouds. ICP is designed to t points in a
target point cloud to points in a control point cloud. For ICP to work we need an initial
transformation to align the point clouds coarsely before ICP is applied. The erroneous
rigid transformation, obtained through the current poses estimation, is used as the initial
transformation.
3.2.3 Occupancy Grid
To estimate and represent unknown space we use an occupancy grid, which is a discretized
probabilistic representation of the environment. This makes it possible to assign every
position in space a probability representing knowledge of the world and use ecient
ray-traversal algorithm to estimate the unobserved space.
Every cell c
x;y;z
in the occupancy grid O is assigned a continuous random variable
p(o) denoting the occupancy probability of the cell. A probability of p(o)= 1:0 stating
the cell is occupied while a probability of p(o)= 0:0 as free. An unobserved cell state is
expressed with p(o)= 0:5.
Initially, all cells c
x;y;z
∈O are initialized with probability 0:5, stating no knowledge
about the state of any of the cells. For every new measurementp∈P we want to update the
corresponding cell c
x;y;z
∈O with a new occupancy probability. We update the occupancy
grid using a stochastic sensor model dened by a probability density function p(mSz),
with m being the actual measurement and z being the true parameter state space value.
In our case z corresponds to the cartesian coordinate of the cell center. We assume the
probability function p(mSz) to be Gaussian.
To determine the cell occupancy probability we incrementally update the occupancy
grid using a sequential update formulation of the Bayes' theorem (Elfes, 1989) . Given a
current estimation of the occupancy probability p(o), we want to estimate p(c
x;y;z
Sm
x;y;z
),
given a new measurement m. The update is formulated with
p(p(o)Sm
t+1
)=
p(m
t+1
Sp(o))p(p(o)Sm
t
)
Q
p(o)
p(m
t+1
Sz)p(zSm
t
)
(3.16)
Furthermore, let U be the set of all cells which have a probability of c
x;y;z
= p(o) >
0:4∧p(o)< 0:6∈O.
25
Unknown space estimation
Point Cloud data structures contain no information about the space where no measurements
have been returned, consequently there is no distinction between space which is free and
space which could not be measured due to occlusion. The distinction between the two types
of space is important, because observing unobserved space gives us new scene information.
With the use of a ray-traversal algorithm we distinguish between observed free space and
occluded unobserved space. The ray-traversal algorithm we are using to estimate the new
occupancy probability of the cells is describe in (Amanatides & Woo, 1987).
To estimate the occluded part of the scene we shoot rays from position P to every
uncertain cell c
x;y;z
∈U. P is the position of the sensor from which it has acquired the
input point cloud. The new probability of the cell depends on the ray ending in the cell
u
x;y;z
∈U. Every ray r contains all cells it penetrates until it hits the target cell. If the
ray contains a cell with probability p(o
x;y;z
)> 0:6 (meaning the ray has penetrated a cell
which is occupied) the target cell probability will remain the same. If the ray contains
only free cells with p(o
x;y;z
)< 0:4 or unobserved cells we change the probability of the cell
according to our sensor model. This changes the occupancy probability of the cell towards
more likely to be free. The change of the probability distribution is justied because P
i
was the actual acquisition position and we can be certain that we see the unobserved cell if
we penetrate only likely to be free or unobserved cells. Otherwise we would have measured
an occupied cell and therefore penetrated an occupied cell.
Cost
Depending on the occupancy grid dimensions the number of cells can be very large. The
cost for estimating the unobserved space from an acquisition position P depends on the
number of unobserved cellsU times the number of cells in each ray. Initially, the setU is
fairly large sinceO is initialized with all cell probabilities set to 0:5 minus the cells that
we have received measurements for and set to most likely to being occupied. However the
number of unobserved cells drastically decreases with every new data acquisition, hence
the cost for reestimating the unobserved space after incorporating new measurements also
decreases.
3.2.4 Markov Random Field
The sparseness of point cloud can lead to holes in the surfaces of objects in the environment
when converting them into an occupancy grid, resulting in cells that should be occupied
remain unobserved. This phenomenon can be seen in Fig. 3.6a and 3.6c, showing a
partially observed box and cylinder. Holes in the objects lead to incorrect estimation of the
unobserved space. Thus we want to identify the unobserved cells which belong to an object
and set their probability to occupied. Intuitively, cells that are surrounded by occupied
cells are likely to be part of the object as well. These correlations between neighboring cells
can be captured using a Markov Random Field (MRF), were each variable only depends
26
(a) (b)
(c) (d)
Figure 3.6: In (a) and (c) we can see missing data of the box and a cylinder. This missing
measurements lead to holes in the objects. The result of the MRF approach can be seen in
(b) and (d) where the red cells are the cells set to occupied after convergence of the MRF.
on the neighboring variables. In a 1D MRF the probability value of a random variable
X
n
depends on its two neighbors
P(X
n
SX
n−1
;X
n+1
): (3.17)
With the point cloud situated inR
3
the MRF in a 3-D setting hasS = {s
x;y;z
} which is
the set of hidden nodes andO = {o
x;y;z
} the set of observation nodes, wherex= 1:::X;y =
1:::Y;z = 1:::Z, with X;Y;Z being the dimensions of the occupancy grid . The nodes
in S are related to one another over a neighboring system. For a xed site s we dene a
neighborhood N(s). To make it more concrete for the sites
x;y;z
the neighborhood is dened
as: N(s
x;y;z
)= {(x− 1;y;z);(x+ 1;y;z);(x;y− 1;z);(x;y+ 1;z);(x;y;z− 1);(x;y;z+ 1)}.
For eciency we are not considering the diagonals. Thus in a 3D setting, the probability
of a node s depends on its neighborhood,
P(sSN(s)) (3.18)
Both the observation variableso
x;y;z
∈ {−1;+1} and the hidden variabless
x;y;z
∈ {−1;+1}
are initialized with the state of the corresponding cell, where +1 represents an occupied
cell and −1 the state unobserved. Furthermore the structure of our graphical model can
27
be summarized by presence of two types of cliques. The rst group of cliques are formed
by {s
x;y;z
;o
x;y;z
} which have an associated energy function modeling the relationship of
the observation variable and the hidden variable. We choose an energy function which
favors equal signs of {s
x;y;z
} and {o
x;y;z
} by giving a lower energy if both have the same
sign and a higher energy when they have the opposite sign
E(s
x;y;z
;o
x;y;z
)=−⋅s
x;y;z
⋅o
x;y;z
; (3.19)
where is a positive constant. The other group of cliques are formed by pairs of neighboring
hidden variables,s
x;y;z
andz
n
∈ N(s
x;y;z
). Here, we also want the energy to be low if both
cells have the same sign and a high energy if they are dierent. We dene the energy
function as follows
E(s
x;y;z
;z
n
)=−⋅x
x;y;z
⋅z
n
; (3.20)
with being a positive constant. Thus, the total energy function of our model is given by:
E(S;O)=−Q
s∈S
M
zn∈N(s)
s⋅z
n
− Q
x;y;z
s
x;y;z
⋅o
x;y;z
(3.21)
To maximize the joint distribution of the MRF we use the iterative conditional modes
(ICM) (Tilton & Swain, 1984) algorithm, which "greedily" maximizes local conditional
probabilities sequentially. The optimal assignment of the hidden variabless∈S is found by
iterating over the eld, taking always one node variable s
x;y;z
at a time and evaluating the
total energy for the two possible states s
x;y;z
=+1 and s
x;y;z
=−1 while keeping all other
node variables xed. After calculating the total energy for both states, we assign s the
state that produced the lower energy. It should be noted, that we only iterate over hidden
variables s∈S that where initialized with state unknown. This is done for two reasons:
On the one hand, we are certain about the assignment of a cell being occupied, thus we
do not want the state of hidden variables, that were initialized with s
x;y;z
=o
x;y;z
=+1,
to change. On the other hand, this leads to faster convergence of the algorithm. The
algorithm has converged if we have visited every site s∈S at least once and no changes to
the variables have been made. A typical result of the MRF optimization step is shown in
Fig. 3.6b and 3.6d.
3.3 Experiments
We evaluate our formulation of the NBV problem in the task of large scale exploration and
detailed data acquisition using a robotic system. The two evaluation scenarios dier in
their size and level of clutter. To evaluate the detailed data acquisition capabilities we use
the robotic system to explore a table top environment and acquire object information. The
table top scene is extremely cluttered and unstructured resulting in many occlusions and
the need to observe the table top from dierent positions. This environment analyzes the
algorithm in the presence of clutter. In the second experiment, which is conducted only in
simulation, we use our approach to explore large oce environments. Oce environments
28
Figure 3.7: The experimental platform (PR2 Willow Garage). In this paper, we use the
tilting Hokuyo UTM-30LX laser scanner, mounted above the shoulder and an RGBD
sensor mounted on the head, for data acquisition. (Image, courtesy of Willow Garage)
are in general less cluttered and consist of large rooms and long hallways, with mostly
free areas. We compare and evaluate our approach to dierent frontier-based exploration
algorithms. Besides the size and the clutter of the two environments, they dier also in
terms of viewing scale of the sensor. For detailed exploration, like the observation of objects
on a table top, the sensor viewing scale is in general far bigger than the environment.
This is dierent for large scale exploration usually, the dimensions of a room or a hallway
exceed the sensor viewing scale.
For experimental evaluation we use the PR2 robot Fig. 3.7, a research and development
platform, from Willow Garage, operated using the Robot Operating System (ROS) (Quigley
et al., 2009). The PR2 robot has a mobile base, with a footprint of 668× 668 mm, two
manipulators as well as several high-end sensors (e.g. tilt laser scanner, stereo cameras,
RGB-D sensor, IMU). The robot has a substantial size, which means the robot can not
reach every position in space the next best view algorithm estimates. The consequence
of this is almost always time consuming, since unreachability can only be determined in
imminent vicinity of an unexpected object due to either unnecessary robot motions or
29
Figure 3.8: PR2 robot acquiring data from a table top. The robot is able to position itself
anywhere around the table.
due to the need of recomputing a new next best view positions. We will explain in the
following chapters how we deal with this issue and what eect this has on the information
gain. The simulation experiments are performed using the robot simulator Gazebo. This
simulator is able to replicate the PR2 robot with all its functionality in a physics simulated
environment. In simulation we are utilizing the tilt laser scanner as well as a RGB-D
camera for data acquisition.
In the following we evaluate our approach in simulation as well as on a real robotic
system. First, we evaluate the detailed exploration of table top environment using a real
robot. Second, we evaluate our approach in a large scale exploration environment of two
oce environments in a simulation environment.
3.3.1 Real Robot Experiments
To analyze the performance of our approach in small and cluttered environments, we
simulate dierent cluttered table top scenes. The scenes, shown in Fig. 3.9, consists of
dierent objects and congurations of the objects on the table, varying in dierent levels
of complexity and clutter. The table is setup in a way that the robot has the ability
to position itself anywhere around it, Fig. 3.8. To fully observe the table top and with
that all the objects on it, we used the robot's mobile base to position the sensor around
our region of interest. For the detailed data acquisition we are using a tilting Hokuyo
UTM-30LX laser scanner, mounted on the upper torso of the PR2 robot, to produce the
input point clouds. The laser scanner is more accurate and less noisy compared to a
30
RGB-D sensor, however it requires approximately 15 seconds to acquire a high resolution
full 3D scan of the environment. Additionally, we restrict the lasers' eld of view to 15
degrees to increase accuracy. This makes an environment measurement costly in terms of
needed time, therefore the goal is to keep the number of needed scans minimal and reduce
the unobserved space maximally for every new scan. Furthermore, the laser scanner is
mounted in a way that the robot cannot see all the objects by looking down at the table.
This makes the setup more general and harder to solve because not all objects are seen in
the rst scan.
Since we are only interested in the objects on the table, we extract the objects from
the table top as an additional pre-processing step. Given a new point cloud, the rst step
is to extract the table top and objects. The surface normals of all points in the point cloud
are computed and are used to estimate all horizontal planar surfaces by using robust SAC
(Sample Consensus) estimators. The approach is described in detail in (Rusu, Holzbach,
Beetz, & Bradski, 2009) and implemented in the Point Cloud Library (PCL) (Rusu &
Cousins, 2011). All points above this planar surface correspond to data points of objects.
We only integrate measurement points belonging to objects into the occupancy grid.
The dimension (w×d×h) of the occupancy grid in
uences the resolution of the nal
measurement acquisition result as well as the runtime of the exploration algorithm. Given
the relative small table top with 1 by 1 meters, we choose the resolution of the occupancy
grid as follows: w = 129,d= 129 andh= 65. The resolution of the occupancy grid in
uences
the runtime of the algorithm greatly, since discretizing the space in smaller cells results in
an increase of unobserved cells. More unobserved cells means more cells to traverse and
process using the ray-traversal algorithm and with that an increases run-time. However,
discretization size also in
uences the level of detail we observe the environment, in general
we decided to have a high resolution for detailed observation while a low resolution is
sucient for observation of large space, for example. The resolution we picked for the
detailed observation of the table-top results in a cell size smaller than 1 cm, which resulted
in a very dense point cloud.
To execute the Markov Random Field preprocessing step to ll in missing measurements
of the objects, the ICM algorithm requires the parameters and . They in
uence the
convergence behavior and are set to = = 1:0 for a conservative convergence. The
parameters in
uence the weight every relationship in a clique receives. Setting the
parameters to = = 1:0 results in an equal weight. If we would set = 0, we eectively
remove the link between the paris of neighboring hidden variables. This would result in
the global most probable solution is s
x;y;z
=o
x;y;z
.
Additionally the estimation of the NBV position depends on the parameter a, in
uenc-
ing how far we suspect to see into the unobserved regions. Best results were achieved with
the parameter set to a= 0:997, which was empirically estimated.
In the detailed exploration experiments the NBV estimation depends on the number
of possible sampling positions K and the angle of each s
k
. We choose a nite set of
viewing positions in such a way, that all of them lie on the perimeter of a circle around
the region of interest. We have found that the discretization does not eect the result in
31
(a) (b)
(c) (d)
Figure 3.9: In the images (a)-(d) we show the experimental test scenarios for the detailed
exploration. The table top scenes have dierent number of object simulating dierent level
of clutter.
a signicant way, since small pose changes of the sensor do not eect the eld of view
in a notable way. However discretization drastically shortens the computation time. For
our experiments, we have set K = 10 and
i
with i= [1; 2; 3] with the angles [-15, 0, 15]
resulting in 30 dierent viewing positions.
We compare our probabilistic framework with two other methods. The simple greedy
approach assumes every unobserved cell is visible from a virtual scanning position, unless
it is obstructed by an occupied cell. This predicted measurementz is then used to estimate
and evaluate the information gain of a virtual scanning position s
k
∈S. This models the
approach used in (Stachniss & Burgard, 2003). The second tested approach chooses the
NBV position randomly after a new real measurement is taken by the sensor. To compare
the three approaches we contrast the actual increase in information gain, which is equivalent
to the decrease of unobserved cells in the occupancy grid. Additionally, we evaluate our
approach in terms of prediction error of the information gain. A large prediction errors
means overestimation of the information gain for a virtual viewing position. This has
32
0 2 4 6 8 10
Number of scans
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
random
potthast_vis_inf_gain
(a)
0 2 4 6 8 10
Number of scans
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
random
potthast_vis_inf_gain
(b)
0 2 4 6 8 10
Number of scans
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
random
potthast_vis_inf_gain
(c)
0 2 4 6 8 10
Number of scans
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
random
potthast_vis_inf_gain
(d)
Figure 3.10: In the graphs (a)-(d) we compare the simple approach which is drawn as blue
line with our proposed method drawn in red and a random approach in green. We can see
that our method drawn in red decreases the number of unobserved cells faster, which is
the eect of choosing NBV positions more optimal.
the aect that the chosen NBV positions is not necessarily a good one. Furthermore to
give statical signicance to our evaluation we conducted multiple runs for each scene and
method. We conducted ten dierent runs for each scene and method, initialized from each
of the sampling positions.
Evaluation
The overall performance shown in Fig. 3.10 shows the average decrease in unobserved cells
over the 10 trials for each scan. We can see that our proposed approach converges faster
and has therefore reduced the number of unobserved cells faster than the simple greedy
approach. This also means that to observe a certain percentage of the unobserved space,
33
0 1 2 3 4 5 6 7 8
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Prediction Error
1e4 Average Prediction Error
simple_inf_gain
potthast_vis_inf_gain
(a)
0 1 2 3 4 5 6 7 8
Number of scans
0
1
2
3
4
5
6
7
Prediction Error
1e4 Average Prediction Error
potthast_vis_inf_gain
simple_inf_gain
(b)
0 1 2 3 4 5 6 7 8
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Prediction Error
1e4 Average Prediction Error
potthast_vis_inf_gain
simple_inf_gain
(c)
0 1 2 3 4 5 6 7 8
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Prediction Error
1e4 Average Prediction Error
potthast_vis_inf_gain
simple_inf_gain
(d)
Figure 3.11: In the graphs (a)-(d) we show the absolute prediction error over the number
of scans. The error is computed by taking the absolute error between the predicted
information gain and the actual number of seen cells after a scan is taken. The green line
in the graph represents the simple method while the blue line shows the prediction error
of our method.
our approach can perform this in most cases much faster than the simple greedy method.
As a consequence this means our method has chosen better next best scanning positions.
An example of chosen positions and their reductions in unknown space can be seen in
Fig. 3.12. Intuitively, the simple approach heavily over estimates the expected number of
cells it can see from a virtual scan. As a result, it chooses next best scanning positions
which decrease far less unobserved cells than expected due to objects, which have not yet
been seen, blocking space which thought to be observable.
To chose the NBV position we have to predict the outcome of a virtual scan. In
Fig. 3.11 we show that the absolute prediction error of our method is much lower than the
prediction error of the simple method. The prediction error is calculated as the dierence
34
between the expected number of hitherto unobserved cells seen and the true number of
hitherto unobserved cells seen in the new (real) scan. Note that due to the nature of the
methods the two approaches computed two dierent sequences of sensor locations. Since
this would result in an unequal comparison we ran the simple approach on the sequence
estimated by our proposed method. Resulting in a comparison of the errors for the same
scanning poses.
3.3.2 Simulated Experiments
In the second experiment we apply our approach to two dierent large scale oce environ-
ments, consisting of hallways and several rooms. Both environments are less cluttered,
compared to the table top scene, but substantially larger. Due to the size of the environ-
ment the main dierence to the rst experiment, besides the level of clutter, is the fact
that the maximal distance a sensor can obtain a measurement in, is generally signicantly
smaller than in the table top environment. The oce environment as well as the robot
is simulated using the robots simulator Gazebo. We constructed two large scale oce
environments shown in Fig. 3.13 and Fig. 3.14. The rst environment consists of two
adjacent large rooms with a total size of 15 x 10 x 2 meters. The second environment
is larger in size (20 x 25 x 2 meters) and consists of long hallways, small and large
rooms. Furthermore, our approach is tested with dierent levels of clutter and varying
starting locations of the robot. To explore the oce environment we are using a simulated
PR2 robot equipped with a simulated RGB-D camera (Microsoft Kinect). We limit the
maximal sensor distance to 3:5 meter, which is approximately the real maximal distance
of the sensor. Additionally, Gaussian noise is added to the measurement by the simulator.
Although the RGB-D sensor is capable of continuous data acquisition, we constrain our
exploration such that the robot has to be stationary to obtain measurements. To fully
observe the environment the robot needs to iteratively estimate NBV positions, position
itself and the sensor at the new location and acquire new measurements until the space is
observed.
Due to the signicant larger environment we initialize the occupancy grid with a
higher resolution of w = 257, d= 257 and h= 65. The parameter for model optimization,
especially for the ICM algorithm, remain the same as in the rst experiment. The visibility
parameter a of our approach is set to 0:9999, resulting in little visibility penalties when
looking into unobserved regions. In general, oce environments consists of long and clutter
free hallways as well as open spaces in oces.
Rather than relying on pre-determined or sampled potential new viewing positions
we estimate new positions on a frontier-region. Frontier-regions are boundaries between
observed free space and unobserved space. After a new point cloud is integrated into the
occupancy grid, we estimate all boundary cells and cluster them to frontier-regions. Each
centroid of a frontier-region is a potential new viewing position and will be evaluated for
its expected information gain. On every NBV positions we capture a full 360 degree sweep
of the environment and integrate the measurements into the occupancy grid. Over the
past decades many frontier-based approach were developed, the most prominent ones are
35
(a) (b)
(c) (d)
Figure 3.12: The gure shows, from left to right, the reduction in unobserved cells after
estimating the NBV position and acquiring new measurements. With each new observation
more information about the environment is revealed, resulting i a reduction in unobserved
(yellow) space.
36
(a) (b)
(c) (d)
Figure 3.13: The gure shows a small oce environment with dierent levels of clutter.
For each environment we start the robot at ve dierent initial starting locations, depicted
as blue circles.
(Yamauchi, 1997) and (H. H. Gonzalez-Banos & Latombe, 2002) to which we compare
our approach. Frontier approaches distinguish each other in the way NBV positions or
frontiers are chosen and explored next.
The oldest but still widely used, because of it's simplicity, is Yamauchi (Yamauchi,
1997). The frontier centroid which is the closest to the robots current position is chosen
as the NBV position. This strategy results in extremely short travel time after new
measurements are acquired, however in general the number of necessary view points is of a
factor of two larger compared to more sophisticated approaches. Latombe (H. H. Gonzalez-
Banos & Latombe, 2002) developed a popular approach combining information theory
and travel cost. For every frontier region the information gain is computed, with the
measurement approximated by assuming innite visibility, and penalized by the distance
the robot would have to travel to get to that NBV position. The position with the highest
reward is chosen as the NBV position and with that the next exploration position.
37
(a) (b)
(c) (d)
Figure 3.14: The gure shows a large oce environment, with dierent levels of clutter.
For each environment we start the robot at ve dierent initial starting locations, depicted
as blue circles.
The robot navigation algorithm tries to navigate the robot to the chosen goal point.
However, not all NBV positions are reachable by the robot, since the estimated centroids
of frontiers could lie within or very close to objects. In this case the navigation algorithm
tries to get the robot as close as possible to the goal point, but eventually has to aboard
and proceeds as if the goal position is reached.
Furthermore, we compare our approach to the simple greedy approximation of the
information gain as described in the previous experiment. The frontier centroid with
the highest information gain is chosen to be the NBV position. Finally, we compare our
approach to a random selection of the frontier centroids.
38
0 5 10 15 20
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
latombe
potthast_vis_inf_gain_0.999
potthast_vis_inf_gain_0.9999
random
yamauchi
(a)
0 5 10 15 20 25
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
latombe
potthast_vis_inf_gain_0.999
potthast_vis_inf_gain_0.9999
random
yamauchi
(b)
0 5 10 15 20 25
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
latombe
potthast_vis_inf_gain_0.999
potthast_vis_inf_gain_0.9999
random
yamauchi
(c)
0 5 10 15 20
Number of scans
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
latombe
potthast_vis_inf_gain_0.999
potthast_vis_inf_gain_0.9999
random
yamauchi
(d)
Figure 3.15: The gure shows the average performance for the small oce environment
Fig. 3.13 of our approach compared to the simple greedy, Latombe, Yamauchi and random.
The observability parameter for our approach is set to a= 0:999 and a= 0:9999. We can
see that our approach is on par with all the other approaches.
Evaluation
The performance for the dierent approaches in a large scale exploration task can be seen
in Fig. 3.15 for the small oce environment and Fig. 3.16 for the large oce environment.
As we can see, by setting the observation parameter close to 1:0 we converge to a similar
behavior as the simple greedy information gain approach. Intuitively, it makes sense that
due to the sparseness of the environment, the best exploration performance in terms of
reducing the number of unobserved cells as quickly as possible, is achieved by assuming
almost innite visibility. In both oce environments this seems to be the best strategy,
and our approach has the
exibility of adapting this rather greedy strategy. For both oce
environments experiments have shown that the performance for dierent values of the
39
0 10 20 30 40 50 60
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
latombe
potthast_vis_inf_gain_0.9999
random
yamauchi
(a)
0 10 20 30 40 50 60
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
latombe
potthast_vis_inf_gain_0.9999
random
yamauchi
(b)
0 10 20 30 40 50 60 70
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
latombe
potthast_vis_inf_gain_0.9999
random
yamauchi
(c)
0 10 20 30 40 50 60 70
Number of scans
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Number of unobserved cells
1e6 Average number of unobserved cells
simple_inf_gain
latombe
potthast_vis_inf_gain_0.9999
random
yamauchi
(d)
Figure 3.16: The gure shows the average performance for the large oce environment
Fig. 3.14. Our approach is at least as good as the other tested approaches. The observability
parameter is set to a= 0:9999.
observation parameter does not degrade substantially. This is probably due to the fact that
both environments are fairly large and sparse in obstacles. Hidden unobserved obstacles
are rare and positions with large unobserved frontiers yield comparable performance.
3.3.3 Practical Issues
The next best view algorithm we have presented in this paper is evaluated on a robotic
system, more specically on the PR2 robot. In general, the proposed next best view
estimation algorithm is independent to a specic robot or any underlining system, however
we use it to acquire data and more importantly get an estimated of the sensor positions in
a word coordinate frame. In the following subsections we will give some insight into the
practical issues when using our specic evaluation system.
40
Robot Limitations
Depending on the system used to move the camera not all positions in space are reachable
by the system. Our robot in particular is fairly large and can only operate on a 2D ground
plane. Practically, this means potentially next best view positions can only be sampled
from a subset of all possible viewpoints. This subset includes only the positions which
lie within the robots conguration space. In contrast to our robot, a robot operating
in 6D like an areal vehicle has a much larger operation space. However, even if we only
sample in the robots conguration space, it is still possible that the positions sampled are
not reachable. This happens if a potential viewing position lies within unobserved space
and is obstructed by a previous unseen object. For the tabletop scene we assume there
are no obstacles surrounding the table which could prevent the robot from reaching a
sampled potential new viewing position. In the large environment exploration task this can
however happen, since the algorithm we use to estimate potential new viewing positions
can return positions which lie within unobserved space. If such a position can not be
reached a fallback plan has to be used. In our case we attempt to get as close as possible
to the position, treating this as the new viewing position and acquire a new environment
scan. However, there are many other operations that can be performed, e.g. choosing a
dierent positions from the set of potential new viewing positions. Problematic with our
fallback plan is that the estimated expected information gain, estimated by our proposed
algorithm, for the fallback position is dierent than for the original position. This means
taking a scan on the fallback position has a worse information gain than estimated on the
original planned position or even as on a dierent position in the set of potential next best
viewing positions. Unfortunately, we only know this once we have actually taken a new
observation and integrated in our world representation. Moving to a dierent positions
once the robot is not able to reach the position is a viable option, but it is not clear
that this has more benets. First, the robot has a lot more cost to actually reach a new
positions, it rst has to drive to the original, if not reachable, it has to drive to another
one. Second, we do not know if this position is in fact better than the one close to the
unreachable rst one, since without taking an observation at the unreachable rst position
we have no information of its expected information gain.
Registration Issues
Registration of sensor data over time is still an unsolved problem and a very active research
eld. In the real world experiment we have a tailored solution which works reasonable well
and produces only small errors in registration. In the simulation environment, we do not
assume perfect position knowledge of the robot, but rather apply gaussian noise to every
position estimate. Registration errors accumulating over time will have an eect on the
nal representation of the world but also on the estimation of the expected information
gain and with that on the choice of the next best view position.
41
Runtime
The runtime of the algorithm highly depends on the number of sampled potential new
viewing positions and the total number of cells that need to be evaluated. The runtime
of estimating the expected information gain of one potential next best view positions
therefore highly depends on the discretization of the environment. This varies from a
second to a couple of seconds, due to costly ray-traversal operations. Currently we have
a fast implementation, however there are GPU implementation which would improve
the speed tremendously. Each additional potential next best view, which needs to be
evaluated for its expected information gain, increases the total runtime by the evaluation
time. Typically, the complete evaluation for the best next best view points takes about 30
seconds. A future goal would be to push this evaluation to under 10 seconds.
3.4 Discussion
The results of the experiments show the usefulnesses of our approach in terms of detailed
and large scale exploration. Comparing the results in the two dierent scenarios, one
can see that reasoning over the observability of the cells is most useful in an extreme
cluttered environment and when the sensor viewing scale is larger than the environment.
In the detailed exploration setting our approach outperforms all other tested methods. On
average, our proposed framework reduces the number of unobserved cells faster than the
simple greedy method. In the large scale experiment the performance of our algorithm
is at least as good as the simple greedy approach and is on par or better than the other
tested approaches. We occasionally see a slightly faster reduction of unobserved cells using
our approach, however in all of the cases it was insignicant.
When comparing our method to dierent approaches found in the literature the real
advantage comes with that fact that we are are able to mimic several dierent exploration
strategies within one approach. Changing the value of the observability parameter a
and with that the observability assumption of an unobserved cell also results in dierent
exploration behaviors. This allows us to adapt our exploration strategy, depending on
the task, within the same algorithm. With that our approach is more general to dierent
exploration scenarios and needs. When changing the observability parameter to a value
close to 1:0 we achieve no penalty for unobserved cells, resulting in the assumption of
innite visibility. In comparison when we set the parameter closer to 0:9 we achieve a
behavior which mimics the behavior of always exploring the biggest frontier. Values in
between 0:9 and 1:0 result in more or less penalization for unobserved cells.
A limitation of our approach as presented here is that the observability parameter a
needs to be set manually, depending on what kind of scene needs to be explored. However,
setting the parameter is very intuitive, for very cluttered scenes a value of a≃ 0:997 is a
good starting point. For large scale scenes with relatively few clutter, a value of a≃ 0:9999
will most likely work well.
42
3.5 Conclusion
We have presented a
exible probabilistic framework for Next Best View estimation. We
have shown that our approach can mimic several dierent explorations strategies. Thus
the proposed framework is a more general approach to NBV estimation. This generality
has been validated in several experiments conducted in simulation as well as on a real
robotics platform. In both experimental settings, the detailed exploration and large scale
oce exploration, we can show that our approach is on par or better than other popular
approaches like the simple greedy method.
43
Chapter 4
Active Multi-View Object Recognition and
Online Feature Selection
Despite decades of research, object recognition from visual percepts is still an unsolved and
challenging problem. In robotics especially, where many tasks build on, or directly involve,
the recognition of objects, the need has grown for creating reliable and fast classication
systems. Conventional approaches for object recognition are tour de force, exclusively
relying in large part on complex statistical models for classication and heavy engineering
of computationally-intensive features (Bo et al., 2011; Lowe, 2004). All too often, systems
are assumed to be unlimited and their processing capabilities are neglected. This stands
in stark contrast to many of today's mobile robots, which often have limited power and
need to be economical with resources for computing and reasoning|being able to move
and execute given tasks is their rst priority!
Active object recognition(Atanasov, Sankaran, Ny, Pappas, & Daniilidis, 2014; Denzler
& Brown, 2002) is an appealing paradigm to overcome the challenges in recognition of
objects. Here, a mobile robot congures and positions its sensors to inspect a target object
and recognize it as a previously learnt object. The advantage of active object recognition
lies in the ability of reacting to unforeseen objects or scenes by exploratory actions. This
allows to seek actively for the information that is the most useful in performing inference
under uncertainty.
Adaptive action selection oers the
exibility that is required to potentially re-use the
statistical modeling power of conventional approaches even under the severe (computing)
constraints present on mobile robots. The general idea is to control the sensors such that
only data with high information content is collected. By running inference recursively
based on previously acquired information (which represents the robot's current knowledge,
i.e., its belief state about the identity of the object), the collection of data can be adapted
dynamically. Therefore, computation time can potentially be reduced, because we only
process useful information and have the ability to improve our belief with each additional
action.
In previous work, there are two common actions that have been explored in order
to increase the recognition accuracy: rst, feature selection (Verleysen & Rossi, 2009),
44
which computes a subset of informative features; second, viewpoint selection or view
planning (Potthast & Sukhatme, 2014; Atanasov et al., 2014), which controls where and
how many additional observations to take. However, previous approaches have not looked
at the potential of reducing computation time due to feature selection. Moreover, existing
work does not exploit the full potential of combining these two strategies and applying
feature and viewpoint selection in concert.
The main idea of our work hinges on the following intuition: Is it possible to reduce
overall costs for recognition by relying on feature subsets gathered from multiple views, in
lieu of the full feature set, potentially taken from a single view, using a complex statistical
model for classication? More concretely, in this paper, we present an information-
theoretic multi-view object recognition framework that unies the two strategies of feature
selection and viewpoint selection. We aim at exploiting local information by selecting
additional features at the current viewpoint and further exploring the object by selecting
new viewpoints around it. The described framework optimizes the viewpoint selection
by reducing ambiguities and selecting features dynamically, such that only useful and
informative features are extracted and incorporated in the recognition process. Unlike
standard feature selection, the two strategies are symbiotic in our algorithm. Feature
selection is an iterative process, thus at any given time, the selected feature depends on the
trajectory of the past viewpoints while simultaneously aecting the future viewpoint(s).
We perform extensive evaluations on a large RGB-D camera dataset, which is composed
of single object scenes. To evaluate our framework, we conduct experiments with two
dierent feature sets, one set consisting of simple features designed by us, and one set of
more complex kernel descriptors proposed by (Bo et al., 2011). The use of the simple
features shows that, in combination with feature selection and view planning, our framework
can compete with state-of-the-art single-view classication systems. In contrast, using the
kernel descriptors shows that our framework is capable of dealing with more advanced
features as well.
We further show the advantages of combining intelligent view planning and online
feature selection. Online feature selection reduces the computation time vefold for the
simple features and 2:5-fold for the kernel features at runtime. Furthermore, in combination
with view planning, we are able to increase the recognition accuracy signicantly by
resolving object ambiguities. In the case of the simple features, we achieve an increase
in accuracies by 8{15%, while in case of the kernel descriptors the increase is about 8%.
Overall, our results show pose estimates within ±45
○
of the ground truth and object
recognition accuracies of over 90% when using the simple features in rather challenging
object recognition experiments. Using the kernel descriptors, we improve the object
recognition accuracy to over 98%. As proof-of-concept, we eventually implemented and
tested the proposed approach on a custom-built quadcopter robot. The quadcopter is
equipped with an RGB-D camera and collects multiple views by
ying around a target
object, which allows to recognize the object.
Additionally, we show how our active multi-view recognition system can be used for
object change detection. Given a prior map of the environment, the task is to determine
45
whether objects in the environment have changed. This can either mean that the object
has changed completely (i.e., it belongs to a dierent object class), or the object has
changed its orientation only (i.e., it belongs to the same class but its rotation diers in
yaw). Our results show that on average our framework can detect such changes in the
environment with an accuracy of larger than 90%.
Prior works on active perception go back as far as the seminal paper (Bajcsy, 1988).
\Active" can either refer to adjustments of the sensor parameters themselves, e.g., adaptively
changing the focal length of a camera, as in (Bajcsy, 1988; Denzler & Brown, 2002), or
mean that the entire sensor moves together with the underlying platform. The latter is
particularly common in robotics, where robots plan new observation locations and viewing
directions actively (Laporte & Arbel, 2006; Hollinger, Mitra, & Sukhatme, 2011; Atanasov
et al., 2014). This is known as robotic view planning. (Potthast & Sukhatme, 2014)
presents a comparison of several representative approaches to view planning from literature.
View planning can be formulated as a purely geometric problem (K. Tarabanis, Tsai, &
Kaul, 1996; H. Gonzalez-Banos & Latombe, 1998) but as well relates to robotic exploration,
where information-theoretic strategies have become state-of-the-art solutions (Stachniss,
Grisetti, & Burgard, 2005; Krainin et al., 2011). The selection of optimal viewpoints for
a robot can be useful in various applications, such as for the inspection of underwater
structures (Hollinger, Englot, Hover, Mitra, & Sukhatme, 2013), for object search in indoor
environments (Ekvall, Jensfelt, & Kragic, 2006; Finman, Whelan, Kaess, & Leonard,
2013) or detecting objects on a table top (Atanasov et al., 2014). Moreover, methods for
view planning and active object recognition provide the basis for operations like object
sorting (Gupta, Muller, & Sukhatme, 2015) and manipulation (Krainin et al., 2011; Holz
et al., 2014), acquisition of object representations (Welke, Issac, Schiebener, Asfour, &
Dillmann, 2010) or change detection (we will show in the end of Section 3.3 how our object
recognition framework naturally extends to perform object change detection).
The common goal of object recognition approaches is to recognize objects and estimate
their poses (Denzler & Brown, 2002; Laporte & Arbel, 2006; Ekvall et al., 2006; Collet &
Srinivasa, 2010; Lai, Bo, Ren, & Fox, 2011). (Denzler & Brown, 2002) presents an active
object recognition framework that, similar to ours, relies on a sequential decision process
and mutual information as information-theoretic measure for the selection of actions.
(Laporte & Arbel, 2006) selects multiple viewpoints by using the Jerey's divergence
instead of maximizing the mutual information. (Ekvall et al., 2006) combines active object
recognition with Simultaneous Localization and Mapping (SLAM) techniques to estimate
object positions and link semantic with spatial information. (Collet & Srinivasa, 2010)
extends a single-view to a multi-view object recognition method for increased eciency by
applying multi-step optimization and extracting SIFT features from camera images. (Lai
et al., 2011) performs object recognition and object detection by using dierent classiers
and several shape and visual features.
To cope with objects that appear ambiguous in single views, (Borotschnig, Paletta,
Prantl, & Pinz, 1998; Paletta & Pinz, 2000; Brown & Lowe, 2005; Collet & Srinivasa, 2010)
propose multi-view object recognition frameworks that use cameras and image databases,
46
whereas (Atanasov et al., 2014; Finman et al., 2013; Luber, Spinello, & Arras, 2011; Lai
et al., 2011) recognize objects by extracting features from laser scanners and RGB-D
depth cameras. (Luber et al., 2011) applies the online boosting approach from (Grabner
& Bischof, 2006) to point clouds in the robotic domain for feature selection. Feature
selection can support the object recognition task by reducing the computation time
and confusions through suboptimal feature sets (Guyon & Elissee, 2003; Verleysen &
Rossi, 2009). A standard alternative to boosting is the selection of features by mutual
information (Peng, Long, & Ding, 2005; Verleysen & Rossi, 2009). (Peng et al., 2005)
tries to select the most relevant features by maximizing the dependency of a feature
on the target object (i.e., maximizing the mutual information), while minimizing the
redundancy between the features. (Ali & Marton, 2014) evaluates the feature selection
methods from (Peng et al., 2005) when applied to the RGB-D dataset of (Lai et al.,
2011). Ensemble methods (Dietterich, 2000) oer further alternatives of how to combine
features; (Schimbinschi, Schomaker, & Wiering, 2015) employs ensemble methods for
3D face recognition and (Marton, Seidel, Balint-Benczedi, & Beetz, 2013) compares the
concatenation of all available features to ensembles with stacking. (Zhou, Comaniciu,
& Krishnan, 2003) proposes a unifying view on active recognition and feature selection,
however, focuses on feature interdependencies and the selection of features given a concrete
context, e.g., a specic target object to detect. Their method, as well as the other feature
selection methods for object recognition mentioned above, do not explicitly consider
viewpoint selection, whereas our object recognition framework applies both feature and
viewpoint selection in concert.
Although many approaches for active view planning as well as online feature selection
exist, to the best of our knowledge, the advantages of both approaches have never been
leveraged in combination. This paper builds on a prior conference paper (Potthast et al.,
2015). The journal version provides a more detailed problem formulation, demonstrates
broader applicability to more complex feature sets and object change detection, and includes
more extensive evaluation of the unied feature and viewpoint selection framework.
The remainder of the article is organized as follows. The problem formulation and
proposed solution of our active multi-view object recognition approach is detailed in
Section 4.1. Section 4.2 introduces the unied selection of actions, which is applied to
both feature selection in Section 4.3 and viewpoint selection in Section 4.4. The object
recognition experiments and results are discussed in Section 4.5, and a conclusion is
provided in Section 4.6.
4.1 Problem Formulation
We look at solving the following problem. Given a static scene and an object in question,
we want to recognize the object and, at the same time, estimate its pose relative to
the coordinate system of the observing sensor, while keeping the computation cost to a
minimum. The recognition process matches an observation of the target object with the
objects stored in a database and computes the belief states of all the objects. Due to
47
noise, ambiguity and occlusions the recognition process does not always lead to certain
matchings, which in turn results in multiple likely object candidates. To this end, our
process seeks to select a minimal sequence of actions which reduces the computation time
but simultaneously maximizes the acquired information about the target object. In other
words, the actions are chosen in such a way as to reduce the uncertainty in the current
belief state estimates for the object candidates.
4.1.1 System Overview
The general system diagram of our active recognition framework is presented in Fig. 4.1.
It consists of the four modules: object observation, feature selection, recognition state
estimation, and viewpoint selection.
In each time step t, we select a next action from the set of feasible actions, which are:
1) stopping the recognition process, 2) staying at the current viewpoint and computing
a next feature f
t+1
(feature selection), or 3) moving the sensor to a new viewpoint by
applying the motion action a
t
(viewpoint selection). Concretely, the action a
t
denes the
relative motion of the sensor to move from the current observation position to the new
observation position. We only allow sensor motions to a restricted set of next observation
positions. The discretization of the viewpoints reduces the complexity in computation
when compared to a continuous representation of viewpoints. When computing a new
feature f
t+1
at the current viewpoint, we set a
t
=∅, dening a zero motion action.
During object observation, the sensor captures the raw data, such as color images and
3D point clouds, which is used to compute the features. The sensor measurements at a
new viewpoint are parametrized by the feature vector
⃗
f = [f
1
;:::;f
N
], which includes
N dierent feature types. Given that the n
th
feature in
⃗
f has been selected at time t,
we extract feature f
t
=f
n
from the measurement data. The observation uncertainty is
captured in our observation model, dened as the conditional probability density function
p(f
t
So
t
), with recognition state o
t
= {c
t
;
t
}. Here, the feature f
t
is conditioned on the
object class c
t
and orientation angle
t
of the observed object. In the recognition state
estimation, we use a Bayesian framework to infer about the current c
t
and
t
from the
measurements. The parameters are assumed to be obtained from a physical object model
and to be trained oine.
At each observation position, we start o with extracting one rst feature from our
total feature set specied by vector
⃗
f. We then have the choice of local exploitation,
i.e., extracting another feature, or global exploration, i.e., moving the sensor to a new
observation position. The premise is to extract as much information as possible at the
current viewpoint since a motion action is inherently more costly. Only after having
exploited all the features that yield useful information, we want to move to a new location.
However, as moving the sensor physically is costly, nally, we move to the next viewpoint
only if the gain of information (in expectation) signicantly reduces the uncertainty in
the object belief states. Put in other words, a next motion action is applied only if the
recognition accuracy is expected to improve by a signicant amount.
48
Object
Observation
p(f
t
So
t
)
Feature
Selection
HMM:
Recognition State
Estimation
p(o
t
So
t−1
;a
t−1
)
Viewpoint
Selection
action a
t
action a
t
=∅
Figure 4.1: System overview of the active multi-view object recognition framework. After
each observation, the HMM updates the recognition state, upon which a new feature (inner
loop) or a new viewpoint (outer loop) is selected. The feature type that is selected rst
at any new location is pre-dened. The iterative processes terminate when the stopping
criteria are met.
Before we extract and add a new feature, we compute the utility of all remaining
features in our arsenal and select the one with the highest utility. We only allow to add
one feature at a time, and once a feature is added it cannot be removed from the set
anymore. This way, integrating a new feature simply becomes a sequential update step
without the need for re-computing the posterior of the entire feature set. We continue
until either a stopping criterion has been reached or all N features are observed at a given
viewpoint, forcing us to either terminate or move to a new viewpoint. The overall idea
is that, at each viewpoint, we have only extracted useful features and left out features
that yield no additional information. Moreover, not extracting a feature saves time, which
helps to reduce the total time needed to recognize the object.
4.1.2 Sequential Bayesian Recognition
With every new observation of a feature f
t+1
, we want to eciently integrate the new
observation with results from prior observations, and thus update our current belief about
the object class and orientation. We formulate the recognition and pose estimation over
the object classes and object poses as a Bayesian network in form of a Hidden Markov
Model (HMM). A Bayesian formulation has distinct advantages, with the main advantage
being that Bayesian methods model all sources of uncertainty in form of random variables.
Furthermore, HMMs have ecient formulations to sequentially update the poste rior
distribution, making it ideal for integrating new observations, such as in our case in the
form of a new feature f
t+1
. Compared to a naive Bayes update, which is often used in
existing work (Denzler & Brown, 2002; Paletta & Pinz, 2000; Laporte & Arbel, 2006;
Borotschnig et al., 1998), the HMM formulation additionally gives us the possibility to
explicitly formulate the state transitions.
49
a
1
o
1
f
1
o
2
f
2
a
2
o
3
f
3
⋯
⋯
⋯
a
t
o
t
f
t
Figure 4.2: HMM for sequential Bayesian recognition. Given a sequence of observed
features f
1∶t
and executed actions a
1∶t
, we reason about the hidden recognition state of an
object at time t, o
t
= {c
t
;
t
}, including its object class c
t
=c
k
and object pose
t
=
q
.
The joint probability distribution of the HMM, as shown in Fig. 4.2, is dened as
P(o
1∶T
;f
1∶T
;a
1∶T
) = P(o
1∶T
)P(a
1∶T
So
1∶T
)P(f
1∶T
So
1∶T
;a
1∶T
)
= P(o
1
)
T
M
t=2
P(o
t
So
t−1
;a
t−1
)
T
M
t=1
P(f
t
So
t
) ;
(4.1)
and the corresponding log probability, log(P(o
1∶T
;f
1∶T
;a
1∶T
)), equals
log(P(o
1
))+
T
Q
t=2
log(P(o
t
So
t−1
;a
t−1
))+
T
Q
t=1
log(P(f
t
So
t
)): (4.2)
The observation sequence is S = {o
1
;:::;o
t
;a
1
;:::;a
t
}, the hidden state of our HMM is
dened as recognition state o
t
with o
1∶T
= {o
1
;:::;o
t
;:::;o
T
}, the observations are given
as observed features f
t
with f
1∶T
= {f
1
;:::;f
t
;:::;f
T
} and the motion actions between
viewpoints are given as a
t
with a
1∶T
= {a
1
;:::;a
t
;
:::;a
T
}. The state of the hidden process satises the Markov property, that is, given the
value of o
t−1
, the current state o
t
is independent of all the states prior to t− 1.
The observation model p(f
t
So
t
) represents the likelihood that featuref
t
is generated by
recognition state o
t
. The transition probability is dened as P(o
t
So
t−1
;a
t−1
), which means
that the transition to the next recognition state is dependent on the previous recognition
state (i.e., the previous object class and orientation) as well as the latest motion action that
has been applied. The posterior marginals P(o
t
Sf
1∶T
;a
1∶T
) of all hidden state variables,
given a sequence of observations, can be eciently computed using the forward-backward
50
algorithm. The algorithm computes a smoothed estimate given all evidence in two passes,
with the rst pass going forward in time and the second pass going backwards in time:
P(o
t
Sf
1∶T
;a
1∶T
) = P(o
t
Sf
1∶t
;f
t+1∶T
;a
1∶t
;a
t+1∶T
)
∝ P(f
t+1∶T
;a
t+1∶T
So
t
) P(o
t
Sf
1∶t
;a
1∶t
):
(4.3)
In the rst pass, we compute the forward probabilities, which are the probabilities for all
t∈ {1;:::;T} ending up in any particular state given the rstt observations in the sequence
P(o
t
Sf
1∶t
;a
1∶t
). In the second step, we compute the probabilities P(f
t+1∶T
;a
t+1∶T
So
t
) of
making the remaining observations given any starting point t.
The recursion of the forward-backward algorithm can be broken up into a forward and
backward part. The forward recursion is dened as:
(o
T
) ≡ P(f
1∶T
;o
1∶T
;a
1∶T
); and
(o
T
) = P(f
T
So
T
)
T
Q
t=2
(o
t−1
)P(o
t
So
t−1
;a
t−1
):
(4.4)
(o
T
) is the joint probability of observing f
1∶T
and being in state o
T
. We can similarly
formulate the recursive backward part:
(o
T
) ≡ P(f
T+1∶1
;o
T+1∶1
;a
T+1∶1
); and
(o
T
) =
T
Q
t=1
(o
t+1
)P(f
t+1
So
t+1
)P(o
t+1
So
t
;a
t
):
(4.5)
(o
T
) is the conditional probability of future observations f
T∶1
, under the assumption of
being in state o
T
. The posterior probability can then be obtained from
P(o
t
Sf
1∶T
;a
1∶T
) =
T
Q
t=1
(o
t
) (o
t
): (4.6)
Before we can make use of the forward-backward algorithm in practice, there is another
important issue to be addressed. In the recursion of the forward and backward parts, we
note that at each step the new value is obtained from the previous value by multiplication.
These probabilities are often far less than unity and the values can go to zero exponentially
fast. There are two approaches to deal with this numerical problem. One option is to use
re-scaled versions of(o
t
) and(o
t
) whose values remain close to unity. However, since our
observation probability is in log-space, log(P(f
t
So
t
)), this is impractical and oftentimes not
even possible. The second option is to work in log-space as well and evaluate the likelihood
functions by taking the logarithms. However, because of \log(∑(x)) ≠∑(log(x))", we
51
cannot easily do that. Instead, we must use the \log-sum-exp" trick, which eventually
leads to the recursive formulation of (o
t
) and (o
t
) in log-space:
log((o
T
))= log(P(f
T
So
T
)) log
T
Q
t=2
exp(log((o
t−1
))
+ log(P(o
t
So
t−1
;a
t−1
)));
log((o
T
))= log
T
Q
t=1
exp log((o
t+1
))
+ log(P(f
t+1
So
t+1
))+ log(P(o
t+1
So
t
;a
t
)):
(4.7)
The posterior probability is then given in log-space as
log(p(o
t
Sf
1∶T
;a
1∶T−1
)=
T
Q
t=1
log((o
t
))+ log((o
t
)): (4.8)
4.1.3 Observation Model
For recognition, we learn a function g∶R
S
⃗
fS
→N that maps the extracted object features
⃗
f to a unique object identier i∈ {1;:::;KQ}, each pointing to a distinct object model
o
i
= {c
k
;
q
}, withk ∈ {1;:::;K} andq ∈ {1;:::;Q}. K denotes the total number of object
classes c
k
and Q denes the number of discretized object poses
l
per object class. The
function is learned in a supervised fashion, with all possible features
⃗
f = [f
1
;:::;f
N
] and
the unique identier i available as the value pair (
⃗
f;i) at model training phase. While we
assume that all features of an object are observed at training phase, we do not make this
assumption during prediction, where not all components of
⃗
f are observed due to feature
selection.
To deal with the missing data problem at prediction time, we use a Gaussian generative
model of the form
log(P(fSo
i
))=
M
Q
m=1
log(N(fS
o
i
;m
;
o
i
;m
)): (4.9)
M is the number of independent normal distributions to model a featuref. Each featuref
is represented as a feature histogram with M bins, and the mean
o
i
;m
and variance
o
i
;m
for each bin m are computed over the training data of an object with recognition state
o
i
. We use M independent normal distributions since a multivariate normal distribution,
with full covariance matrix, would become high-dimensional for high-dimensional features.
High-dimensional models are in general poorly separable as is well understood under the
curse of dimensionality. Dening the problem as an independent Gaussian generative
classier has the advantage of handling missing features by marginalizing them out at
prediction time, i.e., instead of inferring about the missing features, we simply perform
52
inference on a subset of the full feature vector
⃗
f. We can now compute the log-likelihood
log(p(
⃗
fSo
i
)) of generating the model o
i
from feature vector f as
log(p(
⃗
fSo
i
; ))=
N
Q
n=1

n
M
Q
m=1
log(N(f
n
S
o
i
;m
;
o
i
;m
)); (4.10)
with
n
denoting a scaling factor to scale the dierent feature distributions. The feature
distribution in (5.14) allows us to integrate out the marginals very easily. In practice,
marginalization of a feature is simply done by setting the scaling factor to zero for all
the features we do not want to include in the inference. With that, the log-likelihood
log(P(
⃗
fSo
i
;
⃗
)) is only computed over a subset of all possible features, making it indepen-
dent of the dimensionality of
⃗
f during training. Furthermore, the Gaussian representation
of the features is compact and fast to train, since it only requires the computation of the
Gaussian feature parameters
o
i
;m
and
o
i
;m
. Additionally, sequential learning as well as
sequential updates of mean and variance are possible, which has the potential of adaptively
adding new observations to our trained features.
Learning multiple models per object class has two distinct advantages. For one,
inferring about an observation taken from a target object will not only yield the most
probable object class, but also the most probable pose of the object. Second, the model
trained for each object has a smaller variance if trained only for a partial view of the
object. This becomes intuitively clear since an object looks in general very dierent for
dierent viewing directions. And this again is re
ected in the variance of the model.
4.1.4 HMM State Transitions
We dene the state transition probability p(o
t
So
t−1
;a
t−1
) as the probability of a transition
from recognition stateo
t−1
to stateo
t
given an actiona
t−1
(see Fig. 3.2). This means, how
likely is the transition, if at time t− 1 we believe to be in recognition state o
t−1
= {c
k
;
q
}
(i.e., a believed target object with object class c
k
and orientation
q
), then perform the
motion action a
t−1
and acquire a new observation and feature f
t
, and nally believe to be
in state o
t
= {c
k
;
q
} at time t.
In order to determine the state transition probabilities, one uses the Baum-Welch
algorithm, which uses expectation maximization to nd the maximum likelihood estimate
of the state transition parameters given a set of observed data. Commonly, training of
such parameters is done in batch, meaning that all data needs to be available upfront.
This, however, prohibits a sequential update with new data. Sequential update methods
have been developed, but come with their own challenges, such as avoiding to get stuck in
local minima, nding stopping criteria to reduce overtting, or not corrupting existing
knowledge. We will leave the learning of the transition probabilities for future work and
use a custom-dened state transition matrix for now.
53
4.2 Action Selection
When studying object recognition, uncertainty in the state estimation generally leads to
an increase in variance, whereas ambiguity in feature space increases the number of modes
of the belief state. Consequently, to improve the recognition accuracy, we want both to
reduce the variance and to reduce the number of modes toward a unimodal belief state.
The root cause for multimodal belief states is the closeness of sensor data and the training
models in feature space. As a direct result, the sensor data is likely to match with multiple
object hypotheses, and hence a denitive object class cannot be found. In other words,
certain viewing choices or combinations of features may be well explained by more than
just one hypothesis.
In order to reduce uncertainty and ambiguity, we need to select actions and reason
about new information in the form of newly computed features. However, not every
feature or observation position, respectively, reduces the uncertainty in belief state to the
same extent (and some even result in no reduction at all). Intuitively, we only want to
incorporate new features that provide new information and move to new viewpoints that
reduce the ambiguity by oering views of objects that are inherently dierent from views
of objects from other object classes.
In summary, we aim at nding the sequence of actions which maximally reduces the
uncertainty about our current object belief state. The action sequence should be minimal,
depending on the belief state, since every action involves a cost. Finding the sequence
of actions that will reduce the uncertainty is nontrivial because we need to quantify all
feasible actions. Letw ∈
be an action and
be the set of all feasible actions. To quantify
each action w, we use the utility functionU ∶
→R to dene the utility score of action w
at time t as s
t
(w)=U(w). The best next action w
∗
, which reduces the uncertainty of the
belief state the most, is then computed as the action with the maximum utility score
w
∗
= argmax
w∈

s
t
(w): (4.11)
Compared to global viewpoint exploration, the local exploitation of a viewpoint through
local feature exploration has much lower associated cost. For that reason, we do not
want to optimize over the entire action set consisting of extractable features and motion
actions, given by the tuple (f;a), at once. Instead, we sequentially optimize|rst over

f
, the discrete set of actions that are expressed as the features available in
⃗
f, followed
by optimizing over the discrete set of all feasible motion actions

a
.
Regarding feature selection, the action of staying at the same viewpoint and computing a
next featuref
t+1
is obtained from (4.11) withw ≡ (f;a) asf
t+1
=f
∗
= argmax
f∈

f
s
t
(f;a).
Here, the motion action is xed, and in our case assumed to be the zero motion action
a = ∅, i.e., w = (f;∅). In contrast, for viewpoint selection, the motion action to reach
a new viewpoint is obtained after (4.11) by letting w ≡ (f;a) and solving for a
t
=a
∗
=
argmax
a∈
a
s
t
(f;a), without yet selecting a specicf. A rst new feature is then extracted
at the new viewpoint. In addition, a third available action is to end the recognition process,
54
which applies whenever the stopping criteria (Subsection 4.2.4, and further specied
throughout Sections 4.3 and Section 4.4) become true.
Our Bayesian inference framework leads naturally to an iterative information-theoretic
approach for deciding on the next best action w
∗
. Information-theoretic formulations
allow us to quantify actions in terms of information gain and uncertainty reduction,
given our current belief state. Several methods from information theory have been
shown to work well in action selection tasks. The more popular methods include ex-
pected loss of entropy (LE) (Paletta & Pinz, 2000; Borotschnig et al., 1998), mutual
information (MI) (Atanasov et al., 2014; Denzler & Brown, 2002) and Kullback-Leibler
divergence (KL) (Laporte & Arbel, 2006).
First we will formulate all three methods in a general way adapted to our action
selection framework, followed by the specic formulations for feature selection and viewpoint
selection.
4.2.1 Expected Loss of Entropy
LE, on average, measures the expected reduction in uncertainty of our belief state. More
concretely, it measures the dierence in uncertainty between our current posterior belief
P(o
t
Sf
1∶t
;a
1∶t−1
) and the predicted posterior belief P(o
t
Sf
1∶t
;a
1∶t−1
;w), if we were to take
an action w.
The entropy H quanties the uncertainty of a random variable. We are interested in
computing the entropy of the posterior distribution P(o
t
Sf
1∶t
;a
1∶t−1
) because it expresses a
measure of uncertainty (respectively certainty) about our belief. The entropy is zero if the
outcome of the experiment is unambiguous and it reaches its maximum if all outcomes of
the experiment are equally likely. This means, if the uncertainty is high, multiple models
are likely to explain the data. Finally, the entropy over the object classes is given by
H(o
t
Sf
1∶t
;a
1∶t−1
)=−
KQ
Q
i=1
P(o
i
Sf
1∶t
;a
1∶t−1
) logP(o
i
Sf
1∶t
;a
1∶t−1
): (4.12)
Given the denition of the entropy, we can now dene the utility score s
t
(w) for an
action w based on LE as
s
t
(w) =
KQ
Q
i=1
P(o
i
Sf
1∶t
;a
1∶t−1
) E[H(o
i
;f
1∶t
;a
1∶t−1
;w)]; (4.13)
with KQ object models in the model set. LE is expressed as the expected dierence in
entropy E[H(⋅)]; it represents our expectation on the dierence in uncertainty between
the current and predicted posterior distribution. This expected dierence is weighted by
our current belief P(o
i
Sf
1∶t
;a
1∶t−1
), such that the utility score re
ects the reductions in
likely object beliefs. Moreover, we must compute the average LE because we cannot be
certain about our belief state|hence we average over all beliefs.
55
The expected dierence in entropy for possible actionsw ≡ (f;a) is eventually computed
as
E[H(o
i
;f
1∶t
;a
1∶t−1
;w)] = H(o
t
Sf
1∶t
;a
1∶t−1
)
−
S
p(fSo
i
;a)H(o
t
Sf
1∶t
;a
1∶t−1
;w)df:
(4.14)
As we do not know which feature to expect, we need to integrate over the entire feature
space. The feature distribution p(fSo
i
;a) is given by the observation model. Since (4.14)
is not possible to compute in closed form, we approximate by sampling from the feature
distribution, and obtain
E[H(o
i
;f
1∶t
;a
1∶t−1
;w)] ≈ H(o
t
Sf
1∶t
;a
1∶t−1
) −

QH(o
t
Sf
1∶t
;a
1∶t−1
;w); (4.15)
where is the number of samples drawn from the feature distribution P(fSo
i
;a). We can
approximate (4.15) further by sampling with zero variance, which yields the mean
o
i of
our trained object model o
i
, and with that, a mean feature f

o
i
. We eventually write
E[H(o
i
;f
1∶t
;a
1∶t−1
;w)] ≈ H(o
t
Sf
1∶t
;a
1∶t−1
)
− P(f

o
i
So
i
;a)H(o
t
Sf
1∶t
;f

o
i
;a
1∶t−1
;a):
(4.16)
The evaluation of s
t
(w) is quite costly to compute since it involves a prediction step.
With each w ∈
we want to evaluate we need to compute the sequential update of
the posterior distribution given the predicted observation. Even with the mean feature
approximation of (4.16), this still involves the computation of KQ predictive posteriors.
Restricting attention to only the most probable o
i
object hypothesis can further reduce
the computational cost.
4.2.2 Mutual Information
In contrast to LE, which uses the predictive posterior distribution, MI relies on the
conditional entropy to select the next action. We do not need to compute the update of
the posterior distribution, which makes the evaluation cheaper and thus much faster.
The utility score is computed from the averaged MI as s
t
(w) =I(o
t
;fSa), with w ≡
(f;a), by
I(o
t
;fSa) =
KQ
Q
i=1
P(o
i
Sf
1∶t
;a
1∶t−1
)
S
p(fSo
i
;a) log
p(fSo
i
;a)
∑
KQ
j=1
p(fSo
j
;a)
df: (4.17)
Since this quantity again is not possible to compute in closed form, we approximate (4.17)
with the mean feature f

o
i
as well, which results in
s
t
(w) ≈
KQ
Q
i=1
P(o
i
Sf
1∶t
;a
1∶t−1
) P(f

o
i
So
i
;a) log
P(f

o
i
So
i
;a)
∑
KQ
j=1
P(f

o
i
So
j
;a)
: (4.18)
56
Generally speaking, the mutual information can be understood as the extent the
uncertainty about variable o
t
is reduced, when, given an action a, an observation f has
been made.
4.2.3 Jerey's Divergence
Reducing the ambiguity between object classes is equivalent to nding viewing positions
which are inherently dierent. To this end, we can choose new viewing positions by
selecting viewpoints such that, regardless of the true object and pose under observation,
the most likely distributions of the resulting measurements are predictably dissimilar.
Therefore, a new viewpoint must be selected in such a way that competing hypotheses
will appear as dierent as possible, i.e., that a maximum dissimilarity is measured by the
features.
A measure of dissimilarity or \distance" between observations is the relative entropy
or Kullback-Leiber divergence. The KL-divergence presents the amount of information
lost if samples from the distribution P
1
are assumed to be samples from P
2
. The K-L
divergence is dened as follows:
KL(P
1
∥P
2
) =
S
∞
−∞
p
1
(x) log
p
1
(x)
p
2
(x)
dx: (4.19)
However, KL(P
1
∥P
2
) is not a true distance function since it is not symmetric and
does not obey the triangle inequality. We can formulate a symmetric version based on
the K-L divergence, also known as Jerey's Divergence (JD), J(P
1
∥ P
2
) = KL(P
1
∥
P
2
) + KL(P
1
∥P
2
) .
The evaluation of the Jerey's divergence is a potential computational bottleneck.
In our case, the observation probability P(fSo
i
;a) is dened as a continuous probability
density function and would require to evaluate an integral, which is not possible in closed
form. Instead, we approximate the integral once more using the mean features. We
evaluate the best action by computing the utility score
s
t
(w) ≈
KQ
Q
i=1
KQ
Q
j=1
P(o
i
Sf
1∶t
;a
1∶t−1
) P(o
j
Sf
1∶t
;a
1∶t−1
)
⋅ J(P(f

o
i
So
i
;a)∥P(f

o
i
So
j
;a)):
(4.20)
4.2.4 Convergence and Stopping Criterion
The sequential update allows to continuously acquire new information and with that
reduce the uncertainty of the belief state. Unfortunately, one cannot guarantee that the
sequential decision process reduces the uncertainty in every single step. But, on average,
by utilizing the information-theoretic action selection, the uncertainty will be reduced.
For information-theoretic methods, it is important to nd adequate stopping criteria.
In the case of feature selection, we need a stopping criterion that denes when to stop
57
adding new features observed from the current viewpoint and instead rather move to a
next viewpoint. Similarly, with respect to viewpoint selection, we need a stopping criterion
that determines when to terminate the object recognition process and return the inference
result made so far. Unfortunately, the results of an information-theoretic action selection
method highly depend on the stopping criteria as well as the parameters controlling those
criteria. Wrong choices can lead to sub-optimal performance, with all possible actions
being processed in the worst case.
4.3 Feature Selection
Modern sensors produce vast amounts of data, which enables the computation of costly
and very high-dimensional features. Each feature in our total feature set is of value, since
certain objects are better explained by some features than others. This means, on average,
the total feature set increases the classication accuracy. But, seldom all the features are
needed to correctly classify an object because many features are correlated. Features can
be highly correlated across object classes, i.e., features can be very close to each other in
feature space. The result is that, if such features are combined, they do not really decrease
the uncertainty of our belief state.
Feature selection is a way to reduce the amount of features we need to compute during
classication. Consequently, feature selection can help to decrease the computation cost
of extracting features from raw data. This means, we want to extract as few features
as possible, but at the same time, we want to extract those features that reduce the
uncertainty of our belief state the most. Preferably, selected features will result in a
unimodal distribution.
Feature selection can be performed at training time or at prediction time. At training
time, the feature space is reduced in advance by selecting relevant features, such that the
loss of signicant information is minimal. At prediction time, features are selected and
computed online. In this work, we train our classier with all available features, while
during prediction time, we only select and infer over features that yield new information.
Online feature selection increases the
exibility of the classier. It keeps complexity low
during training and facilitates updates by adding new features without the need to re-train
the entire training set.
Feature selection becomes especially important on robot platforms with minimal
computation power and short operation time (e.g., quadcopter robots), since it allows us
to only compute relevant features. In the following subsections, we describe two methods
for feature selection, one using LE and one using MI.
4.3.1 Feature Selection by Expected Loss of Entropy
In feature selection, we are interested in nding the next best featuref
t+1
=f
∗
. For feature
selection by LE, this means that LE expresses the dierence in uncertainty between the
current belief state and the updated belief state after adding one additional feature f.
58
During the selection process, we do not move the robot, so we set the motion action to the
zero motion action,a=∅. To select the next feature, we use the mean feature formulation.
The action w now simply consists of selecting one mean feature f

o
i
we want to evaluate.
f

o
i
is selected from the full mean feature vector
⃗
f

o
i
by marginalization. Since the feature
selection step does not depend on the motion action a, we can neglect the term in the
predictive posterior distribution. Finally, LE for feature selection is derived from (4.13) as
s
t
(w) ≈
KQ
Q
i=1
P(o
i
Sf
1∶t
;a
1∶t−1
) E[H(o
i
;f
1∶t
;f

o
i
;a
1∶t−1
)]; with (4.21)
E[H(o
i
;f
1∶t
;f

o
i
;a
1∶t−1
)] = H(o
t
Sf
1∶t
;a
1∶t−1
)
− P(f

o
i
So
i
)H(o
t
Sf
1∶t
;f

o
i
;a
1∶t−1
):
(4.22)
Stopping Criterion
For feature selection by LE, we stop integrating more features when the expected loss
of entropy for the selected feature is small, i.e., max(s
t
(w))<
1
, where
1
is a constant
positive threshold parameter.
4.3.2 Feature Selection by Mutual Information
Similar to LE for feature selection, the feature selection by MI does not depend on the
robot motion action either. Thus, using (4.18) and the mean feature formulation, we can
compute the utility score as
s
t
(w) ≈
KQ
Q
i=1
P(o
i
Sf
1∶t
;a
1∶t−1
) P(f

o
i
So
i
) log
P(f

o
i
So
i
)
∑
KQ
j=1
P(f

o
i
So
j
)
: (4.23)
Stopping Criterion:
We stop to select a new feature from the current location as soon as s
t
(w) has decreased
compared to the previous value (Verleysen & Rossi, 2009).
4.4 Viewpoint Selection
The goal in view planning is to evaluate and select new viewpoints that yield novel and
useful information about the object. Initially, we have not observed anything. So every
observation has equal usefulness under the assumption that we do not have any prior
knowledge and a uniform belief state. However, every subsequent observation from a
dierent viewpoint bears additional information that may help to identify the object
correctly. The challenge is to evaluate potential new viewpoints which gain us new
information, but also viewpoints that help us reduce the uncertainty of our belief state.
59
We want to nd new viewpoints that reduce the ambiguity and with that reduce the modes
of our belief state. In the following subsections, we formulate three methods for viewpoint
selection based on three dierent information-theoretic measures, namely LE, MI and the
KL-based Jerey's divergence.
4.4.1 Viewpoint Selection by Expected Loss of Entropy
Compared to the LE formulation for feature selection, we now want to move the sensor to
a new observation position, thus we need to incorporate the motion action a. In addition,
we must dene what feature to use. We again rely on the mean features f

o
i
. However, in
contrast to the case of feature selection above, we now use the full mean feature vector
⃗
f

o
i
instead of only the marginals. As the full set of features performs overall on average
the best, it makes sense to employ the full vector including all mean features. Since we
can sample the mean features from our training models, there is no overhead in feature
computation, as there would be for making an actual observation. For viewpoint selection,
we thus dene the action as the tuple w ≡ (
⃗
f

o
i
;a). Again, we do not get around to
compute a complete update of the posterior distribution|this time also including the
transition of the sensor from the currently believed state to a new state by performing
motion action a
t
=a
∗
. Based on (4.13), we can now write
s
t
(w) ≈
KQ
Q
i=1
P(o
i
Sf
1∶t
;a
1∶t−1
) E[H(o
i
;f
1∶t
;
⃗
f

o
i
;a
1∶t−1
;a)]; with (4.24)
E[H(o
i
;f
1∶t
;
⃗
f

o
i
;a
1∶t−1
;a)] = H(o
t
Sf
1∶t
;a
1∶t−1
)
− P(
⃗
f

o
i
So
i
;a)H(o
t
Sf
1∶t
;
⃗
f

o
i
;a
1∶t−1
;a):
(4.25)
4.4.2 Viewpoint Selection by Mutual Information
As seen for feature selection before, the dierence between MI and LE is that for MI the
second term in (4.25) is the conditional entropy instead of the entropy of the posterior.
From (4.18), we now derive the utility score for viewpoint selection, using MI and the full
mean feature vector
⃗
f

o
i
, as
s
t
(w) ≈
KQ
Q
i=1
P(o
i
Sf
1∶t
;a
1∶t
) P(
⃗
f

o
i
So
i
;a) log
P(
⃗
f

o
i
So
i
;a)
∑
KQ
j=1
P(
⃗
f

o
i
So
j
;a)
: (4.26)
The motion action a is indirectly used; the mean feature vector is generated, given a
recognition state o
t
=o
i
, once the motion action a has been applied.
60
4.4.3 Viewpoint Selection by Jerey's Divergence
Similar to the MI formulation in (4.26) above, we can obtain the utility score s
t
(w) for
the viewpoint selection by JD through the general action selection equation (4.20) from
section 4.2.3, utilizing the full vector of mean features
⃗
f

o
i
:
s
t
(w) ≈
KQ
Q
i=1
KQ
Q
j=1
P(o
i
Sf
1∶t
;a
1∶t−1
) P(o
j
Sf
1∶t
;a
1∶t−1
)
⋅ J(P(
⃗
f

o
i
So
i
;a)∥P(
⃗
f

o
i
So
j
;a)):
(4.27)
4.4.4 Stopping Criterion
The stopping criterion for whether to select a new viewpoint or to terminate the recogni-
tion process depends on the entropy. For all three viewpoint selection methods (Subsec-
tions 4.4.1, 4.4.2 and 4.4.3), we will stop and return the MAP estimate of the posterior
distribution whenever H(P(o
t
Sf
1∶t
;a
1∶t−1
)<
2
.
2
is a second threshold parameter, which
is set to a constant positive value.
4.5 Experiments
In this section, we present the results from extensive evaluations of our framework on
real world data and with a quadcopter robot. All the evaluations are performed on
two dierent sets of features. The rst feature set, simple features, are easy and fast to
compute o-the-shelf features. The second set of features, kernel descriptors, are more
complex, generalize better, but have a higher computation cost associated. The evaluation
over the two dierent feature sets provides an insight into recognition performance and
computational cost, and demonstrates that our system is general and can handle dierent
kinds of feature types.
We report on the performance of individual modules and then demonstrate the per-
formance of the complete system. First, we show the performance of single-view object
recognition when using the full feature set, which serves as the baseline. Our feature selec-
tion framework achieves a reduction in computation time, while the recognition accuracy
remains comparable to the accuracy obtained for the baseline evaluation. Following, we
evaluate the unied feature selection and viewpoint selection approach in a multi-view
object recognition setting. For both feature sets, we give an intuition of the trade-o
between increased recognition accuracy and additional computation cost of the multi-view
approach. In addition, we test our system for its applicability to resource-constrained
platforms through quadcopter experiments as well as demonstrate its usability in related
tasks like object change detection.
61
4.5.1 RGB-D Object Dataset
We evaluated our object recognition and action selection framework on the publicly
available RGB-D object dataset introduced in (Lai et al., 2011). The dataset contains
41 877 data points, of which we use roughly one-third as the test points. The dataset
consists of a color image, a 3D point cloud and the orientation of the object, for a total
of 300 everyday objects. For each object, the data is recorded from directions all around
the object, including the three dierent viewing angles of 30
○
, 45
○
and 60
○
per direction
(see Fig. 3.6 on the left and in the center). The overall dataset is challenging, since the
objects in the dataset can look very similar, especially when they belong to the same object
category. Furthermore, the objects in the dataset exhibit large changes in illumination due
to the dierent viewing angles from which the objects were captured, which may make
classication dicult even across dierent categories.
The feature vector
⃗
f, which is used throughout our framework, is comprised of N
independent dierent features for each feature set. During this evaluation, we will use
two dierent feature sets, one containing simple features, the other one containing the
more complex kernel descriptors. In accordance with (5.14), each component of the
feature vector is expressed as an independent normal distribution. The parameters of the
independent normal distribution are learned during training. One big advantage of this
representation is the possibility of sequential training. This means we can sequentially
update already learned parameters or add a new model without re-training all model
parameters. The scaling factor
n
is chosen empirical and set to fColor, Bbox, SIFT,
VFHg = [1.0, 0.02, 0.2, 0.001] for the simple features. When using the Kernel descriptors
we have set the scaling factor to 1:0 for all dimensions.
In all our experiments, we use the same evaluation procedure as proposed in (Lai et
al., 2011) (Bo, Ren, & Fox, 2012) (Bo et al., 2011). To speedup the training process
we subsample the training set to use every 5th data point. We test our framework on
the task of recognizing the instance of an object. We train our object models from
⃗
f
using data captured from viewpoints at 30
○
and 60
○
in each direction, and test them
against features computed from data that is recorded from viewpoints at 45
○
. Based on
the computed features, we generate Q = 8 dierent object models per object instance,
which clusters the viewing directions horizontally into bins spanning 45
○
. This subdivision
trades computation cost o against performance, and denes the accuracy of the objects'
pose estimates.
All the reported accuracies of our multi-view object recognition results are expressed as
recall and are average values over 10 trials. Regarding the stopping criteria, we terminate
the action selection procedure whenever either the entropy of the posterior distribution
has been reduced to
2
= 0:1 or the MAP estimate of the posterior distribution exceeds
60% in accuracy. For the LE formulation in the feature selection, we set
1
= 0:1. After
termination, we use the MAP estimate of the posterior distribution according to (4.3) to
determine the most likely object.
62
(a) (b)
(c)
Figure 4.3: Experimental setup. (a): Each object is placed on a turntable that rotates
around the z-axis (yaw rotation) of the world coordinate frame. Object data is recorded
from three dierent viewing angles of 30
○
, 45
○
and 60
○
per viewing direction. (b): Viewing
directions denote directions in the x-y plane of the coordinate frame from which the object
can be observed. The plane is subdivided into bins of 45
○
around the object. Observations
of the object from the same bin will lead to similar estimations of the object's pose. (c): In
multi-view object recognition, a sequence of viewpoints can be planned in dierent ways.
The shown path (red) results from the simple heuristic \motion along a star pattern",
which assumes that the viewpoint opposite the current viewing direction yields the most
information and thus is the one to visit next.
63
4.5.2 HMM State Transitions
As mentioned in (4.1.4), for this work, we have design four simple state transitions which
are stored in a look-up table Tab. 4.1. The state transition probabilities are choose with
the following premise. When transitioning from one belief state o
t
to the next belief state
o
t+1
given a motion action a
t
we want to favor a transition that stays in the same object
instance or category and ends up in the correct object orientation. This allows us to
incorporate the knowledge we have of how the robot has traveled when taking a motion
action. Furthermore, we dene transitions were the object belief would change into a
dierent instance or category as not favorable. This achieves a constant changing of the
belief state from one object to another, which occurs often in multimodal belief states.
Learning the transition probabilities could certainly improve the overall performance and
lead to higher recognition accuracies. However, we will leave the learning of the transition
probabilities for future work, and for now use the state transitions dened as in Tab. 4.1.
Transition Probability
Same instance, correct angle 0.4
Same instance, wrong angle 0.3
Wrong category 0.2
Wrong instance 0.1
Table 4.1: HMM state transition look-up table
4.5.3 Simple Features
We designed a set of simple feature that are fast and easy to extract from RGB-D data.
We will show that simple and easy to compute feature can be very powerful in terms of
small computation time and can achieve high recognition accuracy. In total we designed
four dierent features and compute from which we create the feature vector
⃗
f with
N = 4 independent features: object bounding box, color histogram, SIFT (Lowe, 2004)
and viewpoint feature histogram (VFH) (Rusu, Bradski, Thibaux, & Hsu, 2010). Each
feature represents a dierent object property: size, color, scale-invariant image description
and geometry. In accordance with (4.10), each single feature or component of a feature
histogram, respectively, is expressed as independent normal distribution. As we will see,
the color feature is the fastest and most powerful single feature among the four features,
and thus the rst feature we evaluate at each location.
4.5.4 RGB-D Kernel Descriptors
In contrast to our simple features, we also tested our framework on more complex and
state-of-the art RGB-D kernel descriptors (Bo et al., 2011; Bo, Ren, & Fod, 2010). We
use the code the authors provide to compute the kernel descriptors, which the authors
64
since publication of the previous two papers have improved. In total, the kernel descriptors
consist of seven N = 7 features, each of which has the dimensionality of 1000. Fro the
RGB-D data we extract three RGB features, two point cloud features and two depth
features. The features are much more expressive than ours, however this comes with a
price of a higher extraction cost for all features. Additionally, to compute the features,
the entire training set need to be available upfront. As the rst feature for our feature
selection process, we extract the RGB gradient kernel, which has performed the best as
single feature.
4.5.5 Online Feature Selection
As a start, we evaluate the usefulness of online feature selection in a single-view recognition
task. We show that selecting the right subset of features can reduce the computation
cost drastically, while keeping comparable recognition performance. We will show the
performance and computation cost on the two feature sets. We present the evaluation for
the simple features rst, followed by the evaluation using the kernel descriptors.
Simple Features
Each feature has a cost associated for computation; the average computation times of
our features are as follows: 0:01 s for the bounding box, 0:0005 s for the color histogram,
0:025 s for the SIFT features, and 2:0 s for the VFH. Fig. 4.4 shows the average total cost
of computation per object and the recognition accuracy plotted against individual feature
combinations. The color feature seems to have the best single recognition performance and
is the cheapest to compute. The VFH on the other hand does not have a lot of recognition
power as such and is rather expensive. From a cost vs. performance standpoint, the feature
combination fColor, Bbox, SIFTg performs best with an accuracy of 68:91% and a low
average feature computation cost of 0:04 s. However, note that the VFH also has its value
since, if included, it increases the recognition accuracy to 74:59%, as detailed in Tab. 4.2.
Additionally, we can see that using feature selection (MI,LE) reduces the cost drastically
while keeping recognition accuracy similar to using all features.
Tab. 4.2 clearly shows that employing feature selection can reduce the average total
cost of the feature computation considerably (see the third and fourth row of column
\F Cost" in Tab. 4.2). Note that the recognition accuracy keeps similar values as if all the
features were used. Here, we utilize LE and MI for feature selection according to Sec. 4.3.
Among the two dierent feature selection methods, the LE measure seems to select more
features, and more importantly, when compared to MI, is computationally much more
expensive because we need to update the posterior distribution and compute a full update
step.
We compared all results with the results of the original dataset in (Lai et al., 2011)
and (Bo et al., 2011). The rst paper has very comparable results to our HMM framework
and uses similar features to ours. No timing has been provided but the computation cost
is expected to be equal to (or slightly higher than) the cost of our features. The latter
65
Color+Bbox+Sift+VFH
Loss Of Entropy
Mutual Information
Color+Bbox+Sift
Color+Bbox+VFH
Color+Sift+VFH
Color+Sift
Color+Bbox
Color+VFH
Color
Sift Feature
Bbox
VFH Feature
0
20
40
60
80
100
Accuracy (%)
Feature Selection
10
-4
10
-3
10
-2
10
-1
10
0
10
1
Computing cost (s)
Figure 4.4: Simple features|Performance and cost of dierent feature combinations in
single-view object recognition. The recognition accuracies are displayed as red bars (left
side scale, in %). The average cost of computing the feature combinations per object is
shown in log scale as blue bars (right side scale, in seconds).
paper reports much higher recognition accuracies; this is mainly due to a more descriptive
feature which seems to generalize very well (also refer to the following subsection). The
cost for such a feature, however, is a very high computation time. Moreover, the features
used in the two papers are learned in batch, which makes them less
exible compared to
our independent feature learning approach.
RGB-D Kernel Descriptors
Similar to the simple features, we evaluate the performance of our feature selection
framework when used together with the kernel descriptors. In Tab. 4.3, we show the
accuracy and cost for single-view object recognition in combination with feature selection.
The rst row of the table shows the recognition performance of the kernel descriptor with
our Bayesian framework. We can see that compared to the linear SVM classier used
66
Method Accuracy F Cost (s) FS Cost (s) Total (s)
C+B+S 68.91% 0.04 0.00 0.04
C+B+S+V 74.59% 2.04 0.00 2.04
Loss Entropy 73.82% 0.19 1.05 1.24
Mutual Information 73.21% 0.1 0.2 0.3
(Lai et al., 2011) (kSVM) 74.80% - - -
(Bo et al., 2011) (Kernel Descriptor) 91.2% 3.2 0.0 3.2
Table 4.2: Simple Feature | Individual performance for single-view object recognition.
\Loss Entropy" and \Mutual Information" denote the feature selection method, with \F
Cost" being the average cost per object for computing the features and \FS Cost" being
the average cost per object for feature selection.
Method Accuracy F Cost (s) FS Cost (s) Total (s)
Kernel Descriptor 90.3% 3.2 0.00 3.2
Loss Entropy 89.94% 0.88 1.71 2.59
Mutual Information 90.61% 0.83 0.46 1.29
(Bo et al., 2011) (Kernel Descriptor) 91.2% 3.2 0.00 3.2
Table 4.3: Kernel Descriptors | Individual performance for single-view object recognition.
\Loss Entropy" and \Mutual Information" denote the feature selection method, with \F
Cost" being the average cost per object for computing the features and \FS Cost" being
the average cost per object for feature selection.
in (Bo et al., 2011), our accuracies are slightly lower with 90:3% vs. 91:2%, respectively.
Furthermore, we can see that feature selection using the LE formulation, compared to the
MI formulation, is still signicantly slower due to the increased computational overhead.
Both approaches, however, show a signicant reduction in the average computation time of
the features, meaning signicantly less time is spent extracting features, when the feature
selection is used. For the MI formulation, for example, we achieve a reduction from 3:2 s to
0:83 s. The MI formulation arrives at the lowest total cost of 1:29 s for feature computation
and feature selection. This is a reduction of a factor of 2:5 in total computation time.
Even though we substantially reduce the cost, and with that the amount of features to
extract, the recognition accuracy stays comparable to the case where the full feature set is
used. The MI approach achieves 90:61% in accuracy.
Discussion
Overall, we can see that feature selection reduces the set of features to extract|and thus
the computation cost|drastically. The result that the accuracy is comparable, or in
67
some cases even slightly better than when using the full feature set, further validates the
usefulness of our approach.
The feature selection in the case of simple features reduces the cost of feature com-
putation the most. From Fig. 4.4 we see that the VFH feature does not hold a lot of
discriminative information for most of the objects. This is re
ected in the large reduction
in computation time, since most of the times, the VFH feature is not computed, hence the
low average feature computation time of 0:1 seconds.
We have done some further investigation about the behavior and performance of the
VFH features. One major reason for the poor performance regarding this dataset is the
object distribution. Compared to previously tested objects, this dataset contains a lot
of similar objects of the same category. For instance, the dataset contains an ?apple?
category with dierent kinds of apples. Geometrically, the apples in the dataset are all very
similar only distinguishing themselves slightly in size but more in color. During instance
classication, many objects are misclassied which results in a very poor classication
performance. We tested the performance of the VFH features on this dataset with category
classication and the performance is much higher. No doubt the performance of the
VFH features, compared to previous experiments is in
uenced by not using a SVM for
classication.
Similar to the simple features, we can also see a reduction of the average feature
computation time for the more complex kernel descriptors. However, here the reduction is
not as pronounced. More features are useful, but more importantly, there is not one single
feature that has, compared to all the others, a large computation cost, which can be saved.
The average computation cost for computing the next informative feature is higher
for the kernel descriptors. The kernel descriptors are of higher dimensionality in total,
which slightly increases the computation time. In contrast to the simple features, the
total average cost of the kernel descriptors is about a factor of four higher. However, this
increase in computation cost is well justied, since it is accompanied by a large increase of
15% in recognition accuracy.
4.5.6 Multi-View Object Recognition
We now present the performance of our unied approach of feature and viewpoint se-
lection. We evaluate the performance for dierent view planning methods; in total, we
compare ve dierent ways to estimate the next viewpoint: Random, Loss of Entropy,
Mutual Information, Jerey's Divergence as well as with a simple Heuristic. The simple
heuristic serves for comparison with our information-theoretic approaches and is based on
the assumption that viewpoints opposite the current viewing directions yield the most
information. Intuitively, the sensor then moves in a \star pattern" around the target
object to acquire new information from the opposite side, as shown by the path in Fig. 3.6
on the right.
68
Method Accuracy Observations Avg. Bin Error
C+B+S+V (no FS) 84:48% ± 1.4 3.4 ± 0.2 2.41 ± 0.07 (bins) (±67:5
○
)
Random 86:76% ± 0.4 3.2 ± 0.2 2.19 ± 0.02 (bins) (±67:5
○
)
Heuristic (Star) 87:16% ± 0.6 3.1 ± 0.3 2.28 ± 0.02 (bins) (±67:5
○
)
Jerey's Divergence 88:34% ± 0.6 2.7 ± 0.1 1.62 ± 0.01 (bins) (±45:0
○
)
Loss Entropy 89:82% ± 1.3 2.4 ± 0.2 1.54 ± 0.01 (bins) (±45:0
○
)
Mutual Information 91:87% ± 0.7 2.5 ± 0.1 1.48 ± 0.01 (bins) (±45:0
○
)
Table 4.4: Simple Features | Performance of our multi-view object recognition framework.
All but the rst row uses the MI measure in the feature selection method. We show the
average recognition accuracy, the average number of observations and the average bin
error of estimated viewing direction. Each bin represents a range of observation angles
of 45
○
.
simple Features
Although the computation time can be substantially reduced through feature selection, the
achievable recognition accuracies are limited around 75% for single-view object recognition.
The reasons are the relative simplicity of our four feature types and their limitation in
generalizing well for the given RGB-D dataset. However, even with fairly simple features,
we can achieve improved recognition accuracies for both object class and pose by utilizing
an information-theoretic multi-view object recognition approach. In the following tests,
we use the MI measure for feature selection, since it is on par with the LE formulation
regarding recognition performance, but the computational cost (see Tab. 4.2) is signicantly
lower.
Tab. 4.4 shows the performance and Tab. 4.5 summarizes the cost of multi-view object
recognition. The rst row shows that using random viewpoint selection with all features
(i.e., no feature selection) has a very high cost but already increases the recognition
accuracy by about 10%. In the second row, we can see a reduction in computation time
and an increase in accuracy due to MI-based feature selection and random viewpoint
selection. On average, random viewpoint selection terminates after a little more than 3
observations. The simple heuristic performs a little better than random selection, but it
similarly needs on average about 3 observations to achieve a comparable accuracy. The
computation time is also very similar. However, the simple heuristic does not perform as
well as the information-theoretic methods. By using the information-theoretic measures
for viewpoint selection, we nd that LE, MI and JD all perform similarly well|with MI
being the best in terms of recognition accuracy. The lowest computation time is achieved
by using JD because it can compute new viewing positions in almost no time. The MI
formulation is superior to the LE formulation in speed, since it does not need to compute
the predictive posterior.
69
Method F Cost (s) FS Cost (s) VS Cost (s) Total Cost (s)
C+B+S+V (no FS) 7.02 ± 0.42 0.00 0.0 7.02 ± 0.42
Random 0.40 ± 0.04 0.83 ± 0.05 0.0 1.23 ± 0.09
Heuristic (Star) 0.45 ± 0.08 0.79 ± 0.04 0.0 1.24 ± 0.12
Jerey's Divergence 0.30 ± 0.03 0.58 ± 0.02 3.E-4 0.88 ± 0.05
Loss Entropy 0.23 ± 0.04 0.50 ± 0.04 5.4 ± 0.6 6.13 ± 0.68
Mutual Information 0.24 ± 0.03 0.51 ± 0.03 1.1 ± 0.2 1.85 ± 0.26
Table 4.5: Simple Features | Average computation cost per object for our multi-view
object recognition framework. The columns show the average cost for computing the
feature (\F Cost"), average cost for feature selection (\FS Cost") and average cost for
viewpoint selection (\VS Cost").
We further evaluate our multi-view approach for estimating an object's pose. As
previously mentioned, we train each object with a number of dierent object models, in
our case Q = 8 models per object. When observing a feature, we can infer from which
model it has most likely been generated, and by this, further infer about the orientation of
the object. The performance of the object's pose estimation is presented in Tab. 4.4. The
table shows the average bin error of the estimated viewing direction, which is computed
from the dierence between the inferred and the true observation angle. For the rst
row, all the features were computed (i.e., no feature selection) and the viewpoints were
selected at random. All the other experiments use the MI formulation to select the
informative features at each given observation position. On average, using random and
heuristic viewpoint selection approaches, we are > 2 bins o in our pose estimation, which
corresponds to an average pose error of about 67:5
○
. If we apply one of the three more
sophisticated viewpoint selection methods, we yield an average bin error of < 2 bins. This
results in an average pose error of 45
○
. For comparison, the experiments in (Bo et al.,
2012) report an average pose error of 44:8
○
, which is on par with our results.
RGB-D Kernel Descriptors
Similar to the simple features, we evaluate the kernel descriptors with our unied feature
and viewpoint selection framework. Tab. 4.6 and Tab. 4.7 summarize the performance of
accuracy and cost, respectively. From Tab. 4.6, we see that, by using a multi-view approach
with random viewpoint selection but no feature selection, the recognition accuracy, has
increased from 90:61% to 95:01%, with 1:8 observations on average (rst row). Furthermore,
we can see that random and heuristic viewpoint selection perform almost identical, still
the heuristic achieves a slightly higher accuracy but also needs on average slightly more
observations. In contrast, the information-theoretic viewpoint selection methods perform
again better as the simple ones, with the best result achieved by the MI formulation. The
MI formulation achieves a respectable recognition accuracy of 98:14% and on average
70
Method Accuracy Observations Avg. Bin Error
Kernel Descriptors
∗
95:01% ± 0.8 1.9 ± 0.1 1.95 ± 0.06 (bins) (±45:0
○
)
Random 95:16% ± 0.6 1.9 ± 0.3 1.85 ± 0.03 (bins) (±45:0
○
)
Heuristic (Star) 95:83% ± 0.4 2.0 ± 0.1 1.88 ± 0.03 (bins) (±45:0
○
)
Jerey's Divergence 96:32% ± 0.5 1.5 ± 0.2 1.53 ± 0.01 (bins) (±45:0
○
)
Loss Entropy 97:98% ± 1.0 1.4 ± 0.3 1.41 ± 0.01 (bins) (±45:0
○
)
Mutual Information 98:14% ± 0.4 1.4 ± 0.2 1.43 ± 0.02 (bins) (±45:0
○
)
Table 4.6: Kernel Descriptors | Performance of our multi-view object recognition frame-
work. All but the rst row uses the MI measure in the feature selection method. We show
the average recognition accuracy, the average number of observations and the average bin
error of estimated viewing direction. Each bin represents a range of observation angles
of 45
○
.
∗
(No feature selection)
needs about 1:4 observations. Interestingly, the kernel descriptors reach similar results
in terms of pose estimation as the simple features. We think the reason is that objects
still look very similar when moving the observation position within 45
○
, making it hard to
classify a target object as the exact object (i.e., correct object class and orientation angle)
the model was created from.
Additionally, we also evaluated the computation cost of individual methods and
modules, as can be seen in Tab.4.7. Due to its high computation cost, we can see, that the
LE formulation is by far the most costly, making it again a poor choice|especially, when
compared to the other information-theoretic approaches. The MI formulation achieves
the highest accuracy and requires the lowest number of observations, however, the cost is
higher than for the random, heuristic or JD formulation. Overall, the fastest method is
the method that is based on JD; it only requires 2:36 s of computation time.
Discussion
With both feature sets, we can clearly see that having the option of taking additional
observations increases the recognition accuracy. In the case of the simple features, the
increase is over 15%. With about 8%, the kernel features do not experience such a large
gain, however, the single-view recognition rate has here already been relatively high.
Information does not automatically mean useful information|this can especially be
seen when we compare the heuristic with the MI-based viewpoint selection approach.
Adding new information does not necessarily add valuable knowledge to nd the correct
object class. In terms of information content, the heuristic should add the most information,
since we move the sensor to the complete opposite sides. Instead, when positions are
chosen in terms of uncertainty reduction, which also reduces object ambiguity, better
performance can be observed.
71
Method F Cost (s) FS Cost (s) VS Cost (s) Total Cost (s)
Kernel Descriptors
∗
6.11 ± 0.31 0.0 0.0 6.11 ± 0.31
Random 2.51 ± 0.16 0.94 ± 0.10 0.0 3.45 ± 0.26
Heuristic (Star) 2.56 ± 0.11 0.98 ± 0.08 0.0 3.54 ± 0.19
Jerey's Divergence 1.64 ± 0.09 0.69 ± 0.02 0.03 ± 0.05 2.36 ± 0.16
Loss Entropy 1.43 ± 0.1 0.67 ± 0.04 8.1 ± 0.5 10.02±0.54
Mutual Information 1.45 ± 0.13 0.68 ± 0.03 1.9 ± 0.4 4.03 ± 0.56
Table 4.7: Kernel Descriptors | Average computation cost per object for our multi-view
object recognition framework. The columns show the average cost for computing the
feature (\F Cost"), average cost for feature selection (\FS Cost") and average cost for
viewpoint selection (\VS Cost").
∗
(No feature selection)
In comparison to the single-view approach, the computation time is increased due to
computing the next viewpoint|but also due to travel time of the robot. Depending on
the robot platform additional costs may be associated with an action like motion planning
or motion risk. Currently we do not incorporate any extra costs associated with motion,
however we think that could be an interesting future research direction.
For the simple feature, on average, we need to take 1{2 additional views for an improved
accuracy. When using the kernel descriptors instead, it suces to take none or only one
additional observation on average. However, the computation cost for the kernel descriptors
is about 2:7 times higher (when using the JD measure) compared to the simple features.
The JD formulation is by far the fastest, i.e., a factor of about 1:7 times faster compared
to MI in nding a new viewpoint. In contrast, the MI method achieves about 2% better
accuracy and needs on average less observations. Finally, view planning with the MI
formulation seems to pick better observation positions, compared to the JD formulation,
trading o accuracy for speed.
For many robotic applications, for instance manipulation, the estimated object pose
estimates are not precise enough. However, the estimation of the pose within a recognition
framework is of great value, because in a sense we get this information for free. For
State-of-the-art object pose estimation methods to work, a rough initialization of the
object pose is required. The values estimated in this work are well suited as an initial pose
for renement methods like ICP.
4.5.7 Quadcopter Experiments
In order to show the overall performance of our active multi-view object recognition
framework, we have conducted experiments on our custom-built quadcopter platform,
shown in Fig. 4.5.
72
Figure 4.5: Shown is our custom quadcopter platform. The platform is build upon a glass
ber 330mm mini quad frame. In the middle of the frame we have built a superstructure
that houses the sensors (e.g. IMU) and processing unit. As the onboard computer we are
using a Hardkernel Odroid U3, which is a 1.7 GHz Cortex-A9 Quad-core processor with 2
GByte RAM. The onboard computer is used as the
ight control hardware, running the

ight control stack for tasks like attitude estimation, stabilization and waypoint execution.
The custom platform allows for a variable motor and battery size, enabling to trade-o
between
ight-time and payload. In the current conguration, as shown in the picture,
the quadcopter is equipped with an ASUS Xtion RGB-D camera, used for data collection.
In the above described conguration the platform has a
ight-time of about 13 minutes.
To accurately estimate the position of the quadcopter indoors we use a VICON motion
capture system.
73
Figure 4.6: Quadcopter experiment and test setup. The quadcopter robot, equipped with
a RGB-D camera, collects multiple views of a target object (e.g., a cereal box) in an active
object recognition task.
As shown in Fig. 4.6, the quadcopter is equipped with an ASUS Xtion RGB-D camera
for data acquisition and can
y autonomously to a new observation position. Given a target
object, the task is to
y the quadcopter around the object and take as many observations
as necessary to correctly recognize the object. Compared to the simulated experiments
above, where data is captured with an RGB-D camera mounted on a stable tripod,
experiments on a robotic platform are generally more challenging. Specic challenges
regarding object recognition on a fast moving platform include motion blur and constant
changes in illumination.
As we do not have any of the objects used in the RGB-D dataset at hand, we captured
10 new objects and added them to the dataset, which now consists of a total of 310 objects.
We captured the data in the same way as described in (Lai et al., 2011) and chose objects
similar to the ones already contained in the dataset. We trained our models with all 310
objects and the two viewing directions of 30
○
and 60
○
. In the actual experiment, the
quadcopter then
ies around the object at a distance and height that allows for a viewing
angle of 45
○
roughly.
74
Method Accuracy Obsv. Avg. Bin Error Avg. Cost (s)
Single-View
C+B+S+V
∗
82:16% 1 2.1(bins)(±67:5
○
) 2.14
Feature Selection (MI) 87:32% 1 1.9(bins)(±45
○
) 0.19
Multi-View
Mutual Information
∗
96.5% ± 0.5 2.0 ± 0.1 1.6 ± 0.1(bins)(±45
○
) 5.63 ± 0.3
Mutual Information 99.8% ± 0.1 1.6 ± 0.01 1.1 ± 0.1(bins)(±45
○
) 1.48 ± 0.2
Table 4.8: Simple Features | Single-view and multi-view object recognition based on data
from the quadcopter robot. In both cases, results with and without feature selection are
presented. Advantages of online feature selection as well as multi-view object recognition
are revealed by the experiments.
∗
(No feature selection)
In each run of the experiments, the robot starts at a random position with respect to
the target object, from where it acquires the rst observation of the object. From there on,
it selects the following actions as described in Sections 4.2, 4.3 and 4.4|either inferring
about another feature from
⃗
f or
ying to a new viewpoint. We terminate the process
once our stopping criteria are reached. Fig. 4.6 shows an example of the quadcopter robot
taking observations of a cereal box object during one of the experiments.
Simple Features
In Tab. 4.8 we summarizes the experimental results from the quadcopter experiments,
averaged over eight runs with dierent starting locations. We can see that for all experi-
ments, whether conducted with single-view or multi-view object recognition, online feature
selection not only helps to decrease the computation time but also increase the recognition
accuracy. The average pose error is similar to the error in the simulation experiments,
however, the average bin error is smaller, which results in more correctly classied bins in
total.
Multi-view recognition on average only required 1:6 observations, which means that
often we are able to make a condent decision after only one observation. In some instances,
however, by acquiring additional observations, the recognition accuracy could be increased
by more than 10% to totally 99:8%. This, of course, comes at the price of actually moving
the robot to the new viewpoint, which in turn increases the cost of recognizing the object.
Whether the extra cost of moving is justied in practice, nally depends on the robot
platform used, the surrounding environment, as well as the trade-o between desired
recognition accuracy and energy savings. With respect to online feature selection, we can
clearly see that the adaptive selection of features oers huge benets by decreasing the
computation time, which is especially benecial for vehicles with low energy budgets like
quadcopters.
75
Method Accuracy Obsv. Avg. Bin Error Avg. Cost (s)
Single-View
(Bo et al., 2011) (Kernel Descriptor) 94:27% 1 1.5(bins)(±45:0
○
) 3.2
Kernel Descriptor
∗
93:67% 1 1.6(bins)(±45:0
○
) 3.2
Feature Selection (MI) 94:05% 1 1.5(bins)(±45
○
) 1.7
Multi-View
Mutual Information
∗
100.0% 1.3±0.05 1.3±0.03(bins)(±45:0
○
) 9.42 ± 0.5
Mutual Information 100.0% 1.2 ±0.02 0.7±0.2(bins)(±22:5
○
) 3.63 ± 0.3
Table 4.9: Kernel Descriptors | Single-view and multi-view object recognition based
on data from the quadcopter robot. In both cases, results with and without feature
selection are presented. Advantages of online feature selection as well as multi-view object
recognition are revealed by the experiments.
∗
(No feature selection)
Kernel Descriptors
We present results of the quadcopter experiments using the kernel descriptors in Tab. 4.9.
Again, the kernel descriptors generalize much better than the simple features, achieving
a much higher recognition accuracy in single-view object recognition. However, the cost
of recognizing the target object is much higher compared to the simple features. The
MI-based approach for multi-view object recognition achieves 100% recognition accuracy
with on average 1:2 observations needed. It seems that the pose estimation has also
improved by the more complex features, with the best result achieving an average angle
error of 22:5
○
only. Basically, we can see that the recognition result of the single-view
approach is already very good. The multi-view approach can be seen as a complement for
these experiments|often, it only takes one view to recognize the object, at other times,
there is a benet from taking more than one observation.
Discussion
The experiments in this subsection show our multi-view system applied to a quadcopter to
perform information gathering. First of all, the experiments conrm the practicability of
our approach regarding the real application on a robot platform. The accuracy presented
for these experiments will probably not hold in general. Although we added 10 objects to
the database, which we tried to pick, such that they were similar and of the same categories
as the objects already contained in the database, they seem to be dierent enough to show
a rather drastic increase in recognition accuracy. Therefore, the accuracy results need to
be taken with some caution. Nevertheless, what the system does show is the advantages
of a multi-view system in combination with online feature selection. We again achieve an
increase in accuracy when given the chance of taking additional observations. Furthermore,
we see a reduction in computation time thanks to the online feature selection framework.
Given the limited processing capabilities of a quadcopter, these are very promising results.
76
With regard to energy consumption and cost to move, quadcopters are somewhat
special platforms. To be able to hover or
y, the energy a quadcopter consumes is in
general quite high. Compared to other robots which do not consume a lot of battery
power when stationary (e.g., ground or aquatic robots), for quadcopters, moving to a new
position by
ying does not cost that much more energy than staying in place by hovering.
This makes an active multi-view object recognition system, as the one we have presented
in this paper, particularly suitable for quadcopter robots.
4.5.8 Object Change Detection
As a nal application, we now show how to utilize our framework for detecting changes
in the environment. Given a prior map of the environment and an object database, we
want to detect if objects in the environment have been replaced, taken away or changed
their pose. We use our generative object model to express the probability P(o
i
Sf) that
the object has been generated by the feature f. Given an expected object model ^ o
i
(prior
information), we can compute the probability P(u) that the object has changed with
P(u)= 1 − P(^ o
i
Sf). If the probability P(u)>, with ∈ [0; 1], we know that the feature
observed cannot be generated by the model ^ o
i
, hence either object class or object pose
has changed. This can also occur when the feature does not match the model anymore
due to changes in lighting or noise; in either case we need to perform further observations
to arrive at a denitive conclusion about the change. If we are uncertain about the object
after our rst observation, we compute new viewpoints that allow for observations that
are unique in terms of feature space. We acquire new observations, evaluate additional
features and compute new likelihoods of the features given the expected object model ^ o
i
.
In the following, we explore three dierent scenarios, when 1) the object has not
changed, 2) the object has changed completely (i.e., it belongs to a dierent object class),
or 3) the object has changed its orientation only (i.e., it belongs to the same class but its
rotation diers in yaw). All experiments are conducted with threshold = 0:6, meaning
that we need to have a high enough certainty of the object being changed. All experiments
are conducted with feature selection by MI, and then evaluated for the dierent view
planning methods.
No Object Change
No change in object and pose refers to the scenario where the object and pose remain
the same as the reference object given our prior map knowledge. This means, we want to
validate whether the measurement(s) we take of the currently observed object conforms
with the object we expect to see. Knowing which object we expect to see makes the
recognition or validation task somewhat easier since observations need to conform very
strongly with the expected object model. Similarly, when selecting new viewpoints,
the expected feature at a new observation position will be very similar to the actual
measurement. This makes it easier to select new viewpoints, which leads to observations
that are very dissimilar to observations of other likely object candidates.
77
Method Accuracy Observations Avg. Cost (s)
Random 91.19 ± 0.19 2.2 ± 0.18 1.02 ± 0.36
Heuristic (Star) 92.82 ± 0.26 2.1 ± 0.21 0.91 ± 0.49
Jerey's Divergence 96.13 ± 0.62 1.4 ± 0.12 0.54 ± 0.27
Loss Entropy 96.71 ± 0.48 1.3 ± 0.2 3.43 ± 0.49
Mutual Information 98.33 ± 0.53 1.3 ± 0.13 0.83 ± 0.38
Table 4.10: Simple features|Scenario where the object has not changed compared to the
prior knowledge. The table shows the detection accuracy, number of observations needed
as well as the total average computation cost in seconds.
Method Accuracy Observations Avg. Cost (s)
Random 95.92 ± 0.11 1.9 ± 0.12 3.3 ± 0.47
Heuristic (Star) 96.83 ± 0.15 1.8 ± 0.14 3.2 ± 0.51
Jerey's Divergence 99.15 ± 0.17 1.3 ± 0.23 2.15 ± 0.27
Loss Entropy 99.81 ± 0.21 1.2 ± 0.19 9.01 ± 0.26
Mutual Information 99.74 ± 0.24 1.2 ± 0.17 3.8 ± 0.23
Table 4.11: Kernel descriptors|Scenario where the object has not changed compared to
the prior knowledge. The table shows the detection accuracy, number of observations
needed as well as the total average computation cost in seconds.
In Tab. 4.10 and Tab. 4.11, we show the results for the case of no change in the
environment, both for the simple features and the kernel descriptors, respectively. In the
two tables, we can see that both feature sets perform very similar with respect to accuracy
of detecting no change and number of required observations. Both feature representations
achieve on average accuracies of more than 98% and need 1:3 or fewer observations.
However, we can see that the simple features are by far less expensive to compute, with
0:83 seconds for the simple features compared to 3:8 seconds for the kernel descriptors.
The high accuracies show that the task of validating the measurements with respect to the
expected object model is easier compared to the task of pure object recognition without
any prior knowledge.
Object Change
In this scenario, the object and pose have changed compared to the map previously
acquired. The task here is to detect that the target object has indeed changed compared
to the expected object model. Compared to the object recognition results, this task is
more dicult due to the stricter criteria for correct estimation of change. In the object
recognition setting, for correct recognition, we require the MAP estimate to be the correct
78
Method Accuracy Observations Avg. Cost (s)
Random 80.24 ± 0.25 2.4 ± 0.18 0.98 ± 0.37
Heuristic (Star) 81.71 ± 0.28 2.5 ± 0.21 1.12 ± 0.32
Jerey's Divergence 86.25 ± 0.36 1.9 ± 0.12 0.78 ± 0.23
Loss Entropy 89.25 ± 0.27 1.7 ± 0.2 3.03 ± 0.43
Mutual Information 88.95 ± 0.31 1.8 ± 0.13 1.16 ± 0.29
Table 4.12: Simple features|Scenario where both the object and pose have changed
compared to the prior knowledge. The table shows the detection accuracy, number of
observations needed as well as the total average computation cost in seconds.
Method Accuracy Observations Avg. Cost (s)
Random 90.84 ± 0.25 2.2 ± 0.21 3.72 ± 0.53
Heuristic (Star) 89.75 ± 0.28 2.1 ± 0.19 3.61 ± 0.46
Jerey's Divergence 92.68 ± 0.36 1.8 ± 0.26 3.01 ± 0.36
Loss Entropy 94.91 ± 0.27 1.5 ± 0.16 10.97 ± 0.41
Mutual Information 93.17 ± 0.31 1.4 ± 0.21 4.12 ± 0.29
Table 4.13: Kernel descriptors|Scenario where both the object and pose have changed
compared to the prior knowledge. The table shows the detection accuracy, number of
observations needed as well as the total average computation cost in seconds.
object. In contrast, here, to be correctly classied as change, we require the probability
P(u)>. This means, objects that look very similar and are only observed from similar
positions will also have similar likelihoods. The result is that P(u) will in general not be
greater than . Finding new observation positions with object beliefs that are inherently
dierent from other object beliefs is equally dicult as for the object recognition task,
since the prior knowledge does not provide us with any further knowledge about the
current object we observe. And with that, the expected features when moving the sensor
might be dierent from the features actually measured after moving the sensor.
In Tab. 4.12 and Tab. 4.13, we show again results for both feature representations.
We can see that both accuracies are lower compared to the object recognition task in
Section 4.5.6 due to the stricter recognition criteria. On average, we achieve correct
change classication for 88:95% of the objects using the simple features and for 93:17%
of the objects using the kernel descriptors. Again, similar to the object recognition task,
the kernel descriptors seem to be more descriptive, achieving better accuracy, with the
trade-o of a higher cost. The computation cost of the kernel descriptors is by about a
factor of four higher compared to the simple features.
79
Method Accuracy Observations Avg. Cost (s)
Random 87.15 ± 0.31 2.7 ± 0.23 1.31 ± 0.29
Heuristic (Star) 88.68 ± 0.36 2.6 ± 0.16 1.21 ± 0.36
Jerey's Divergence 95.97 ± 0.25 1.7 ± 0.15 0.61 ± 0.19
Loss Entropy 97.75 ± 0.14 1.5 ± 0.11 2.72 ± 0.31
Mutual Information 97.12 ± 0.18 1.6 ± 0.16 0.91 ± 0.21
Table 4.14: Simple features|Scenario where only the object's pose (yaw angle) has
changed. The table shows the detection accuracy, number of observations needed as well
as the total average computation cost in seconds.
Pose Change
In the third scenario only the object pose changes, while keeping the object the same.
In our case, this means the object has rotated around its z-axis (yaw). Given our rough
object pose estimation based on model training for dierent viewing directions, we are
only able to estimate pose changes that exceed the angle discretization. In our case, we
can possibly detect pose changes that are greater than 22:5
○
in yaw angle. A correct
classication is made when the probability P(u)>, indicating the object has changed its
orientation.
Compared to the previous case, where the entire object has changed, a pose change is
again easier to detect, since the expected object corresponds to the object we are observing.
This in turn simplies the task of nding new viewpoints that are dierent in feature
space from other likely candidates. This, of course, is only a problem for objects that look
very similar to other objects (in feature space) contained in the database.
In Tab. 4.14 and Tab. 4.15, we show results for the simple features and kernel descriptors.
We can see that the accuracy results for the two feature representations are fairly similar
with 97:12% for simple features and 98:11% for kernel descriptors, respectively. The kernel
descriptors need on average 0:2 observations less but again have a higher computation
time of about a factor of four.
Quadcopter Experiments
Similar to the quadcopter experiments in Section 4.5.7, we also evaluated the change
detection framework on our quadcopter platform. The experimental setup remains the
same as with the previous quadcopter experiments. However, instead of recognizing a target
object, we are interested in detecting any change of the object given prior information.
This again means, we want to detect whether the object remains unchanged, the complete
object has changed, or only the pose of the object has changed.
The experiments conducted make use of the MI formulation for feature selection as
well as viewpoint selection, with all parameters remaining set as before. In Tab. 4.16,
we show the averaged results for the detection accuracy, number of observations needed
80
Method Accuracy Observations Avg. Cost (s)
Random 93.23 ± 0.44 2.2 ± 0.18 3.92 ± 0.13
Heuristic (Star) 93.98 ± 0.31 2.2 ± 0.20 3.89 ± 0.16
Jerey's Divergence 96.48 ± 0.19 1.6 ± 0.21 3.01 ± 0.21
Loss Entropy 98.42 ± 0.21 1.4 ± 0.16 10.12 ± 0.34
Mutual Information 98.11 ± 0.36 1.4 ± 0.11 4.51 ± 0.27
Table 4.15: Kernel descriptors|Scenario where only the object's pose (yaw angle) has
changed. The table shows the detection accuracy, number of observations needed as well
as the total average computation cost in seconds.
Method Accuracy Observations Avg. Cost (s)
Simple features
No Change 98.3 ± 0.21 1.2 ± 0.19 0.79 ± 0.25
Pose Change 99.4 ± 0.12 1.3 ± 0.22 0.89 ± 0.32
Object Change 92.4 ± 0.15 1.9 ± 0.27 1.63 ± 0.46
Kernel descriptors
No Change 100 1.4 ± 0.13 4.01 ± 0.48
Pose Change 100 1.6 ± 0.11 4.35 ± 0.29
Object Change 98.5 ± 0.15 2.1 ± 0.12 5.46 ± 0.38
Table 4.16: Quadcopter experiments|Feature selection and viewpoint selection are eval-
uated for the three dierent change detection scenarios using MI. The table shows the
detection accuracy, number of observations needed as well as the total average computation
cost in seconds.
and computation cost in seconds, evaluated for the simple features as well as the kernel
descriptors. The quadcopter experiments conrm that detecting a complete change of an
object with certainty is more dicult than detection in the other two cases. Furthermore,
the quadcopter experiments show results comparable with the results of the simulation
experiments evaluated on the two feature sets.
Discussion
The experimental results show that, given some prior information in form of a map, our
framework can also be used to detect change in the environment. In our multi-view
framework, on average, we can detect that no changes have occurred with an accuracy
higher than 98% and a required number of equal or less than 1:4 observations. Detecting
the change of the complete object, meaning the object was exchanged with another one, is
81
clearly a more dicult task. Results show that we can detect such cases with an average
accuracy of 88{93%. Lastly, due to our ability of roughly estimating object orientations,
we can also detect change in the yaw rotation of an object. For this case, we achieved
average accuracies of 97% and more. As of now, our framework can only detect changes of
objects in place, meaning translational changes would need to be detected separately, for
instance by utilizing global position information.
4.6 Conclusion
We have presented an information-theoretic action selection framework for object recogni-
tion (and object change detection) which is capable of sequential training and classication,
view planning as well as online feature selection. The recognition framework has success-
fully been tested in simulation and on a custom-built quadcopter robot equipped with an
RGB-D camera.
Our online feature selection method has been shown to drastically reduce the com-
putation time by computing only informative features used for inference during runtime.
Online feature selection, compared to oine estimation, allows for much greater
exibility
during training as well as execution. It is especially useful for robotic tasks like ours, since
there decisions are made online, which stands in contrast to estimating the best performing
set of features a priori during training phase. Furthermore, our experiments show that
smart view planning, when we are uncertain about our belief state, can help to increase
the recognition accuracy substantially.
Through extensive evaluations of various methods, we have shown the strengths and
weaknesses in cost and accuracy of information-theoretic, heuristic as well as random
strategies for feature and viewpoint selection. In general, one can say that information-
theoretic viewpoint selection outperforms random selection in recognition accuracy, but
increases computation cost. The selection of informative viewpoints is important to
increase the accuracy and, at the same time, keep the number of observations minimal.
In particular, this becomes apparent when using a simple heuristic like \motion along
a star pattern". From an information point of view, moving to the opposite side yields
a lot of new information. However, this information does not necessarily help us in
distinguishing objects from each other in feature space|not every information is equally
useful. Information-theoretic approaches allow for selecting the most informative actions
in a principled way; they increase recognition accuracy and reduce operating cost.
Compared to state-of-the-art single-view object recognition methods, our multi-view
object recognition approach, when used with simple features, achieves comparable results.
Our approach is not primarily meant to replace single-view methods but rather to comple-
ment them. Put in other words, if a condent decision can be made about an object after
only one observation, there will be no need for taking a second view. However, there will
always be objects with inherent ambiguity, and it is in those cases in which the multi-view
approach is brought to bear. Moreover, feature selection is useful regardless of the number
82
of views and the object in question, since it reduces the dimensionality of the feature space
and decreases the overall computation cost.
Our framework can also utilize more complex features, such as the kernel descriptors
from (Bo et al., 2011). Although these features are more expensive to compute, compared
to the simple features, they result in an increase of recognition accuracy. An interesting
trade-o can be seen here, the complex features have more expressiveness whereas the
simple features are more cost-ecient to compute.
83
Chapter 5
Online Trajectory Optimization to Improve
Object Recognition
There is growing interest in using robotic vehicles for inspection, to clear buildings, and
to identify predened targets. Because robots are replaceable, this interest is especially
high when such tasks are dangerous. In order to clear the interior of a building, a robot
must identify its surroundings while also avoiding collisions as it moves as eciently as
possible through the environment. Specically, the robot should traverse the building
while searching for and identifying specic objects, then reporting either their presence or
absence. Assuming an optimal trajectory to
y through the building is computed oine,
this could be computed from building blue print, the challenge would be to alter the initial
trajectory online during
ight so that the vehicle would avoid collisions and increase its
chances of correctly identifying objects.
When the robot's sensors observe an object, dierent positions yield information of
varying content and measurements of varying quality. This means some positions are
much more useful than others in recognizing an object. For instance, if the camera is too
far from the object, the image quality is poor; too close, and only a portion of the object
is captured. Further, occlusions often prevent the sensors from observing the object from
all angles, limiting the distinguishing features that are observable. The initial trajectory
points of a robot's path might be optimal in terms of some cost function but unfavorable
in terms of recognizing new objects in the environment. Consequently, we seek to optimize
the initial trajectory in a way that signicantly improves the robot's ability to acquire
data that are useful in recognizing objects.
In this paper, we formulate an approach for optimizing the trajectory online that
improves the ability to acquire information useful in recognizing objects while the vehicle
approaches its goal location. Formulating the problem as a derivative-free stochastic
optimization allows us to dene arbitrary cost functions and thus improve upon the
initial trajectory. The cost function we have developed alters the initial trajectory during
execution to one that yields data for object recognition that are far superior to those
observation data that would have been obtainable given the initial trajectory.
84
Figure 5.1: Our quadrotor platform taking an observation of a target object we want to
recognize.
We demonstrate our approach both on a quadrotor platform in simulation and on
a real platform Fig. 5.1. The quadrotor is given an initial trajectory that needs to be
followed or altered online such that unknown objects are recognized while keeping the
platform from colliding with it's environment. Our experiments show that our online
optimization method greatly improves the accuracy with which objects are recognized,
but more importantly reduces the posterior class distribution uncertainty greatly. In
addition, we show that the number of observations needed to achieves these results are
lower compared to following the initial trajectory.
Trajectory optimization methods can be found in many dierent robotic applications.
A survey of current optimization techniques can be found in (Rao, 2014). Optimizing
trajectories to
y aggressive maneuvers using a quadcopter is shown in (Richter, Bry, &
Roy, 2013). Trajectory optimization for robotic manipulators is presented in (Kalakrishnan
et al., 2011), (Ratli, Zucker, Bagnell, & Srinivasa, 2009), (Park, Pan, & Manocha, 2012)
and (Hauser & Ng-thow hing, 2010).
Target tracking for unmanned areal vehicles is presented in work by (Dille, 2013),
(Theodorakopoulos, 2009), (Geiger, 2009) and (McEnteggart & Whidborne, 2012). Here,
trajectory optimization is used to keep the target in the image frame and maximizes
85
surveillance time while observing the performance limits of the aircraft and accounting
for external disturbances such as wind or target motion. In (Geiger, 2009) the authors
present a neuronal network approach that removes the need to numerically compute the
objective, constraint derivatives and removes the need for collocation, thus reducing the
nonlinear programming problem size. A non real-time version is proposed in (McEnteggart
& Whidborne, 2012) for a multi-objective trajectory optimization approach that nds
environmentally ecient trajectories for commercial airplanes. The authors frame the
problem as an optimal control problem and solve it by using a stochastic solver that solves
for the states and controls of after the problem is discretized.
Active exploration (Kahn et al., 2015), (Kollar & Roy, 2008), (Charrow et al., 2015)
uses trajectory optimization to gather more information which is unknown beforehand. In
(Kahn et al., 2015) the trajectory of a robotic manipulator is optimized to explore the
objects in the environment and nd feasible grasps handles. Environment exploration and
map building is presented in (Kollar & Roy, 2008) and (Charrow et al., 2015). In (Kollar
& Roy, 2008) a trajectory is optimized and learned that lead to more accurate maps.
In (Charrow et al., 2015) the authors develop a trajectory optimization technique that
maximizes information collected from the environment to more eciently build dense 3D
maps while simultaneously satisfying the robot's motion constraints. The paper propose
a gradient-based trajectory optimization that can rene a trajectory in the continuous
control space using sequential quadratic programming.
As far as we know, there is no direct prior work of optimizing trajectories for object
recognition. Our work is base on the stochastic trajectory optimization method presented
in (Ratli et al., 2009) and (Kalakrishnan et al., 2011). In there, the optimization and it's
cost function is used to nd feasible trajectories for a robotic manipulator. In our work,
we formulate the optimization and cost function as an online optimization to optimize the
trajectory of a quadrotor with the goal of improving the performance of object recognition.
5.1 Trajectory Optimization
Given an initial collision-free trajectory
init
we want to nd an optimized trajectory that
improves recognition performance. In Fig. 5.2 we show a smoothed trajectory optimized
to yield better measurements of the object we want to recognize. To this end, we treat
the trajectory optimization problem as a stochastic optimization problem to search for
a smooth trajectory that minimizes the costs corresponding to collision, constraints and
improvement of classication. Specically, we consider the initial trajectory to be of a
xed duration T , discretized into N waypoints. In other words, the discretized trajectory
is composed of N congurations q
1
;:::;q
N
, where q
i
is a trajectory waypoint at time
i−1
N−1
T. Furthermore, the trajectory is represented as a vector Q∈R
D∗N
and written as
Q = [q
T
1
;q
T
2
;:::;q
T
N
]. During the optimization, we assume that the start q
s
and end q
e
position of the trajectory are xed.
At every waypoint, we update the trajectory along the future path of the vehicle. Since
the vehicle can not observe its environment far into the future and to keep computation
86
time low, we do not optimize over the entire future trajectory every time. Instead, we only
optimize over a xed time or waypoint horizon. Let K =
be the number of waypoints
within a given horizon
. Then the trajectory we are optimizing over is given byq
1
;:::;q
K
with the start point q
s
=q
1
and end point q
e
=q
K
.
Similar to previous work (Kalakrishnan et al., 2011) and (Ratli et al., 2009) we
formulate the optimization problem as following:
min
~
Q
E
K
Q
i=1
J(
~
Q
i
)+
1
2
~
Q
T
R
~
Q; (5.1)
with
~
Q=N(Q; ) is a noisy parameter vector with mean Q and variance . J(⋅) is an
arbitrary state-dependent cost function, which we dene in section 5.2. R is a positive
semi-denite matrix representing the smoothness costs. Here, R is chosen such that
~
Q
T
R
~
Q represents the sum of squared accelerations along the trajectory. Let A be a nite
dierencing matrix
A=
⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
1 0 0 0 0 0
−2 1 0 ::: 0 0 0
1 −2 1 0 0 0
⋮ ⋱ ⋮
0 0 0 1 −2 1
0 0 0 ::: 0 1 −2
0 0 0 0 0 1
⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦
;
when multiplied by the position vector Q produces acceleration

Q =AQ, with

Q repre-
senting the second order derivative of the trajectory.
5.1.1 Stochastic Optimization
In general, solving the optimization in Eq. 5.1 is dicult. Previous work (Ratli et al.,
2009) has shown to solve the optimization using covariant functional gradient descent
techniques. However, gradient descent techniques require the cost function to be smooth
and dierentiable, which is oftentimes dicult in practice. Instead, we follow the proposed
method of (Kalakrishnan et al., 2011) and optimize Eq. 5.1 using a derivative-free stochastic
optimization method. Allowing the optimization of an arbitrary cost functions, for which
derivatives are not available, or are non-dierentiable or non-smooth.
Taking the gradient of the expectation in Eq. 5.1, with respect to Q results in:

^
Q
G
=E∇
~
Q

N
Q
i=1
J(
~
Q
i
) (5.2)
As proposed in (Kalakrishnan et al., 2011) due to limitations of the gradient base
optimization of non-smooth cost functions, we use a gradient of the form
^
Q
G
=
∫
dP.
This gradient is essentially the expectation of the noise in the parameter vector
~
Q, under
87
Figure 5.2: Smoothed optimized trajectory around an object we want to identify.
the probability metric P∝ exp−
1

J(
~
Q), with J(
~
Q) being the trajectory cost. The
stochastic gradient is then dened as follows:

^
Q
G
=
S
exp−
1

J(Q+) d (5.3)
We estimate the gradient in Eq. 5.3 by sampling a nite number of U trajectories:

^
Q
G
=
U
Q
u=1
P(Q+
u
) (5.4)
P(Q+
u
)=
exp(−
1

J(Q+
u
))
∑
U
l=1
exp(−
1

J(Q+
l
))
(5.5)
5.1.2 Trajectory Updates
In each iteration, we want to iteratively update the previously computed trajectory by
generating U noisy sample trajectories. For this, we compute the trajectory cost per
time-stepJ(Q
u
;t) as well as the probability of each trajectory per time-stepP(Q
u
;t). The
trajectories are generated, by sampling the noise from a zero mean normal distribution,
with

=R
−1
and R
−1
= (A
T
A)
−1
. This ensures the exploration of the trajectory space
and simultaneously keep the trajectory cost low.
Computing the probability per time-step requires us to evaluate the exponential term
of Eq. 5.5. Here, is a parameter that regulates the sensitivity of the exponential cost.
e
−
1

J(Qu;t)
=e
−h
J(Q
u;t
)−minJ(Q
u;t
)
maxJ(Q
u;t
)−minJ(Q
u;t
)
; (5.6)
88
with h= 10 set to a constant.
Updating the trajectory Q is done using the probability-weighted convex combinations
of noisy parameters for that specic time-step as shown in Eq. 5.4. However, to ensure
a smooth updated trajectory, we smooth the gradients using a projection onto the basis
vectors of R
−1
. The trajectory update step thus looks as follows: Q=Q+R
−1

^
Q
G
. The
iterative update rule of the trajectory guarantees that the average cost is non-increasing,
if the sampling is assumed to be dense.
After updating K trajectory points we move the vehicle to the next waypoint and
restart the optimization process to optimize the next K waypoints given new sensor
measurements about the environment.
5.2 Cost Function
The cost function to optimize the trajectory consists of obstacle cost c
o
(q
i
), recognition cost
c
r
(q
i
), information cost c
i
(q
i
) and center object cost c
v
(q
i
) and is computed as follows:
C(Q)=
K
Q
i=0
c
o
(q
i
)+c
v
(q
i
)+c
r
(q
i
)∗c
i
(q
i
): (5.7)
The summation of the cost function over the horizon states is the sum over the obstacle
cost, the object center cost and the product of the recognition and information cost. The
product part of the equation becomes zero if we have collected sucient information about
the object. In other words, we have enough information if we are sucient certain about
the posterior estimate of the object class. In this case, we do not want to collect more
data and with that stay close to the initial optimal trajectory, but still penalize trajectory
points for being to close to an object the vehicle could collide with.
5.2.1 Obstacle Cost
To avoid collisions with obstacles we incorporate an obstacle cost that forces the vehicle
away from the obstacle. Obstacles can be the objects we want to identify or other objects
in the environment we have no knowledge o when the initial trajectory was created. Let
all objects that are closer as of the vehicle to the trajectory point be dened as O
c
with
c∈ {1;:::;M} and their position be dened as ⃗ o
c
.
The obstacle cost is computed by approximating the vehicle with a sphere b and is
computed as follows:
c
o
(q
i
)=
M
Q
c=1
max(+r
b
−dist(⃗ x
0
;⃗ o
c
); 0)SS
_
⃗ x
b
SS; (5.8)
with dist(⋅;⋅) being the euclidean distance between two points, r
b
begin the radius of the
sphere, ⃗ x
o
being the 3D position of the sphere b and begin a safety margin. To prevent
89
the vehicle of traversing high cost region with high speed, we multiply the cost by the
magnitude of the workspace velocity SS
_
⃗ x
b
SS of the sphere b.
The obstacle cost c
o
(q
i
) is zero if all obstacles are at least away of the vehicle sphere
b.
5.2.2 Center Object in Camera View
The center object cost keeps the target object in the center of the image plane. The cost is
dened such that it has it's minimum value when the target object is in the center of the
image plane and reaches its maximum when the object is out of the camera frame. The
center object cost function is calculated by transforming the target's world coordinates
into image plane coordinates, ⃗ v = [v
x
;v
y
; 1], using a perspective plane transformation. We
express the center object cot as with the following formulation:
c
v
(q
i
)= min(v
2
x
+v
2
y
; 1)= min(⃗ v⋅ ⃗ v; 1): (5.9)
If no object is in close proximity of the vehicle we set ⃗ v such that the next waypoint of
the trajectory is in the center of the image plane. This way, the camera is directed into
the direction the vehicle moves and can spot potential objects or targets.
5.2.3 Recognition Cost
To increase recognition accuracy and improve the certainty of the posterior class estimate,
we incorporate a recognition cost into our cost function. Intuitively, we want to have
the vehicle keep the target object O
r
, with position o
r
at a certain distance such that
the object is completely in frame of the camera. This is due to the fact that partially
observed objects can lead to wrong object class estimates. Furthermore, we want to steer
the vehicle to new observation directions o
v
with v ∈ 1;:::;V to collect new information
about the object in question. The observation direction is a point around the object to
which the robot is maneuvered as shown in Fig. 5.2 as green and red squares. We choose
the observation direction closest to the robot as the one to be attracted to. Once we have
taken an observation from this position, we treat the view of the object as observed and
want to steer the vehicle to the next observation point along the path of the vehicle. This
means we select the next closest viewpoint along future waypoints as the next observation
position o
v
.
The object recognition cost function is dened as follows:
c
r
(q
i
)=dist(o
r
;q
i
)+PLdist((o
r
;o
v
);q
i
) (5.10)
withPLdist((⋅;⋅);q
i
) as the distance between the waypoint q
i
and the line passed through
the object target o
r
and the observation point o
v
. The distance attracts the vehicle closer
to the observation point, while the point to line distance attracts it to the right observation
angle.
90
5.2.4 Information Cost
We only want to collect as much information about the target object as necessary to
achieve high probability identifying the object correctly. Once enough information is
collected, we want to proceed towards the goal or focus on an object that is in close
vicinity of the vehicle. A measure of uncertainty is dened in the Shanon entropy, which
measures the uncertainty in a random variable. The entropy is zero if the outcome of
the classication is unambiguous and it reaches its maximum if all object classes are
equally likely. The entropy of the posterior object classication distribution is dened
as H(o
t
Sf
1∶t
)=−∑P(o
i
Sf
1∶t
) logP(o
i
Sf
1∶t
). We dene the information cost c
i
such that it
becomes zero if we are suciently certain about the class estimate given by the MAP
estimate of the posterior distribution. Therefore, we dene the information cost as:
c
i
=
⎧
⎪
⎪
⎨
⎪
⎪
⎩
0; if H(o
t
Sf
1∶t
)<
1; otherwise
(5.11)
Here, if the entropy H(o
t
Sf
1∶t
) becomes smaller then we set c
i
= 0, indicating we are
certain about the object class of the target object.
5.3 Object Recognition
Given a static scene and an object in question we want to correctly recognize the object.
The recognition process matches an observation of the target object with the objects
stored in a database and computes the belief states of all possible objects. Due to noise,
ambiguity and occlusion the recognition process does not always lead to certain matchings,
which in turn results in multiple likely object candidates. To this end, we seek the minimal
number of observations that accurately identies the object in question.
During object observation, the sensor captures the raw data, such as color images and
3D point clouds, which is used to compute the features. The sensor measurements of a
new observation are parametrized by the feature vector
⃗
f = [f
1
;:::;f
N
], which includesN
dierent feature types. The observation uncertainty is captured in our observation model,
dened as the conditional probability density function p(
⃗
f
z
So
z
), with recognition state o
z
and feature vector
⃗
f
z
captured at time z. In the recognition state estimation, we use a
Bayesian framework to infer about the current object class o
z
from the measurements.
The parameters are assumed to be obtained from a physical object model and to be trained
oine.
5.3.1 Sequential Bayesian Recognition
With every new observation of a feature
⃗
f
z+1
, we want to eciently integrate the new
observation with results from prior observations, and thus update our current belief about
the object class. We formulate the recognition process over the object classes as a Bayesian
network in form of a Hidden Markov Model (HMM). A Bayesian formulation has distinct
91
advantages, with the main advantage being that Bayesian methods model all sources of
uncertainty in form of random variables. Furthermore, HMMs have ecient formulations
to sequentially update the posterior distribution, making it ideal for integrating new
observations, such as in our case in the form of a new feature
⃗
f
z+1
. Compared to a naive
Bayes update, which is often used in existing work (Denzler & Brown, 2002; Paletta
& Pinz, 2000), the HMM formulation additionally gives us the possibility to explicitly
formulate the state transitions.
The joint probability distribution is dened as
p(o
1∶Z
;
⃗
f
1∶Z
) =p(o
1
)
Z
M
z=2
p(o
z
So
z−1
)
Z
M
z=1
p(
⃗
f
t
zSo
z
): (5.12)
The observation sequence is S = {o
1
;:::;o
z
}, the hidden state of our HMM is dened
as recognition state o
z
with o
1∶Z
= {o
1
;:::;o
z
;:::;o
Z
} and the observations are given as
observed features
⃗
f
z
with
⃗
f
1∶Z
= {
⃗
f
1
;:::;
⃗
f
z
;:::;
⃗
f
Z
}. The state of the hidden process
satises the Markov property, that is, given the value of o
z−1
, the current state o
z
is
independent of all the states prior to z− 1.
The observation model p(
⃗
f
z
So
z
) represents the likelihood that feature
⃗
f
z
is generated
by recognition state o
z
. The transition probability is dened as p(o
z
So
z−1
), which means
that the transition to the next recognition state is dependent on the previous recognition
state (i.e., the previous object class). The posterior marginals p(o
z
S
⃗
f
1∶Z
) of all hidden
state variables, given a sequence of observations, can be eciently computed using the
forward-backward algorithm. The algorithm computes a smoothed estimate given all
evidence in two passes, with the rst pass going forward in time and the second pass going
backwards in time:
p(o
z
S
⃗
f
1∶Z
) = p(o
z
S
⃗
f
1∶z
;
⃗
f
z+1∶Z
)
∝ p(
⃗
f
t+1∶Z
So
z
) p(o
z
S
⃗
f
1∶z
):
(5.13)
In the rst pass, we compute the forward probabilities, which are the probabilities for
all z ∈ {1;:::;Z} ending up in any particular state given the rst z observations in the
sequence p(o
z
S
⃗
f
1∶z
). In the second step, we compute the probabilities p(
⃗
f
z+1∶Z
So
z
) of
making the remaining observations given any starting point z.
5.3.2 Observation Model
For recognition, we learn a function g∶R
S
⃗
fS
→N that maps the extracted object features
⃗
f
to a unique object identieri∈ {1;:::;K}, each pointing to a distinct object modelo
i
=c
k
,
with k ∈ {1;:::;K} and K denotes the total number of object classes c
k
. The function
is learned in a supervised fashion, with all possible features
⃗
f and the unique identier i
available as the value pair (
⃗
f;i) at model training phase.
The observation model is dened as a Gaussian generative model of the form P(fSo
i
)=
∏
M
m=1
N(fS
o
i
;m
;
o
i
;m
), with M is the number of independent normal distributions to
model a feature f. Each feature f is represented as a feature histogram with M bins,
92
and the mean
o
i
;m
and variance
o
i
;m
for each bin m is computed over the training
data of an object with recognition state o
i
. We use M independent normal distributions
since a multivariate normal distribution, with full covariance matrix, would become high-
dimensional for high-dimensional features. High-dimensional models are in general poorly
separable as is well understood under the curse of dimensionality.
We can now compute the likelihood p(
⃗
fSo
i
) of generating the model o
i
from feature
vector
⃗
f as
P(
⃗
fSo
i
;
⃗
)=
N
Q
n=1

n
M
Q
m=1
N(f
n
S
o
i
;m
;
o
i
;m
); (5.14)
with
n
denoting a scaling factor to scale the dierent feature distributions. The Gaussian
representation of the features is compact and fast to train, since it only requires the
computation of the Gaussian feature parameters
o
i
;m
and
o
i
;m
. Furthermore, sequential
learning as well as sequential updates of mean and variance are possible, which has the
potential of adaptively adding new observations to our trained features.
Instead of learning just one model per object class, we learn multiple models. This
has the advantage that the model trained for each object has a smaller variance if trained
only for a partial view of the object. This becomes intuitively clear since an object looks
in general very dierent for dierent viewing directions. And this again is re
ected in the
variance of the model.
5.3.3 HMM State Transition
We dene the state transition probability p(o
z
So
z−1
) as the probability of a transition from
recognition state o
z−1
to state o
z
. This means, how likely is the transition, if at time z− 1
we believe to be in recognition state o
z−1
=c
k
(i.e., a believed target object with object
class c
k
), then move the vehicle to a new waypoint and acquire a new observation and
feature
⃗
f
z
, and nally believe to be in state o
z
=c
k
at time z.
In order to determine the optimal state transition probabilities, we uses the Baum-
Welch algorithm, which uses expectation maximization to nd the maximum likelihood
estimate of the state transition parameters given a set of observed data.
93
5.4 Experiments
In this section, we present the evaluation results of our framework on a quadrotor platform
both in simulation and on a real platform. The quadrotor is given an initial trajectory,
which is to be followed or altered, such that the vehicle can recognize objects along its
path. At the beginning of the mission, position, identity and number of objects in the
environment are unknown and need to be discovered as the robot makes progress along the
given initial trajectory. As the robot moves through the environment, along the waypoints,
the quadrotor is able to detect objects of interest up to a distance of 3.0m. As the robot
gets closer to the current target object ⩽ 2:0m, data is collected and used as input to the
object recognition framework.
The object recognition framework is trained on a total of 326 objects. The training
set is comprised of a publicly available RGB-D dataset introduced in (Lai et al., 2011)
and objects recorded by us. The RGB-D dataset consists of a color image, a 3D point
cloud and the orientation of the object, for a total of 300 everyday objects. However,
since we do not have any of the objects or models we can use for our simulation or real
world experiments, we created the same data for 26 additional objects. For real world
experiment we record data from real object while in simulation we create a dataset from
virtual models. For each object, the data is recorded from directions all around the object,
including three dierent viewing angles of 30
○
, 45
○
and 60
○
per direction. We train our
object models from
⃗
f using data captured from viewpoints at 30
○
and 60
○
in each direction,
and test them against features computed from data that is recorded from viewpoints at
45
○
.
In our experiments we only select objects from our dataset, however the inference is
done over the entire 326 object dataset, to increase overall diculty. The overall dataset is
challenging, since the objects in the dataset look very similar, especially when they belong
to the same object category. Furthermore, the objects in the dataset exhibit large changes
in illumination due to dierent viewing angles from which the objects were captured,
which may make classication dicult even across dierent categories.
The feature vector
⃗
f, which is used throughout our framework, is comprised of three
independent features: object bounding box, color histogram and SIFT (Lowe, 2004). Each
feature represents a dierent object property: size, color and a scale-invariant image
descriptor. In accordance with eq. 5.14, each single feature or component of a feature
histogram, respectively, is expressed as independent normal distribution. The scaling
factor
n
is chosen empirical and set to {Color;Bbox;SIFT}= [1:0; 0:02; 0:2]. For each
object instance we train in total eight dierent models which divides the training set into
45 degree viewing intervals. All reported accuracies of our recognition results are expressed
as recall and stem from the MAP estimated of the posterior distribution.
In this work the features and recognition framework is rather simple, compared to a
state-of-the-art system. In a single-view recognition scenario the recognition performance
of our system in a controlled environment is rather poor performing with an accuracy
of only 82:35%. The advantage of the system however, is that the features and class
94
predictions can be computed extremely fast. This makes it possible to run the entire
system in real time. Nevertheless, the recognition framework actually performs quite
suitably in a multi-view scenario, demonstrating that even simple features are capable
of performing well when additional information is collected and utilized as is shown in
(Potthast et al., 2015). That being the case, the recognition system used herein is not
novel or state of the art. In fact, any other Bayesian recognition framework could be
substituted for the one herein employed.
We test the recognition performance with two dierent path following methods. In
the base case, the robot is just blindly following the initial waypoints, collecting data
as it progresses through the environment. The second method is our online trajectory
optimization method, as the robot moves through the environment, the path is optimized
to minimize the cost computed in eq. 5.7. The trajectory and with that the waypoints
are represented in cartesian space as well as a yaw angle for orientation and is dened
as q
i
= [x;y;z;]. To keep computation time reasonable and still be able to update the
trajectory fast, we choose the waypoint horizon
= 10. To penalize a potential collision
with an object, we dene the parameters of the obstacle cost with = 2:0m as objects that
potentially could collide with the quadrotor, the safety margin = 0:5m and the robots
sphere r
b
= 0:5m. The information cost entropy parameter which denes the cut-o as
when to stop collecting more data is set to = 0:1. All experiments are conducted over 10
trials, each time, the set of objects is exchanged randomly and the robot placed at the
beginning of the initial trajectory.
5.4.1 Simulation results
We test the performance of our trajectory optimization method in three dierent simulation
scenarios, varying in the initial trajectory and the number of objects we need to identify.
We show the three scenarios with their initial trajectories and object placement in Fig. 5.3,
5.5 and 5.7 and the optimized trajectories in Fig. 5.4, 5.6 and 5.8. In both versions, the
non-optimized and optimized version, the waypoints that the quadrotor has followed are
shown in green dots. Objects that the robot needs to identify are circled with square
boxes. The square boxes represent the observation directions o
v
of the target object, a
green box represents the direction from which we have taken a measurement, a red box is
a direction from which we have not collected any information yet. For each observation
direction, we only capture one observation.
The quantitative results of the simulation experiments are shown in Table 5.1 and
Table 5.2 . We can see that the time, on average, the vehicle needs to traverse the trajectory
in the non-optimized version is shorter compared to the optimized version. This is due to
the time the online trajectory optimization algorithm takes to compute and update the
trajectory. The optimized version on the otherhand enables the vehicle to collect better
information about the target object as we can see in the accuracy of recognizing the object
correctly. On average the optimized trajectory achieves much better accuracy, but more
importantly we can see that the average entropy of the posterior estimation is much lower.
A lower entropy estimate means we are more certain of the class estimate of the target
95
#Waypoints #Objects Avg. Time(sec)
(1) Initial Trajectory 45 5 99.8 ± 2.3
(1) Optimized Trajectory 45 5 115.6 ± 4.0
(2) Initial Trajectory 45 7 94.7 ± 4.0
(2) Optimized Trajectory 45 7 115.5 ± 3.2
(3) Initial Trajectory 56 10 104.9 ± 2.2
(3) Optimized Trajectory 56 10 135.1 ± 2.8
Table 5.1: Simulation results { The table shows the average performance by following the
initial trajectory or optimized trajectory. The three scenarios are dissimilar in number
of total waypoints and object to be recognized. All results are averaged over 10 dierent
trials, with the objects we want to recognize chosen at random.
Avg. Observations Avg. Accuracy Avg. Entropy
(1) Initial Trajectory 22 72.0% ± 13.3 0.26 ± 0.03
(1) Optimized Trajectory 14.7 ± 2.6 92.0% ± 9.8 0.12 ± 0.05
(2) Initial Trajectory 22 61.43% ± 11.16 0.28 ± 0.05
(2) Optimized Trajectory 18.8 ± 0.9 94.29 ± 7.0 0.10 ± 0.03
(3) Initial Trajectory 28 69% ± 15.13 0.27 ± 0.02
(3) Optimized Trajectory 22 ± 1.7 93.0 ± 7.81 0.11 ± 0.02
Table 5.2: Simulation results { The table shows the average performance by following
the initial trajectory or optimized trajectory. We show the needed average observations,
average accuracy and average total entropy of the objects to be recognized.
objects. A higher entropy of the posterior class distribution is the result of partial or
poor quality target object observations. This can happen if the vehicle is too far away
or if the vehicle is too close and the object does not t completely into the image frame.
Additionally, we can see that less observations are needed which can also be attributed to
the fact of better observations, but also due to the fact that we stop collecting data once
we have enough certainty about the target object.
96
Figure 5.3: Simulation Experiment 1 { In this experiment the vehicle follows the initial
trajectory shown as green dots. The vehicles goal is to follow the trajectory and recognize
5 objects depicted as circles with green/red boxes. The green/red boxes show the possible
observation angles, once an observation has been taken from a certain angle the box is
marked as red and no other observation is taken with similar angle.
97
Figure 5.4: Simulation Experiment 1 { In this experiment the vehicle follows the online
optimized trajectory. The red dots show the initial trajectory while the green dots show
the optimized trajectory given the initial waypoints. The new trajectory enables the
vehicle to more reliable recognize the 5 objects depicted as circles with green/red boxes.
The green/red boxes show the possible observation angles, once an observation has been
taken from a certain angle the box is marked as red and no other observation is taken
with similar angle.
98
Figure 5.5: Simulation Experiment 2 { In this experiment the vehicle follows the initial
trajectory shown as green dots. The vehicles goal is to follow the trajectory and recognize
7 objects depicted as circles with green/red boxes. The green/red boxes show the possible
observation angles, once an observation has been taken from a certain angle the box is
marked as red and no other observation is taken with similar angle.
99
Figure 5.6: Simulation Experiment 2 { In this experiment the vehicle follows the online
optimized trajectory. The red dots show the initial trajectory while the green dots show
the optimized trajectory given the initial waypoints. The new trajectory enables the
vehicle to more reliable recognize the 7 objects depicted as circles with green/red boxes.
The green/red boxes show the possible observation angles, once an observation has been
taken from a certain angle the box is marked as red and no other observation is taken
with similar angle.
100
Figure 5.7: Simulation Experiment 3 { In this experiment the vehicle follows the initial
trajectory shown as green dots. The vehicles goal is to follow the trajectory and recognize
10 objects depicted as circles with green/red boxes. The green/red boxes show the possible
observation angles, once an observation has been taken from a certain angle the box is
marked as red and no other observation is taken with similar angle.
101
Figure 5.8: Simulation Experiment 3 { In this experiment the vehicle follows the online
optimized trajectory. The red dots show the initial trajectory while the green dots show
the optimized trajectory given the initial waypoints. The new trajectory enables the
vehicle to more reliable recognize the 10 objects depicted as circles with green/red boxes.
The green/red boxes show the possible observation angles, once an observation has been
taken from a certain angle the box is marked as red and no other observation is taken
with similar angle.
102
5.4.2 Quadrotor results
In order to show the real world performance of our online trajectory optimization method,
we have conducted experiments on our custom-build quadrotor platform. As shown in
Fig. 5.1, the quadrotor is equipped with an ASUS Xtion RGB-D camera for data acquisition
and can
y autonomously along the waypoints of the trajectory. The experiment is setup
identically to the simulation experiment, with the quadcopter optimizing the trajectory
online, following the updated waypoints and collecting data of target objects along the way.
The results of the real world experiment are shown in Table 5.3. Similar to the simulation
results, we can see a similar performance of the optimized trajectory compared to the
non-optimized trajectory. The smooth optimized trajectory achieves a higher average
recognition accuracy with a lower average uncertainty of the MAP estimate. Furthermore,
the optimization results in a lower average number of observations taken.
#Waypoints #Objects Avg. Time(sec)
Initial Trajectory 44 4 58.8 ± 1.7
Optimized Trajectory 44 4 81.7 ± 1.35
Avg. Observations Avg. Accuracy Avg. Entropy
Initial Trajectory 15 74.29 % ± 17.04 0.27 ± 0.02
Optimized Trajectory 10.8 ± 1.8 90% ± 12.25 0.13 ± 0.01
Table 5.3: Quadrotor results { Average performance with random objects placed into the
scene over 10 dierent trials
103
Figure 5.9: From top left to bottom right we show in order how the quadrotor captures
information about the target objects along the optimized trajectory.
104
Figure 5.10: Quadrotor results { Optimized trajectory of the quadrotor, 4 objects are
being recognized.
105
5.5 Conclusion
In this work, we have presented an online trajectory optimization approach that optimizes
waypoints towards improving recognition of objects. The formulated stochastic optimiza-
tion approach allows us to change the trajectory in real-time such that observations taken
of a target object result in more accurate recognition estimates of the target object. We
achieve this by preventing inference with partial observations of the target object and in
addition by taking the uncertainty of the posterior distribution into account. Considering
the entropy of the posterior class distribution allows us to determine whether we need to
collect more information about the current target object or if the information collected
yields enough information to make a class prediction of high certainty. In numerous
experiments, simulation as well as on a real robot, we have shown the usefulness of our
approach. We have shown that the optimized trajectories not only achieve, on average, a
higher recognition accuracy, but more importantly that the posterior class distribution is
less uncertain. This results in more certainty of the class prediction given by the MAP
estimate of the posterior distribution. Currently, all computation, trajectory optimization
as well as object recognition, is run on an o-board computer, a future plan is to run
everything onboard the quadrotor.
106
Chapter 6
Conclusions
In this thesis we have presented information theoretical frameworks for data acquisition
and scene understanding. In extensive experiments we have shown that adaptive action
selection is a useful tool for robots to understand the surrounding they operate in. In this
chapter, we summarize the contributions made in this thesis.
First, in Chapter 3 we presented an information gain-based variant of the next best
view problem for occluded environment. Our proposed method utilizes a belief model of
the unobserved space to estimate the expected information gain of each possible viewpoint.
More precise, this belief model allows a more precise estimation of the visibility of occluded
space and with that a more accurate prediction of the potential information gain of new
viewing positions. We presented experimental evaluations on a robotic platform for active
data acquisition, however due to the generality of our approach it also applies to a wide
variety of 3D reconstruction problems. With the evaluation done in simulation and on
a real robotic platform, exploring and acquiring data from dierent environments, we
demonstrated the generality and usefulness of our approach for next best view estimation
and autonomous data acquisition.
Second, in Chapter 4 we presented an active multi-view object recognition approach
and describe an information-theoretic framework that combines and unies two common
techniques: online feature selection for reducing computational costs and view planning
for resolving ambiguities and occlusions. Our algorithm adaptively chooses between the
two strategies of either selecting features that are most informative or moving to a new
viewpoint that optimally reduces the expected uncertainty on the identity of the object.
This two step process allows us to keep overall computation cost minimal but simultaneously
increase recognition accuracy. Extensive evaluation on a large RGB-D dataset with two
dierent feature sets have validated the eectiveness of the proposed framework. Our
experiments show that dynamic feature selection alone reduces the computation time at
runtime 2:5 to 6 times and, when combining it with viewpoint selection, we signicantly
increase the recognition accuracy on average by 8{18% absolute compared to systems that
do not use these two strategies. By establishing a link between active object recognition
and change detection, we were further able to use our framework for the follow-up task
of actively detecting object change. Furthermore, we have successfully demonstrated the
107
framework's applicability to a low-powered quadcopter platform with limited operating
time.
Finally, in Chapter 5 we presented an online trajectory optimization approach that
optimizes a trajectory such that object recognition performance is improved. Inspired
by prior work, we formulate the optimization as a derivative-free stochastic optimization,
allowing us to express the cost function in an arbitrary way. The cost function is dened
such that information acquisition of target objects is improved, while simultaneously
moving towards the goal point. We show the evaluation of our approach on a quadrotor
platform in simulation as well as on a real robot. The results show that by using an online
optimization approach recognition accuracy is greatly improved, but more importantly
the optimized trajectory reduces the uncertainty of the posterior class distribution greatly.
Hence, verifying that the optimized trajectory collects more valuable information.
Through extensive experiments, in simulation and on real robotic systems, this the-
sis shows the usefulness of adaptive action selection. We have shown that adaptive action
selection is a useful tool to increase reliability and eciency for 3D data acquisition and
object recognition. However, the use cases for adaptive approaches reach far beyond what
we have shown in this work. We believe that adaptive approaches can be a viable solution
to make tasks, the robot needs to executes, more reliable and ecient.
108
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Abstract (if available)

Abstract For robots to one day become fully autonomous and assist us in our daily lives, they need to be able to self reliantly acquire information about their environment. Challenges arise from the limited energy budget to operate the robot, occlusion from the environment, and uncertainty in data captured by noisy sensors. To cope with such challenges, the robot needs to be able to rely on a system that enables it to capture information efficiently while respecting constraints. Furthermore, information acquisition should be reactive to sensor measurements, incorporate uncertainty and tradeoff information gain with energy usage. In this thesis we study such systems using information theoretical measures to formulate as general and versatile a framework as possible. Specifically, we examine the task of defining objective functions that enable us to tradeoff information with acquisition cost, enabling the robot to gather as much useful information as possible, but at the same time keep energy consumption to a minimum. We address this challenge for a variety of different tasks. ❧ First, we examine the problem of 3D data acquisition, which is of outmost importance to a robotic system since the robot needs to know the environment it is operating in. We present an information gain-based variant of the next best view problem for an occluded environment. The developed framework enables the robot to quickly acquire information by sequentially choosing next observation positions that maximize information. Next, we look at adaptive action selection in the context of object recognition on robots with limited operating capabilities. We propose an information-theoretic framework that combines and unifies two common techniques: view planning for resolving ambiguities and occlusions and online feature selection for reducing computational costs. Concretely, this framework adaptively chooses two strategies: utilize simple-to-compute features that are the most informative for the recognition task or move to new viewpoints that optimally reduce the expected uncertainties on the identity of the object. Lastly, we present an online trajectory optimization approach that improves object recognition performance. With the idea in mind that the robot needs to make progress towards a goal, a cost function is formulated that allows the robot to improve recognition performance, maneuver safely through the environment and reduce information acquisition cost, while simultaneously moving towards the goal point. Through extensive experiments, in simulation and on real robotic systems, this thesis shows the usefulness of adaptive action selection. We have studied adaptive action selection on two concrete problems, but the use case and need for such an approach can be found in many other applications.

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Creator Potthast, Christian (author)

Core Title Information theoretical action selection

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Computer Science

Publication Date 08/02/2016

Defense Date 04/28/2016

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag active perception,information theory,multi-view object recognition,next best view,OAI-PMH Harvest,object recognition,quadrotor,robotics,trajectory optimization,view planning

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Sukhatme, Gaurav S. (committee chair), Gupta, Sandeep K. (committee member), Schaal, Stefan (committee member)

Creator Email potthast.chris@gmail.com,potthast@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-291952

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