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Boundary estimation and tracking of spatially diffuse phenomena in sensor networks

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Boundary estimation and tracking of spatially diffuse phenomena in sensor networks

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BOUNDARY ESTIMATION AND TRACKING OF
SPATIALLY DIFFUSE PHENOMENA IN SENSOR
NETWORKS
by
DIVYA DEVAGUPTAPU
A Thesis Presented to the
FACULTY OF THE SCHOOL OF ENGINEERING
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
ELECTRICAL ENGINEERING (Computer Networks)
December 2003
Copyright 2003 Divya Devaguptapu
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This thesis, w ritten by
b l V Y A b g v A ^ u P T A F U
under the guidance of his/her Faculty Committee and
approved by all its members, has been presented to and
accepted by the School of Engineering in partial
fulfillm ent o f the requirements fo r the degree of
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Acknowledgements
I would like to express my sincere gratitude to my advisor Prof. Bhaskar
Krishnamachari for Us guidance, support and encouragement through the course of
my masters. I would also like to extend my thanks to my thesis committee members
Prof. Ahmed Helmy and Prof. Konstantinos Psounis.
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Table of Contents
Acknowledgements .... ii
List of Tables and Figures .... ....iv
Abstract.. ....... vi
1. Introduction ..... 1
1.1 Wireless Sensor Network.... ..... 1
1.2 Related Work ......... 5
2. Application of Image Processing Techniques to Sensor Networks ... 7
2.1 Introduction .... 7
2.2 Image Processing Techniques ...... 9
2.2.1 Noise Cleaning ....................................................................9
2.2.2 ...Edge Detection................................................................. 10
2.3 Image-based Processing............................................................................12
2.3.1 Assumptions and Simulation Framework .......................... 12
2.3.2 Noise Cleaning.................... 13
2.3.2.1 Methodology .... 13
2.3.2.2 Simulation Results ..... 14
2.3.3 Edge Detection............................................................................. 17
2.3.3.1 Methodology .... 17
2.3.3.2 Simulation Results... ....... 20
2.4 Naive Edge Detection ............................... 24
2.4.1 Simulation Framework............... 24
2.4.2 Simulation Results............................. 25
2.5 Conclusion............................................................................................... 27
3. Tracking Spatially Diffuse Phenomena .... .28
3.1 Assumptions and Simulation Framework ....................................28
3.2 Sensor Gradient-based Querying ...... ......29
3.3 Adaptive Network Topology Formation ...... 31
3.4 Simulation Results................................................ 33
3.4.1 Expanding Phenomena.......................................... 33
3.4.2 Moving Phenomena ...... 39
3.5 Conclusion................................................. 41
4. Conclusions ... 44
5. References........... 47
iii
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List of Figures and Tables
Figures
2.1 MSE vs communication range for similar sensing environments ............... 15
2.2 MSE vs Communication Range for diverse environments ...... .17
2.3 MSE with respect to varying density for similar environment ...... 18
2.4 MSE with respect to density for diverse environments....................................... 18
2.5 Performance of Image-processing based Edge Detection...................................20
2.6 Mean offset versus communication range for image 1..... 21
2.7 Mean offset versus communication range for image 2........................................22
2.8 Optimal communication ranges for image 1 ......................... 23
2.9 Optimal communication ranges for image 2 ..... 23
2.10 Optimal communication ranges for varying densities.......................................24
2.11 Naive edge detection for expanding phenomenon ...... ...26
3.1 Querying an expanding phenomenon ..... 31
3.2 Network topology generation based on two metrics............................. 35
3.3 Cost involved with using node time as metric............. 36
3.4 Cost involved with using node ID as metric. .... 36
3.5 Comparison of node ID and node time metrics ...... 37
3.6 Querying based on random-walk............................. 37
iv
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3.7 Querying based on less noisy sensor-gradient .... 38
3.8 Number of hops taken by query7 for varying noise levels....................................38
3.9 Detection and tracking of a moving phenomenon...............................................39
3.10 Cost associated with using two metrics for a moving area................................40
3.11 Number of hops taken by query to converge for varying noise.................... 41
Tables
2.1 Comparison between naive and image-based edge detection............................26
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Abstract
In this thesis, we propose and investigate some distributed strategies by which sensor
networks can determine the boundaries of and track spatially diffuse phenomena.
We first investigate the possibility of applying traditional image- processing
techniques for boundary detection to sensor networks. Our results show that the
performance of the image processing techniques depends critically upon sensor
density and radio range. We note that there is a tradeoff between complexity and
accuracy in using complex image processing-based techniques as compared to more
naive techniques.
We then propose techniques to track mobile spatially diffuse phenomena by forming
an adaptive network topology. We investigate the performance of different leader-
node election metrics on the communication costs involved in maintaining and
updating such a topology. We also investigate querying mechanisms that use sensor
and temporal gradients to efficiently gather information about the dynamic
phenomena, and examine the impact of sensor noise on query completion times.
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Chapter I
Introduction
1.1 Wireless Sensor Networks
The emergence of sensor networks is considered to be a major paradigm shift in
technology. Sensor network research, involves networking large numbers o f low-
cost, power efficient devices called nodes, which are deployed in remote or urban
regions to sense and monitor phenomena. It is envisioned that advances in
microprocessor and radio technology will enable these tiny nodes to perform
sensing, communication and computation.
Sensor networks may be used for applications spanning several domains ‘including
military, medical, industrial, and environmental management. Large-scale sensor
colonies can be deployed in both urban and civil areas. Sensor networks will have
sensors that can monitor ambient conditions, temperature, pressure, humidity, noise,
light intensity and other such phenomena. These will be equipped with signification
data processing, memory and wireless communication capabilities. For habitat or
environmental monitoring of remote geographical regions or in the battlefield,
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sensors can be randomly deployed as simply as throwing from an aircraft. Once
deployed, the sensors will coordinate with each other to establish a communication
network to gather data required from that particular region. The biggest constraint of
these nodes will be energy. Since these nodes should be very cost-effective and
small, they need to operate on battery power. However, the battery power may not
last very long. Hence, they will have to do all the communication and data
processing in an energy efficient manner and simultaneously manage the network
that they have formed by accounting for contingencies such as node failures etc.
These networked sensors will revolutionize information gathering and processing in
urban environments and unmanned regions.
Networking researchers have been drawn toward sensor networks since it is hitherto
an unexplored area with many challenging research problems. Some key challenges
include scalability o f network protocols to large number o f nodes, design of simple
and efficient protocols for different network operations, design of power-conserving
protocols, design o f security mechanisms, design of data handling techniques
including data querying, data mining, data fusion and data dissemination, and
development of exciting new applications that exploit the potential of wireless sensor
networks. What makes sensor network research most fascinating is that unlike wired
networks, all the protocols must be energy efficient, since these nodes are battery
powered devices and the lifetime of these nodes is very limited.
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Sensor network applications are distributed in nature. Most of the existing wired
network algorithms can help design sensor network applications. But sensor network
algorithms will have to be localized where sensors collectively achieve a global
objective. Centralized computation will result in a single point failure and need to be
avoided due to their limited battery power. Low-level, low-power protocols to
effectively network these sensors must be designed to collaborate and perform a
given task; this poses the greatest challenge since sensor networks are application
specific and data centric.
In sensor networks, boundary estimation is a very important problem. A sensor
network could be deployed in a region where there exist two distinct sensing
environments. To detect and track the demarcation o f this boundary is the primary
focus of our work.
We propose methods that incorporate classical image processing techniques to
wireless sensor networks for boundary detection. We also conduct a parallel study on
applying image processing based techniques to mitigate noise in the sensor
environment. We propose to combine information from neighboring sensors since
the sensor readings are spatially correlated in order to moderate noisy measurements.
Noise cleaning and edge detection are two widely studied problems in image
processing and we employ those techniques to solve similar problems in sensor
networks.
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However, we consider the use of image-processing based techniques to determine
boundaries only when the phenomenon is static. For dynamic phenomena such as an
oil spill or a chemical leak, we suggest that a method as nai've as determining edges
by means of comparing readings obtained in the sensor neighborhood could provide
satisfactory results. We argue that since the naive technique provides comparable
results to the image processing based techniques, applications not requiring a high-
accuracy of boundary estimation could save considerable energy expended by
avoiding computationally intense image processing techniques.
We propose techniques to track spatially diffuse phenomena by forming an adaptive
network topology using the spanning tree algorithm. Our results indicate that an
optimal choice of metric is necessary in order to minimize the cost associated with
building and maintaining a spanning tree for cases when the phenomenon is
expanding over time or moving through the network. We consider two metrics based
on node time and node IDs and analyze the performance o f these metrics for moving
or expanding scenarios. We believe that the network topology formation takes care
of the data gathering in the network, however there must be an efficient querying
mechanism in order to route the data back to the source. We propose a sensor-
gradient and temporal-gradient based routing scheme to route these queries through
the network.
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The rest of the thesis is organized in the following manner. In chapter 2, we discuss
applications of localized image processing techniques in wireless sensor networks.
We describe our proposed algorithms to track spatially correlated dynamic diffuse
phenomena in chapter 3. We summarize our results and conclude in chapter 4.
1.2 Related Work
We note that other recent efforts have also been made to examine the parallels
between image processing and sensor networks, particularly for edge/boundary
detection and tracking. [Liu02] present a centralized scheme that uses Hough
transforms to track a moving boundary as a point in the dual space. [Ganesan02]
have proposed a generalized hierarchical architecture for multi-resolution querying
of regularly-placed sensor networks that is based on wavelet-transforms; this
architecture is shown to be useful for queries involving boundaries and edges.
[Nowak03] present a hierarchical boundary estimation algorithm that is shown to be
asymptotically optimal in trading off energy for mean square error. The non-
hierarchical decentralized edge detection algorithm we investigate focuses on
identifying nodes near the boundary. This algorithm is also discussed by
[Chintalapudi03 ]. Their results are corroborated by our complementary work which
utilizes different performance metrics and provides additional insights into the
relationship between radio range and sensor placement density.
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Most o f the research in the area o f tracking boundaries in sensor networks till date
has been focused only on determining the edge of the phenomena. There exists very
minimal literature that deals with tracking a. dispersed dynamic phenomenon and
determining the contour of the boundary. [DantuG3] have proposed an algorithm to
track contours. They show that a static sensor network augmented with a single
mobile node can be put to a contour finding task to detect concentric contours that
have the property that they monotonically degrade in each direction from the source.
Though target tracking is an active area of research in sensor networks, most of the
work involves tracking a single or point target. Some of the preliminary work in this
area includes IDSQ [ZhaoQ2], location-centric tracking [Ramanathan02] [Brooks02],
and tracking with mobile nodes [Jung02], Significant issues that deal with multi
target tracking have also been addressed by [Li02], [Fang02], and [BejarOl].
However, tracking spatially correlated dispersed phenomena has not been considered
much previously.
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Chapter II
Boundary Estimation and Noise Removal in Sensor Networks
using Localized Image Processing Techniques
2.1 Introduction
We describe the application of image processing techniques for data refinement in
sensor networks by mapping network nodes to pixels in an image. Due to their
localized, distributed nature, image processing techniques are inherently scalable and
therefore desirable for use in large sensor networks. We focus on two data-
processing problems that arise in sensor networks, noise cleaning and edge detection,
and discuss the performance of localized image processing-based techniques for
these problems as a function of network density and radio range. Sensor
measurements are likely to be noisy, but when the environmental phenomena of
interest are spatially correlated and sensor noise is uncorrelated, it is possible to
combine information from nearby sensors in order to mitigate the noise. The edge
detection problem is of considerable interest in scenarios involving diffuse
phenomena such as chemical leaks whose perimeter needs to be tracked.
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Both noise cleaning and edge detection are standard problems in classical image
processing. There is a natural analogy between data processing in sensor networks
and image processing techniques. If we consider an instantaneous snapshot, the
environmental phenomena of interest in an operational area can be represented with
arbitrary fidelity by a sufficiently high-resolution Image (which we refer to as the
environment image). Due to their localized, distributed nature, classical image
processing techniques are inherently scalable and therefore desirable for use in large
sensor networks. In order to apply these techniques, one can envision individual
sensors as providing values of specific pixels in the image. One main challenge in
applying the image processing techniques then lies, in the fact that nodes may not be
regularly placed and not placed with sufficient density. In particular, these
techniques perform well at high densities when each pixel contains a sensor node. A
second challenge has to do with the notion of neighborhood. In classical image
processing the neighbors of each pixel are the eight adjoining pixels; in the case of
sensors, the concept of neighborhood is determined by the radio transmission power:
each node can communicate locally with other nodes that lie within its effective
radio range. The optimal choice of radio range for the best performance o f an image
processing-based technique can be highly dependent on the node density. We
examine these issues through experimental simulations.
In the sections that follow, we introduce classical image processing techniques for
noise removal and edge detection and our methodologies, simulations, and results
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pertaining to the application of these techniques to the corresponding problems in
sensor networks.
2.2 Image Processing Techniques
We first present a brief tutorial on classical image processing techniques pertinent to
noise cleaning and edge detection.
2.2.1 Noise Cleaning
In images, noise usually appears as discrete isolated pixel variations that are spatially
un-correlated. Pixels in error often appear visually markedly different from their
neighbors. This visual perception is the basis for many noise reduction algorithms in
image processing. Several linear and non-linear techniques have proven highly
effective for noise cleaning.
Noise added to an image generally has a higher spatial frequency spectrum than the
normal image components since it is spatially un-correlated. Hence, simple low pass
filtering proves effective for noise cleaning. A spatially filtered output image G(i,j)
can be formed by the discrete convolution of an input image F(i,j) with an MxM
impulse response array H (ij) according to the relation
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G(i,j) — XX F(m,n)H(m-i-C, n-j+C)
where C =(M+l)/2
For noise cleaning H should be of low-pass form with all positive elements. There
are several spatial domain linear noise cleaning filters, among which the Mean filter
is popular. The impulse response array for the mean filter is given as
ff =•-1/9
1 1 1
1 1 1
1 1 1
These arrays are called masks, and are normalized to unit weighting so that the
noise-cleaning process does not introduce an amplitude bias in the processed image.
2.2.2 Edge Detection
Local discontinuities in image amplitude attributes can be defined as edges. An edge
is characterized by height, slope angle and the horizontal coordinate o f the slope
point. The two generic approaches to edge detection are differential detection and
model fitting. In the differential detection approach, spatial processing is performed
on an original image to produce a differential image with accentuated spatial
amplitude changes. Then a differential detection operation is executed to determine
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the pixel locations of significant differentials. There are two major classes of
differential detection: first-order derivative and second-order derivative. For the first
order class, some form of spatial first order differentiation is performed and the
resulting edge gradient is compared to a threshold value. An edge is judged present if
the gradient exceeds the threshold value. Where as, in the second order derivative, an
edge is deemed present if there is a significant spatial change in "polarity of the
second derivative.
In our work we will focus on the first order derivative edge detection technique for
sensor nets. This technique involves generation of gradients in two orthogonal
directions of an image. The edge gradient in the discrete domain is generated in
terms of a row edge gradient G_r(i,j) and column edge gradient G_c(i,j), and the
spatial amplitude gradient is given by
G(i.j) = J(G r(i,j)2 + Gfi,j)2)
A good discrete approximation of the continuous differentials is to form the running
difference of pixels along rows and columns of the image. The Prewitt filter is one
commonly used approximation involving 3x3 pixel edge gradient operators given by
the following masks:
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Row Gradient
1 0 -1
= 1 0 - 1
1 0 -1
Column Gradient
-1 -1 -1
Gc =
0 0 0
1 1 1
Clearly the application of this technique to sensor networks is non-trivial and
requires modification since the nodes are not placed regularly in pixel-like grids. We
will discuss the pertinent modification in the next section.
2.3 Image-Based Processing in Sensor Networks
2.3.1 Assumptions and Simulation Framework
The following are some assumptions we make about the sensor network. We assume
that every node knows its location in terms of an (x,y) coordinate in space. The
neighbors o f a particular node are determined based on its radio range R. All nodes
that fall within the communication radius R of a particular node are taken as its
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neighbors, all of whose locations are then communicated to this node. In our
simulations we take this communication radius R in terms o f pixels. So, if R is 25,
then, every node located within 25 pixels of a particular node would be its neighbor.
We also assume that there is an underlying protocol that takes care of all the
necessary communication of information within the network.
We use gray-scale image files as an environment on which these image processing
algorithms can be simulated. These images create an effective platform to carry out
the simulations since sensor nodes can be randomly deployed as points on these
images. Sensor measurements are taken as the pixel intensities on which the nodes
lie. The operating range of measurement Is taken as 0-255 (where 0 is low intensity-
black and 255 high intensity-white). For both noise cleaning and edge detection we
test our algorithms using different sensor environments.
2.3.2. Noise Cleaning
2.3.2.1 Methodology
To create distinct simulation environments, we consider two images, one which is
predominantly white, i.e having similar intensity pixel values, and another which has
almost equal high and low intensity pixels with visually apparent differences in pixel
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intensities. Gaussian noise is added to both these images in order to simulate faulty-
sensor measurements. Nodes are then randomly deployed as points on these images.
In Image processing, the mean filter is a 3x3 mask and the filtering is done at every
pixel using the 8 neighbors that surround It. But sensor nodes are not placed in a
regular grid fashion and hence do not have 8 distinct neighbors as do pixels. They
could have more or less than 8 neighbors, since their neighbors are obtained based on
communication range.
In order to appropriately apply the mean filter to sensor nets, we approximate the
effect o f this filter by computing the mean o f all the neighbors that surround a
particular node. Since we assume that every node not only knows the locations of its
neighbors but also their measurements, the node computes the mean of all the
readings so obtained and replaces its original reading with this computed mean.
2.3.2.2 Simulation Results
To analyze the results obtained using our approach, we first execute the conventional
noise cleaning algorithm on a noisy image A, to obtain a filtered image A _l. We
compare A_1 with image A_2 which is obtained by using our noise filtering
technique for sensor nets.
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The metric we use to evaluate the performance o f our algorithm is the mean square
error (MSE), which we define as the mean of the square of the difference in pixel
intensities obtained using the traditional image processing noise cleaning technique
and our noise cleaning technique for sensor nets. We compute this MSE using
images A_1 and A_2.
Figures indicate the variation of MSE based on the communication range o f the
sensor network. From these figures it is clearly evident that error increases as the
communication range of the nodes is increased.
70
65
60
s _55
250
uj45
mAn
m o
§25
J 2 G
15
10
5
0
0 5 10 15 20 25
Communication Range
Figure 2.1: Increase in MSE with respect to increasing communication ranges for an
environment image whose pixels have similar intensity values
-e~ d1 = 800 node s
d2 = 150 nodes
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An explanation for this could be due to the fact that as the communication range is
increased the number of neighbors with which a particular node is averaging out its
value also increases - The probability that a node can average its value with
uncorrelated sensor readings increases, thus increasing the mean square error. The
performance o f these algorithms also depends heavily on the environment in which
these nodes are placed. In figure 2.1 the variation in the MSB is not as significant as
is in figure 2.2. The image environment used for figure 2.2 Is more uncorrelated than
figure 2.1 due to the presence of pixels with distinct pixel intensity variations. Thus
an obvious increase in error with the increase in communication range for this figure
is apparent.
Figures 2.3 and 2.4 indicate that density of deployment also has a substantial impact
on the performance of this algorithm. As is apparent from these figures, for this
algorithm to work favorably, not only must there be an optimal value of density and
communication range, but there also must exist correlated sensor readings. Figure
2.4 shows that the increase in the density of deployment has an adverse effect on the
MSE value. For small radio ranges, the performance of the mean filter improves with
high density, but for large radio ranges, the performance drops drastically even with
increase in density.
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800
•a™ d1 = 800 nodes
-0- d2 = 150 nodes
700
§400
co
§300
CD
^200
100
0
0 5 10 15 20 25 30
Communication Rartqe
Figure 2.2: The MSE increases significantly with increasing communication ranges
when an environment image with distinct pixel intensity variations is used.
2.3.3. Edge Detection
2.3.3.1 Methodology
Similar to noise cleaning, the image environment is an image with the white segment
of the image representing the phenomena. We again use two different images as
shown in figure 2.5, one with a definite edge and the other with a curved edge.
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200
5150
£
H I
f f i
tu rn
5 3
g.100
c o
C
< 3
< D
2 50
°0 500 1000 1500 2000
Density
Figure 2.3: MSE decreases with increasing densities when an environment image
with similar pixel intensities is used.
k*-..
+ * '* A
Radio Range 2
-H3- Radio Range 20
~ s - Radio Range 50
300
250
O
ffiOO
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< 5
g-150
T O
§100
s
50
Radio Range 2
- 0 - Radio Range 5
— M Radio Range 7
- ~ © -
500
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- s . .
1000
Density
1500 2000
Figure 2.4: MSE decreases with intensity when communication is low and increases
with intensity when communication range is high for environment image with
distinct pixel intensity variations.
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Every node determines locally whether it lies on an edge or not, by applying the
Prewitt Filter. The fundamental difference between pixels in an image and sensor
nodes is that the sensor nodes do not have spatial regularity o f information like
pixels in an image. Most image processing algorithms rely on the fact that
information is regularly placed, but sensor nodes are usually deployed in a random
fashion. Hence, the Prewitt mask cannot be directly applied. Due to random
deployment there could be a case where nodes may not have neighbors that fall into
a particular sector of the mask.
Under these conditions, the values for nodes in those sectors are assigned the value
of the node that is computing the edge, which is the central node. Conversely, there
could be multiple nodes in a sector. In such a case, the sector value assigned is the
mean of all node values lying in that sector. Every node determines the values of
both x and y gradients by applying the mask. The magnitude of this gradient G is
then computed. If the gradient is greater than a certain threshold T the node deems
itself present on the edge.
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Figure 2.5: The scattered points on the environment images indicate the edge nodes
obtained by the sensor network localized edge detection algorithm. For a higher
communication range (top and bottom left) many nodes show up as edge sensor
nodes but they may be farther from the actual edge on average; the reverse occurs at
a lower communication range (top and bottom right).
2.33.2 Simulation Results
To analyze the performance of this algorithm, we define a metric mean offset as the
distance between the edge obtained using the sensor nodes and the edge as obtained
using a traditional image processing technique on the image. We calculate this mean
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offset in two ways, one as the mean distance between every edge sensor from the
closest edge pixel and the other as the mean distance between every edge pixel to its
closest sensor.
Through simulations we leam that the algorithm works best only when the density of
the nodes is extremely high. For smaller densities, the edge is not as definitive as it is
for high densities. This again is due to the fact that the image processing algorithms
work best only when there is dense spatial regularity o f information. As can be seen
from figures 2.6 and 2.7 the mean offset of the edge nodes from the closest edge
pixel decreases as communication range increases. Whereas, the mean offset of the
actual edge to the closest edge node increases as the communication range increased.
®
sg
o
c
m
®
2
60
50
AO
30
20
10
0.
- a - Mean offset of ed ge nodes from ed ge
Mean offset of ed ge from edge nodes
n— B~g-~
5 10 15
Communication Range
20
Figure 2.6: Variations in mean offset with communication range for 1750 nodes on
image 1
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£40
Mean offset of edge nodes from edge
■-B- Mean offset of edge from edge nodes
-o
Communication Range
Figure 2.7: Variations in mean offset with communication range for a density of
2052 nodes on image 2
We also choose another metric n/d to determine the optimal performance o f this
algorithm which we define as the number o f edge nodes/mean offset, n/d when
plotted against communication range for various densities, gives us the optimal
communication range for a given density. As seen in figures 2.8 and 2.9, the peak of
the curve determines the optimal communication range. Also, from figure 2.10 we
can see that the value of this optimal communication range decreases as the density
increases.
2 2
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given density o f nodes, for image 1.
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d1 = 2052 nodes
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d5 = 3 1 5 nodes
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2.4. Naive Edge Detection:
2.4.1 Simulation Framework
To compare the performance of the complex image based processing technique, we
implement a naive edge detection scheme based on neighborhood comparison. In
this scheme, when a node senses that it is inside the area, it compares its sensed
value with that of its neighbors. If even a single neighbor reads a value different
from that node, then the node gives itself the status of an edge node. We compare the
performance o f both naive edge detection and image-based edge detection scheme
using similar metrics as described in section 2.3.2. However, we test the performance
24
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of these algorithms in a slightly modified simulation framework. We assume that the
phenomenon is expanding at a constant rate Er. Both the image-based and naive edge
detection techniques are suited for static phenomena. In order to apply these static
edge detection techniques to a dynamic phenomenon we consider instantaneous
snapshots of the sensor environment at which nodes periodically perform edge
detection.
2.4.2. Simulation Results
A phenomena or target area is considered to be expanding at a constant rate. As the
node senses that it is inside the area, it computes whether it is a boundary node or
not. If a node deems itself a boundary node, it lights up. The process continues as the
area expands, changing the boundary nodes at each expansion. To determine whether
a node is a boundary node or not, it can do one of two things. The first is to use the
image processing based edge detection technique as mentioned in above, and the
second is a naive technique to determine its edge status. We compare the
performance o f both image-processing-based edge detection and the nai've edge
detection techniques. To analyze the performance, we use similar metrics as those
used for image-based edge detection. From table 2.1 we learn that for both high and
low densities o f deployment the naive edge detection technique performs comparable
to the image-processing based technique.
25
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Figure 2.11: Edge detection of an expanding phenomena using naive detection
strategy.
Naive Edge
Detection
Image-based Edge
Detection
Density = 1:4 2.22 1.92
Density = 1:2 2.63 2.04
Table 2.1 Mean offset values o f naive and image-based edge detection techniques for
high and low densities
2 6
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2.5 Conclusion:
In this chapter we have described a boundary detection algorithm that determines the
boundary of a diffuse phenomenon. We studied the application o f image processing
based algorithms to detect boundaries in sensor networks and also to clean noisy
sensor environments. Our results indicate that these algorithms work efficiently if an
optimal communication range and density o f deployment is chosen. We evaluated
the performance of complex image-based techniques with a naive edge detection
scheme and noticed that the naive technique performs comparable to the image-
based scheme.
2 7
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Chapter III
Tracking Spatially Diffuse Phenomena
3.1 Assumptions and Simulation Model
We consider a sensor network of a given density of nodes deployed in a 275x175
unit region where a dynamic spatially diffused phenomenon such as an oil spill,
exists. Every node is assumed to have a unique node ID. We consider two cases in
which tracking and detecting a dynamic area is essential - one where the
phenomenon is expanding at a certain rate and the other wherein the phenomenon is
moving with a given velocity. In the expanding case the size o f the phenomenon
changes over time, but in moving case the size of the area remains constant. All
nodes inside the area at the given point in time are assumed to have a reading of 1
unit and nodes outside are assumed to read a value based on the noisy sensor
gradient that decays as the nodes move farther away from the phenomena. We also
assume that every node is aware of its position in space in terms of its (x,y)
coordinate and that o f its neighbors which lie within a sensing radius of R units from
the node. For experimental analysis we consider the shape of the phenomenon to be
circular. In the following few sections we discuss the details o f the protocol that we
propose to detect and track the boundary of a dynamic spatially correlated diffuse
28
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phenomenon. We also discuss a localized querying and data gathering technique
wherein the network locally gathers and processes data relevant to the query.
All our experiments and simulations were done using Java (Swing and Graphics
AWT).
3.2 Sensor Gradient-based Querying
To route the queries we use a sensor gradient-based routing. We assume that the
information gradient in the nodes decays as the nodes are located farther away from
the target area. We add uniformly distributed noise to the gradient to make our
assumption realistic. The equation for the gradient value at every node outside the
phenomenon is given as
Gi — 1 /d 2 + £
where Gi is the gradient value of a given node i, d is proportional to the distance of
that node from the edge of the area, and e is noise added.
The query is routed using a gradient-based random walk until it reaches any node
inside the phenomenon. Once inside the target area the query uses temporal
information, if any, or the network topology until it is resolved. By temporal
information we mean, the query uses time stamps o f nodes that have once seen the
29
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phenomenon by are no longer inside it in order to route itself towards the
phenomenon. In the next section we will discuss in detail about the adaptive network
topology formation by nodes inside the phenomenon. The query could use the
current network topology o f nodes in order to reach the root node, which contains
information needed by the query to get resolved.
We consider different types of queries, which may seek information about the rate of
expansion of the target, or the center of origin of this area or shape o f the area. The
query calculates the expansion rate based on the difference in times at which two
nodes determined their edge status, divided by the distance between those nodes. If
the time difference o f the two edge nodes that the query has seen is zero, the query
moves on and gets resolved only it comes across two different edge node times. The
center of origin o f the area is determined based on maximum time that a node has
been inside the network. In the event o f a tie, the query uses the node IDs as a
tiebreaker. This at times may not accurately determine the center o f origin, but
provides a definite approximation.
To gather any information regarding the network, the query will have to reach the
root node of the adaptive network topology in order to get the required data. Sections
that follow will discuss query times for network topology formation.
30
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Figure 3.1: Querying an expanding phenomenon for expansion rate based on naive
edge detection strategy
3.3 Adaptive Network Topology Formation
We propose a technique to track the extent of the dynamic phenomenon by forming a
network among nodes present inside the area that is covered by the phenomenon for
efficient data collection and processing. We use the spanning tree algorithm to form
a connectivity graph inside the area. The idea is to elect a root node using the
spanning tree algorithm, which will entail the responsibility o f answering any query
that comes into the network. Our motivation behind the tree formation is to minimize
query processing time and to also avoid flooding the network to resolve a query.
Although the tree formation does involve considerable amount of message
exchanges which is proportional to energy spent, we believe that the energy utilized
for this is lesser than that required to flood the network. We consider two metrics for
31
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tree formation and through experiments leam that one of them performs better than
the other in terms of cost effectiveness.
The spanning tree algorithm ensures that a root node is formed based on some metric
and also a shortest path is formed between every node inside the area to the root
node. The algorithm works as follows. At the beginning, every node is given a preset
status as a root node. Every node communicates with its neighbors to determine
which node has the highest metric value, and the one with the highest metric
becomes its next hop. If none of the neighboring nodes has a metric value higher
than itself, the node does not change its status of being the root node. All nodes
continue with this process until all of them converge on a single node as the root
node. At the end o f the tree formation, a shortest path between every node to the root
node is formed.
Once the network topology is established, continuously fluctuating edge nodes send
their information to the root node through the shortest path. Thus the root node
periodically receives updates regarding the status of the edge nodes. Since the root
node has most o f the network information, it will enable efficient query handling. All
queries can be directed to the root node to retrieve information regarding the
network. For example, queries can determine the number of edge nodes, shape of
phenomenon, rate of expansion. We implement and test the algorithm described
algorithm for both the moving and expanding scenarios.
32
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3.4 Simulation Results
3.4.1 Expanding Phenomena
We consider that a phenomenon is expanding at a certain rate in a given region of
sensor deployment. Here we assume that the area is originally a point in the network,
and expands by a certain radius after constant intervals of time. At the instant when a
sensor node senses that it is covered by the phenomenon, it communicates with its
neighbors to first determine whether it is an edge node or not. It then starts to
compare its metric with that of its neighbors thus starting the tree formation process.
All nodes inside the area carry out this process, thus building the tree. We consider
two metrics for the tree formation and discuss below the pros and cons of using
them.
The first metric is based on the maximum time that a node has been inside the area.
Thus, the node that is elected as the root node will be one that has been inside the
area for the longest period o f time. In the event that two nodes record the same time
that they have been inside the area, we use their node IDs as a tiebreaker. Every time
a new node discovers that it is inside the region, the tree will not have to be built
from scratch. This node will get appended to the already existing tree. The tree is
built from basics only for the very first expansion of the phenomena. This being the
case, the root node does not change throughout the expansion. From figures 3.3 and
33
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3.4 we notice that the number of messages exchanged by the nodes inside the area
depends on the radius of area and also on the communication radius o f the nodes.
The second metric however is based only on node ID. In this case, the node that has
the highest node ID will be judged the root node. As the region expands, the node
that was Initially the root node need not necessarily be elected the root node for the
next expansion level, since there could be another node that has a node ID higher
than the already existing root node. Because of this, the tree will have to be re
constructed each time the area expands. Figure 3.2 shows a screenshot o f using both
nodelD and nodeTime metrics.
Our simulation results as shown in figure 3.5 illustrate the cost associated with using
these metrics. This can be seen clearly in both cases from figures 3.3 and 3.4. We
learn that the cost associated with the node time metric is significantly lesser than the
cost associated with using node id as the metric. Although using the node time metric
comes at the cost o f the single point of failure, we believe that savings in terms of
cost is much more essential as compared to the impending risk o f being a single
point of failure.
3 4
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Figure 3.2: Comparison of network topology generation based on metric chosen for
root node election for. an expanding phenomenon
Figures 3.6 and 3.7 show screen shots of queries based on random walk as well as
query based on the sensor gradient. Clearly from these figures, the sensor-gradient
based query routing scheme performs better. Figure 3.8 illustrates the number of
hops taken by the query to get resolved for varying levels of noise in the gradient,
when the optimal metric is used for tree formation. We notice that the number of
hops required for the query to get resolved decreases as the radius o f area increases.
35
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-Range = 12
-Range = 10
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20 40 60 80
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Figure 3.3: Number of messages exchanged to build/append tree when node time is
used as the metric for tree formation.
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♦ —Range = 12
• —Range = 10
Range = 8
Figure 3.4: The cost incurred in building the tree each time when random node id is
used as a metric for tree formation.
36
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100000
90000
80000
70000
60000
50000
40000
30000
20000
10000
0
- Node Time Metric
• Node ID Metric
10 20 30 40 50 60 70 80
Radius of area
Figure 3.5: Using node time as the metric for tree formation scores over using node
id as the metric in terms of the number of messages exchanged by the nodes, which
is proportional to the energy expended in the network.
Start ' ; Query Stop ;
Figure 3.6: Query routed based on a random walk. The query takes very long to
converge since it is a random walk.
3 7
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! Stan ; I Queiy ; i Stop
Figure 3.7: Query being routed using a less noisy sensor-gradient-based technique
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—♦— Noise = 0.01
Noise = 0.1
.N oise = 0.5
— Noise = 1
Radius of Area
Figure 3.8: Number of hops taken by query to converge for varying noise levels
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3.4.2 Moving Phenomenon
Here, we assume a circular region of a given area that is moving across the sensor
network at a constant speed. Every time a sensor node comes under the influence of
this region, it communicates with its neighbors to determine its next hop in order to
be able to reach the root node. As in the expanding case, we consider the
performance of the tree formation algorithm for both the node time metric and node
ID metric.
, < .
■Q'=i j . i v' i-Vi:1 ;:-
Figure 3.9: Screen shot for detection, tracking and querying for a moving
phenomenon.
3 9
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3000
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2000
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1000 -|
500
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■ NodeTime as Metric
0 20 40 60 80 100 120 140
Position of area
Figure 3.10: Cost associated with using node ID and node time as metrics to resolve
the query for varying positions of the area in the network.
Our results indicate that the choice o f metric for the moving phenomena does not
matter, as seen in figure 3.10. The cost associated with both metrics is approximately
the same. This is because there is a very high possibility that if a given node is
present inside the region at one instant may not be present inside the region at the
next instant. Since nodes under the influence of the region are constantly being
added and removed, the tree will have to be re-built each time the area has moved by
a certain distance. As before, we compare the number o f hops taken by the query to
reach the root node as the position of the area changes over time. From figure 3.11
we can see that the number of hops taken by the query to get resolved increases as
40
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the target area moves further away from the where the query is injected into the
network. In our simulations we consider that the query is always injected from one
comer o f the network. Hence the results shown in figure 3.11 are rather intuitive.
However, we also notice that for a noisier gradient the query takes much longer to
converge.
300 i
250 -
■*— Noise = 0.001
♦ —Noise = 0.01
Noise = 0.1
Noise = 0.5
■ * — Noise = 1
c 200 J
150 -
a
f 100 -
■ g 50 -
100
Position of area
Figure 3.11: Number o f hops taken by query to reach the root node as the position of
the area changes over time and for varying noise levels.
3.5 Conclusions
In this chapter we have described an algorithm to detect and track dynamic
phenomena. We also discussed efficient data gathering and querying techniques in
41
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sensor networks. Our results indicate that simpler techniques such as naive edge
detection perform just as well as the more complex image-processing-based edge
detection. A gradient-based query routing technique performs much better than
random walk.
4 2
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Chapter IV
Conclusions
In this thesis we proposed boundary estimation techniques for dynamic dispersed
phenomena based on classical image-processing algorithms. There were several
challenges involved in adapting image processing techniques to sensor networks.
Firstly, unlike pixels in an image, sensor nodes are randomly deployed and
determine their neighborhood based on their communication ranges. Through slight
modifications, we were successful in adapting image processing based boundary
estimation technique to sensor networks.
Though the main focus of our work was to investigate the application of image-
processing based edge detection techniques in sensor networks, we also considered
another widely studied area in image processing, that of noise removal. We proposed
to use the mean filter to mitigate the noise in sensor readings. We showed that for
small radio ranges, the performance of mean-filter improves with higher density,
while for larger radio ranges, it deteriorates with higher density.
For image processing techniques to work efficiently in sensor fields, our results
indicated that the optimal choice of communication range depends critically upon the
44
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density of deployment and vice-versa. We showed that for a fixed density, the
performance initially improves with radio range, but after an optimal point, it
deteriorates with increasing radio range. The optimal radio range for edge-detection
decreases with increasing sensor density. However, image processing based
techniques are computationally very intense. We compared the performance of
complex image-based technique with a naive technique that was based on
neighborhood comparison of sensed readings. We used similar metrics as those of
image processing to compare and contrast the performance of the naive technique
with that of the image-based technique. We showed that using the naive technique
performs comparably to the image based technique. However, with an optimal
choice of communication ranges and densities of deployment, the image processing
technique does perform more efficiently than the naive technique. However, there is
a trade-off of the complexity and the accuracy between the image-based and the
naive technique. We showed that both these techniques work well for static
phenomena. If we consider static snapshots of dynamic phenomena at given
instances of time these techniques could be used to detect boundaries of dynamic
phenomena as well.
By far, most o f the work related to tracking in sensor networks dealt only with single
point tracking. In this thesis, we presented a scheme to track dynamic dispersed
phenomena using adaptive network topology formation and efficient querying
techniques. We proposed a noisy sensor-gradient-based-querying as an efficient way
45
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to route queries in the network in order to collect information on the network
dynamics. Every node that was outside the phenomenon recorded a gradient value
that decayed as the nodes moved farther away from the edge o f the network. Our
work on edge detection dealt only with determining the edge nodes. In order to
obtain more information about the network dynamics such as expansion rate, shape
of phenomenon, we proposed an efficient querying mechanism. For noisy sensor
gradients we noticed that the query took much longer to converge than for sensor
gradients with less noise. Irrespective of noise levels, we showed that the gradient
based querying method performs better than a random walk in routing the query.
We proposed an adaptive network topology formation mechanism that makes use of
the spanning tree algorithm to form a connectivity graph among the nodes that are
inside the network. We evaluated the performance of the root node election based on
certain metrics. For experimental simplicity concerns we considered the
phenomenon to be circular, we argue that our algorithms are scalable to any arbitrary
shape.
As future work, we would like to compliment our simulation-based results with
pertinent mathematical analysis.
4 6
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Asset Metadata

Creator Devaguptapu, Divya (author)

Core Title Boundary estimation and tracking of spatially diffuse phenomena in sensor networks

School School of Engineering

Degree Master of Science

Degree Program Electrical Engineering (Computer Networks)

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

Tag engineering, electronics and electrical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Krishnamachari, Bhaskar (committee chair), Helmy, Ahmed Abdel-Ghaffar (committee member), Psounis, Konstantinos (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-310629

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