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Volume rendering of human hand anatomy
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Volume rendering of human hand anatomy
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Content
VOLUME RENDERING OF HUMAN HAND ANATOMY
by
Jingtao Huang
A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(COMPUTER SCIENCE)
August 2022
Copyright 2022 Jingtao Huang
Dedication
To my grandparents, in loving memory.
ii
Acknowledgements
I would like to thank my advisor, Jernej Barbič, for his exemplary guidance, support, and encouragement
during my master’s degree. A special thanks to my friends Mianlun Zheng, Bohan Wang, Rongxin You, and
Yuanhan Zhang for their inspiration and friendship. Finally, I thank my loving parents for their constant
and unconditional support.
iii
TableofContents
Dedication ii
Acknowledgements iii
ListofTables vi
ListofFigures vii
Abstract ix
Chapter1: Introduction 1
1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter2: TheoreticalBackground 4
2.1 Volume Rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Volume Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Optical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.3 Volume Ray Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.4 The Volume Rendering Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.5 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.6 Compositing Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Human Hand Anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Skeletal System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.2 Muscular System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Vascular and Nervous System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.4 Integumentary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter3: RelatedWork 19
3.1 Volume Rendering Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Design of Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Volume Rendering of the Human Hand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Chapter4: VolumeRenderingPipelineforHandAnatomy 24
4.1 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Volume Traversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
iv
4.4.1 Material Assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.4.2 Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4.2.1 Interior-Emphasized Style . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.4.2.2 Fat-Emphasized Style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.5 Pre-Multiplication with Opacity, and Final Composition Equations . . . . . . . . . . . . . . 37
Chapter5: Results 38
5.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Results and Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter6: Conclusion 48
6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Bibliography 50
v
ListofTables
4.1 Transfer functions for interior-emphasized style. . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 Transfer functions for fat-emphasized style. . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.1 Software environment and hardware specification. . . . . . . . . . . . . . . . . . . . . . . . 39
5.2 Specifications of meshes of all hand tissues. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3 The time cost for each animation sequence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
vi
ListofFigures
2.1 Volume data represented by a discrete uniform grid. . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Interactions between light and particles that affect the energy along the light ray. . . . . . 5
2.3 Ray-casting principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Bone anatomy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 The bones and joints of the human hand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 Muscles of the human hand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.7 Tendons of the human hand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.8 Nerves, veins and arteries of the hand. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.9 Types of blood vessels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.10 Different layers of the skin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1 The classification of transfer functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Examples of volume rendering from related work. . . . . . . . . . . . . . . . . . . . . . . . 23
4.1 MRI slices and corresponding mesh geometry in the neutral pose. . . . . . . . . . . . . . . 25
4.2 Volume rendering without and with stochastic jittering of the sampling positions. . . . . . 26
4.3 Tri-linear interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.4 An example of material assignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.5 Comparison of renders without and with priority assignment. . . . . . . . . . . . . . . . . 30
4.6 Comparison of segmented bone renders between “3D slicer” and our method. . . . . . . . 31
vii
4.7 Volume rendering with interior-emphasized style. . . . . . . . . . . . . . . . . . . . . . . . 32
4.8 Frequency histogram of MRI values in the neutral pose. . . . . . . . . . . . . . . . . . . . . 34
4.9 Volume rendering with fat-emphasized style. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.10 Venous system of the hand with annotation. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.1 “American Sign Language”: letters A to E, rendered with "interior-emphasized" style; front
and back view. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 "Numbers 1-5", rendered with the “fat-emphasized” style; front and back view. . . . . . . . 42
5.3 “Opposition of the thumb,” rendered from the side view with interior-emphasized and
fat-emphasized styles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.4 Comparison between standard surface rendering and our volume rendering in the “close
the fist” motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.5 Comparison of volume renders of Rhee et al. 2010 and our method. . . . . . . . . . . . . . 47
viii
Abstract
This thesis investigates volume rendering techniques and the design of transfer functions to improve the
visualization of human hand anatomy using medical resonance imaging (MRI). Volume rendering of the
human hand is a challenging but crucial problem for understanding hand anatomy in three dimensions.
The hand is inherently complex, and it is difficult to design volume rendering transfer functions that are
suitable for each specific application. We first introduce the fundamentals of volume rendering and hand
anatomy, and discuss the related work on hand anatomy visualization. Then, we propose a ray-casting
pipeline that uses both the hand MRI volume data, and the geometry of its inner structures and their
known segmentation, permitting fine control over the appearance of each tissue. Additionally, we devise
two sets of transfer functions to emphasize different hand tissues of interest, while preserving the visual
context of the hand, inspired by the concept of "focus-plus-context." We also present pipeline extensions
to tackle several artifacts of standard volume ray-casting. We evaluate our volumetric rendering on five
challenging hand motion sequences. Finally, our experimental results show that our volumetric rendering
improves hand anatomy visualization, compared to standard surface and volume rendering techniques.
ix
Chapter1
Introduction
The human hand is a vitally important part of the human body. Hands are capable of a wide range of
precise motions due to their delicate and complex structures. Each hand consists of 27 bones, 34 muscles,
over 100 ligaments and tendons, and many blood vessels and nerves, all confined into a small volumetric
region. Visualizing the hand anatomy can help us understand its underlying structure and functionality,
and visualize how anatomy inside the human hand moves under realistic hand motions.
Unlike surface rendering, volume rendering of medical image scans, such as magnetic resonance imag-
ing (MRI), and computerized tomography (CT) data, can visualize the underlying interior structures. MRI
scanning is preferable over CT since it is non-invasive and involves no ionizing radiation, and because it
has a better contrast on soft tissues. However, volume rendering is challenging due to the following facts:
(1) volume rendering is computationally more expensive than surface rendering; (2) the design of transfer
functions, a crucial component of volume rendering, is a manual, tedious, and time-consuming process;
(3) special attention needs to be paid to avoid rendering artifacts.
The MRI signal is a scalar-valued quantity available at points of a regular 3D grid with some small
resolution (typically around 1mm). As such, the MRI signal alone has no color or opacity, it is a simple
grayscale value, and there is no a prior way of mapping it to colors. By opacity we mean the standard
transparency quantity in computer graphics, i.e., opacity=0 means a fully transparent object, and opacity=1
1
is a fully opaque object, and the in-between values indicate partial transparency. A transfer function maps
the MRI intensity value to optical properties such as the (R, G, B) color and opacity. Essentially, a transfer
function is a “colormap” that determines how the scalar-valued MRI values are converted into color and
opacity. The transfer function is a critical ingredient of volume rendering, and its selection is highly
non-trivial for biological tissues. A key contribution of this thesis is how to select the transfer function,
potentially on a spatially-varying or per-tissue basis, to produce high-quality volume renderings of the
human hand.
1.1 Objectives
This thesis aims to explore volumetric rendering of the human hand’s internal anatomy, specifically to
improve the visualization of hand MRI volume data. To do so, we define the following objectives:
• Implement the state-of-the-art volume rendering method, namely the volume ray casting [17] (re-
ferred to as “ray casting” in this thesis), to visualize MRI volume data directly. Ray casting evaluates
the volume rendering integral by casting a ray into the volume, and integrating the optical properties
along the ray at discrete sample positions.
• Propose a ray-casting-based rendering pipeline that takes not only the MRI volume data, but also
the surface geometry of the internal structures as inputs, and produces high-quality volume renders
that present interior structures with smooth boundaries.
• Study the human hand anatomy and design transfer functions that are suitable for hand tissues,
including bones, muscles, tendons, joint ligaments and fat.
• Test our volumetric rendering method on multiple hand animations. Compare our results with ren-
ders produced by both standard surface-based rendering techniques and volume rendering done by
related work.
2
1.2 Outline
The remainder of this thesis is organized as follows. Chapter 2 explains the theoretical background of
volume rendering and human hand anatomy. Chapter 3 introduces the related work. Chapter 4 describes
our volume rendering method and our choice of the transfer function. Chapter 5 presents the experimental
results. Finally, Chapter 6 concludes this thesis with a summary and potential future work.
3
Chapter2
TheoreticalBackground
2.1 VolumeRendering
The material in this section follows the ray casting algorithm and descriptions as given by [9] and [27];
we modify it as needed to accommodate our hand volumetric rendering.
2.1.1 VolumeData
Different from surface rendering, volume rendering visualizes information from a 3D volumetric data,
which can be written as a mapping
ϕ :R
3
→R,
from 3D space to a scalar value. The 3D scalar field, defined on a discretized grid, typically comes from
measurements or simulations, and each volume element (called voxel) represents a unit of space, as illus-
trated in Figure 2.1.
2.1.2 OpticalModels
Volume rendering treats volume as a distribution of light-emitting particles of certain densities. Thus,
it can display the volume data by evaluating an optical model which describes how the volume emits,
4
Figure 2.1: Volume data represented by a discrete uniform grid.
(a) emission (b) in-scattering (c) out-scattering (d) absorption
Figure 2.2: Interactions between light and particles that affect the energy along the light ray.
scatters, and absorbs light. To achieve this, scalar value is mapped to physical quantities that describe
the light interaction at the respective point in 3D space. This mapping performs the classification, and is
usually considered to be a part of the transfer function. The physical quantities are then used to synthesize
images. The following types of interaction are usually taken into account:
Emission. The particle actively emits light (Figure 2.2a), increasing the radiative energy.
Scattering. The particle scatters light, essentially changing the direction of light propagation, increasing
or reducing radiative energy along a light ray. Through in-scattering (Figure 2.2b), additional energy
is redirected into the direction of the ray; conversely, out-scattering (Figure 2.2c) removes energy
from the current ray.
Absorption. The particle absorbs light (Figure 2.2d) and converts radiative energy into heat.
5
Figure 2.3:Ray-castingprinciple. For each pixel, one viewing ray is traced. The ray is sampled at discrete
positions to evaluate the volume-rendering integral.
There are a few optical models [24] for volume rendering: emission only, absorption only, absorption
plus emission, scattering and shading/shadowing, and multiple scattering. Among them, the emission
plus absorption model is the most widely used, because it provides a good compromise between generality
and efficiency of computation. In this model, the particle can emit light and absorb incident light while
scattering and indirect illumination are neglected.
2.1.3 VolumeRayCasting
Volume ray casting [17] is the most basic, but also the most flexible volume rendering algorithm. The basic
idea is to evaluate the volume-rendering integral (Section 2.1.4) along camera rays directly. As illustrated
in Figure 2.3, for each pixel in the rendered image, a single ray is cast into the volume. At equispaced
intervals along the ray, the discrete volume data is resampled, usually using tri-linear interpolation (more
on Section 4.3) as the reconstruction filter. After resampling, the scalar data value is mapped to optical
properties by means of a transfer function, yielding an RGBA quadruplet that includes the corresponding
emission and absorption coefficients for this location. The volume rendering integral is then approximated
via either front-to-back or back-to-front compositing (section 2.1.6), where usually the former is used in
ray casting.
6
2.1.4 TheVolumeRenderingIntegral
We denote a ray that has been cast into the volume by x(t), and parameterize it by the distance t from
the camera. The scalar MRI value corresponding to a position along the ray is denoted bys(x(t)). For the
emission plus absorption model, absorption coefficients κ (accounting for absorption of light) and emissive
color c (accounting for radiant energy actively emitted) can be simplified as function of the distance t
instead of the scalar values:
c(t):=c(s(x(t))),
κ (t):=κ (s(x(t))).
If this model are employed, the volume rendering integral integrates absorption coefficients κ (t) and
emissive colorsc(t) along a ray:
C =
Z
∞
0
c(t)e
− τ (0,t)
dt, (2.1)
where the term
τ (d
1
,d
2
)=
Z
d
2
d
1
κ (
ˆ
t)d
ˆ
t, (2.2)
is defined as the opticaldepth between distancesd
1
andd
2
. It measures how long the light travels before it
is absorbed. Smaller values of optical depth mean that the participating medium is more transparent, and
higher values mean that it is more opaque. The emissive colorc(t) has three components (R, G, B); each
component is treated separately. Also note thatc(t) must already be pre-multiplied with opacity, i.e., it is
the (R, G, B) returned by the transfer function, multiplied by the opacity given by the transfer function;
this is called associated color [36].
7
2.1.5 Discretization
The main goal of volume rendering is to compute the volume-rendering integral (Equation 2.1). Typically,
the integral cannot be evaluated analytically. Instead, numerical methods are applied to find an approxi-
mation as close to the exact value as possible.
The optical depth τ (Equation 2.2), which is the cumulative absorption up to a certain position x(t)
along the ray, can be approximated by a Riemann sum
τ (0,t)≈ ˆ τ (0,t)=
⌊T/∆ t⌋
X
i=0
κ (i· ∆ t)∆ t, (2.3)
with ∆ t denoting the distance between successive sampling locations. The summation in the exponent
can immediately be substituted by a multiplication of exponentiation terms:
e
− ˆ τ (0,t)
=
⌊T/∆ t⌋
Y
i=0
e
− κ (i·∆ t)∆ t
. (2.4)
Now, we define the opacity as α i
=1− e
− κ (i·∆ t)∆ t
, and rewrite Equation 2.4 as:
e
− ˆ τ (0,t)
=
⌊T/∆ t⌋
Y
i=0
(1− α i
). (2.5)
This allows the opacityα i
to be used as an approximation for the absorption of thei-th ray segment,
instead of absorption at a single point.
Similarly, the emitted color of the i-th ray segment can be approximated by
C
i
=c(i· ∆ t)∆ t. (2.6)
8
Having approximated both the emissions and absorption along a ray, we now arrive at the approximate
evaluation of the volume rendering integral as (denoting the number of samples byn=⌊T/∆ t⌋)
ˆ
C =
n
X
i=0
C
i
i− 1
Y
j=0
(1− α j
), (2.7)
which can be evaluated iteratively by performing either front-to-back or back-to-front compositing. We
note that Equation 2.7 is evaluated separately for each color channel R, G, B.
2.1.6 CompositingSchemes
Equation 2.7 can be evaluated iteratively in front-to-back order by steppingi from1 ton:
C
′
i
=C
′
i− 1
+(1− α ′
i− 1
)C
i
,
α ′
i
=α ′
i− 1
+(1− α ′
i− 1
)α i
.
(2.8)
New valuesC
′
i
andα ′
i
are calculated from the colorC
i
and opacityα i
at the current locationi, and from
the composited colorC
′
i− 1
and opacityα ′
i− 1
at the previous locationi− 1. The starting condition isC
′
0
=0
andα ′
0
=0.
The alternative iterative formulation evaluates Equation 2.7 in back-to-front order by steppingi from
n− 1 to0:
C
′
i
=C
i
+(1− α i
)C
′
i+1
,
(2.9)
A new value C
′
i
is calculated from the color C
i
and opacity α i
at the current location i, and from the
composite color C
′
i+1
at the previous location i+1. The starting condition is C
′
n
= 0. Unlike front-to-
back compositing, back-to-front compositing does not require tracking the alpha values.
9
2.2 HumanHandAnatomy
The structure of the human hand is extremely complex. It is composed of bones, joints, ligaments, muscles,
tendons, blood vessels, nerves and skin. Bones are linked with joints. The hand has ligaments that hold the
bones and cartilage together and provide flexibility. Muscles and tendons connect the bones, and through
activation, create contractile forces and torques that bend the joints. The descriptions of the anatomy in
this section were obtained using public medical websites ([25], [2], [7]), and were then condensed and
paraphrased for consistency and clarity.
2.2.1 SkeletalSystem
Bones provide shape and support for the hand; they also serve as a storage site for minerals and provide
the medium (marrow) for the development and storage of blood cells. They are made up of compact bone,
spongy bone, and bone marrow, as illustrated in Figure 2.4. Compact bone makes up the outer layer of
the bone. Spongy bone is found mostly at the ends of bones and contains red marrow. Bone marrow is
located in the center of most bones and has many blood vessels. There are two types of bone marrow: red
and yellow. Red marrow contains blood stem cells that can become red blood cells, white blood cells, or
platelets. Yellow marrow is made mainly of fat.
There are three major types of bones in the hand (Figure 2.5), including:
Phalanges. The 14 bones that are found in the fingers of each hand. Each finger has 3 phalanges (the
distal, intermediate or middle, and proximal); the thumb only has 2 (the distal and proximal).
Metacarpalbones. These 5 bones compose the middle part of the hand.
Carpalbones. These are the 8 bones located in the wrist; they are arranged in two rows. There are
4 bones in the distal row (hamate, capitate, trapezoid, and trapezium); and 4 in the proximal row
(pisiform, lunate, triquetrum, and scaphoid).
10
Figure 2.4: Bones consist of compact bone, spongy bone, and bone marrow. Compact bone makes
up the outer layer. Spongy bone is found at the ends of the bone. Bone marrow is located in the center
of the bone. Image downloaded and adapted from https://commons.wikimedia.org/wiki/File:Bone_Marrow_
in_a_cross-section-FR.svg by Pbroks13 under licence CC-BY-3.0.
Figure 2.5: Thebonesandjointsofthehumanhand. Source: Wikimedia Commons.
11
The joints in our hands are made up of cartilage surfaces that cap the bones, which allows the bones
to glide smoothly against one another as they articulate. There are four types of joints in our hand (Figure
2.5):
Distalinter-phalangeal(DIP)joints. The 5 joints closest to the fingertips.
Proximalinter-phalangeal(PIP)joints. The 4 joints in the middle of fingers.
Metacarpo-phalangeal(MCP)joints. The 5 joints at the base of fingers, referred to as the "knuckles."
Carpal-metacarpal(CMC)joints. The 5 joints located at the bottom of the hand.
The ligaments are tough bands of connective tissue that connect the bones to support them and keep
them in place. Important ligaments of the hand are:
Collateralligaments. Strong ligaments on either side of the finger and thumb joints, which prevent
sideways movement of the joint.
Volarplate. A ligament that connects the proximal phalanx to the middle phalanx on the palm side of
the joint. As the joint in the finger is straightened, this ligament tightens to keep the PIP joint from
bending backward.
Volarradiocarpalligaments. A complex web of ligaments that support the palm side of the wrist.
Dorsalradiocarpalligaments Ligaments that support the back of the wrist.
2.2.2 MuscularSystem
The skeletal muscles are responsible for the movement of the hand and fingers. The dexterity of the
hand comes from the unique configuration of bones, joints, and muscles: flexion , bending in the anterior
direction (e.g., forming a fist); extension, straightening or bending in the posterior direction; abduction,
12
movement away from the center the the hand (i.e., spreading the fingers); and adduction, movement toward
the center of the body (i.e., bring the fingers together). The hand muscles consist of five groups (Figure
2.6):
Thenarmuscles. A collection of three muscles at the fleshy base of the thumb on the palmar side that act
to exert movement of the thumb. The thenar muscles include abductor pollicis brevis (APB), flexor
pollicis brevis (FPB) and opponens pollicis (OP).
Hypothenarmuscles. A collection of three muscles at the fleshy base of the pinky finger on the palmar
side that act to exert movement of the pinky finger. The hypothenar muscles include abductor digiti
minimi (ADM), flexor digiti minimi brevis (FDMB) and opponens digiti minimi (ODM).
Lumbricals. The lumbrical muscles are composed of four muscles that act to flex their respective MCP
joint and extend the PIP and DIP joints.
Interosseimuscles. They are comprised of three palmar interossei (PI) muscles and four dorsal (DI)
muscles.
Adductorpollicis. Adductor pollicis muscle adducts the thumb. It has two heads: transverse and oblique.
Tendons are bands of connective tissue that attach the muscles to the bone, enabling the muscles to
move the bones. The main tendons of the hand (Figure 2.7) are:
Superficialistendons. They pass through the palm side of the wrist and hand, and attach at the bases of
the middle phalanges. They act with the profundus tendons to flex the wrist, MCP, and PIP joints.
Profundustendons. Similar to superficialis tendons, except they attach at the bases of the distal pha-
langes. They act with the superficialis tendons to flex the wrist and MCP and PIP joints. They also
flex the DIP joints.
13
Figure 2.6: Muscles of the human hand. Image downloaded from https://commons.wikimedia.org/wiki/
File:1121_Intrinsic_Muscles_of_the_Hand.jpg by OpenStax under license CC-BY-4.0.
14
Figure 2.7: Tendonsofthehumanhand. © 2022 Elsevier. Image adapted, with permission, from https:
//3d4medical.com under student license.
Extensortendons. They attach to the middle and distal phalanges and extend the wrist, MCP, PIP and
DIP joints.
Flexortendons. Nine long tendons which pass from the forearm through the carpal tunnel of the wrist.
They diverge in the palm, where two go to each finger and one goes to the thumb.
Extensorpollicisbrevisandabductorpollicislongus. They originate from the muscles in the top of
the forearm and enable movement of the thumb.
2.2.3 VascularandNervousSystem
There are three main nerves which supply the hand and wrist, the median, radial, and ulnar nerves, as
shown in Figure 2.8 in yellow. Nerves are like fiberoptic cables that carry signals. The brain sends signals
15
Figure 2.8: Nerves (yellow), veins (blue) and arteries (red) of the hand. © 2022 Elsevier. Image
adapted, with permission, from https://3d4medical.com under student license.
16
Figure 2.9: Typesofbloodvessels. Source: Wikimedia Commons.
down the spine and then through the nerves in the arm to control the muscles. Sensory signals like tem-
perature, vibration, and pain travel from nerves in the hand up the arm, through the spine, and back to the
brain.
Blood vessels are channels that carry blood throughout the body. They form a closed loop, like a circuit,
that begins and ends at the heart. There are three types of blood vessels:
Arteries. Arteries (Figure 2.8 in red) are strong, muscular blood vessels that carry oxygen-rich blood from
the heart to the body. They handle a large amount of force and pressure from the blood flow but do
not carry a large volume of blood. At any given time, only about 10% to 15% of the body’s blood is
in the arteries.
Veins. Veins (Figure 2.8 in blue) do not have to carry highly pressurized blood, but they do have to carry
large volumes of deoxygenated blood back to the heart. Thin, less elastic walls help them handle
high volumes and low pressure. Most veins have valves that open and close. The valves control
blood flow and keep the blood flowing in one direction. About 75% of the blood is in the veins.
Capillaries. Capillaries (Figure 2.9) are the smallest blood vessels that connect arteries and veins at the
finger tip. Capillaries are where oxygen and nutrients are exchanged for carbon dioxide and waste.
17
Figure 2.10: Differentlayersoftheskin. Source: Wikimedia Commons.
2.2.4 IntegumentarySystem
The skin functions as a barrier against the external environment. It prevents fluid loss, provides the sen-
sation of touch, pressure, pain, and temperature. It also performs important functions like Vitamin D
synthesis. The skin consists of three layers, including the superficial epidermis, the dermis in the middle,
and the deep subcutaneous/fatty tissue, as illustrated in Figure 2.10.
18
Chapter3
RelatedWork
3.1 VolumeRenderingAlgorithms
In general, volume rendering methods can be coarsely classified into two categories: indirect volume ren-
dering (IVR), and direct volume rendering (DVR).
IVR or “surface rendering” fits geometric primitives from the volume data and then renders these
primitives. Methods in this category include iso-surfacing [22] and frequency domain rendering [31].
DVR or simply “volume rendering” does not explicitly extract geometric structures from volume data,
but rather renders the volumes based on fuzzy segmentation through the transfer function. Several volume
rendering algorithms have been proposed over the years. Splatting [35] works by virtually “throwing” the
voxels onto the image plane. In the process, every voxel in the object space projects/leaves a splat/footprint
in the image plane that will represent the object. Shear-warp rendering [6][18] is based on a factorization
of the viewing matrix into a 3D shear parallel to the slices of the volume data, a projection to form a
distorted intermediate image, and a 2D warp to produce the final image. Texture slicing [5][32] takes
advantage of GPU hardware to render the volume data represented by the 2D or 3D texture. In volume ray
casting [20][17], which has been described in detail in Section 2.1.3, camera rays are cast into the volume,
optical properties at sample positions are then integrated along these rays, and the results are the pixels
19
that contribute to the final image. Of all volume rendering algorithms, volume ray casting has seen the
largest body of publications and achieves images of highest quality [26].
3.2 DesignofTransferFunctions
Suppose we have a volumetric dataset that contains scalar values that represent some spatially varying
physical property. In general, there is no natural way to obtain emission and absorption coefficients from
such data. Instead, the user must decide how the different structures in the data should look by assigning
optical properties to the data values using an arbitrary (artificial) mapping. Such a mapping is called a
transfer function.
Although a few approaches exist to automatically generate transfer functions by some image- or data-
driven mechanisms [12], the process of finding an appropriate transfer function is in general a manual,
tedious, and time-consuming procedure. It also requires detailed knowledge of the spatial structures that
are represented by the dataset.
Arens and Domik (2010) [1] published a survey of transfer functions for volume rendering in which
they subdivided transfer functions into the following six categories: 1D data-based, gradient 2D [20][15],
curvature-based [13], size-based [8], texture-based [4], and distance-based [30]. Later, a state-of-the-art
(STAR) report of transfer functions for volume rendering was published by Ljung et al. (2016) [21]. This
STAR report classified transfer function research based on the following aspects: dimensionality, derived
attributes, aggregated attributes, rendering aspects, automation, and user interfaces (Figure 3.1).
A transfer function is essentially a special, but important case of a classification . With such classifica-
tion, certain region in the three-dimensional domain are identified to be the same material, such as bone,
vessel, or soft tissue. However, a challenge presents itself when the values of these materials are not stan-
dardized and when they overlap with each other, which makes the material assignment ambiguous. This
problem is particularly pertinent when dealing with MRI data.
20
Figure 3.1: The classification of transfer functions. © 2022 John Wiley and Sons. Reproduced, with per-
mission, from Ljung et al. [21].
Segmentation is the process of identifying or tagging individual voxels as belonging to one of several
materials contained in a volume. Rendering with segmented volume data [28][11] can be seen as an ex-
tension of standard volume rendering, owing to the fact that different segmented regions can be rendered
using different optical properties, via spatially varying classification and/or transfer functions.
3.3 VolumeRenderingoftheHumanHand
The goal of volume rendering of medical scans (CT or MRI) is to provide insight into human anatomy,
such as the geometric shape and function of bones, muscles, tendons, skins, etc. This is a difficult problem
because, when visualizing a three-dimensional dataset, it is in general not possible to concurrently show
all the data. Instead, certain selective representations of the data must be used for visualization.
Laidlaw et al. (1998) [19] proposed an algorithm for identifying the distribution of different material
types in the volume data without explicit segmentation. They allowed for mixture of materials inside a
voxel; therefore stair-case artifacts caused by partial volume effects are reduced. These artifacts are usually
introduced by segmentation algorithms and appear along the boundaries between materials. Different op-
tical properties then can be assigned to different materials for volume rendering. Figure 3.2a demonstrates
21
their result on a MRI hand data. The opacity of different materials is decreased above cutting planes to
show details of the classification process within the hand.
The combination of different rendering styles is of particular interest, as it allows one to put emphasis
on features of interest. Hadwiger et al. (2003) [11] presented a two-level volume rendering approach using
explicit segmentation information, where different objects can have different transfer functions, different
rendering modes that are not only limited to DVR (e.g., iso-surfacing, and non-photorealistic rendering),
and different compositing modes (e.g., alpha blending, maximum intensity projection). The latter capability
enables two-level volume rendering, which consists of one local compositing mode per object, and a second
global compositing level that combines the contributions of different objects. Figure 3.2b shows their result
on a CT segmented hand dataset with different rendering modes. In particular, the skin is rendered with
non-photorealistic contour rendering and MIP compositing, the bones are rendered with DVR, and vessels
are rendered with tone shading.
Bruckner et al. (2006) [3] proposed a context-preserving volume rendering model as a function of
shading intensity, gradient magnitude, distance to the eye point, and previously accumulated opacity to
selectively reduce the opacity in less important data regions. They took inspiration from illustration,
where theghosting is commonly used by artists when they want to visualize specific internal structures as
well as the exterior. The name "context-preserving" is related to the concept of focus-plus-context, which
is well-known in information visualization. Especially interesting subsets of the data, are considered to
be "in focus," whereas the rest of the data merely provides context. Figure 3.2c shows their illustrative
visualization of a CT hand dataset.
Rhee et al. (2010) [28] present the first anatomically accurate 3D volume rendering of the hand MRI
data in motion, including bone animation and soft tissue deformation driven by a joint skeleton. The
bones are segmented from the hand MRIs. In their work, two styles of renders were used. One uses a
22
(a) Laidlaw et al. [19]. © 1998 IEEE. (b) Hadwiger et al. [11]. © 2003 IEEE. (c) Bruckner et al. [3]. © 2006 IEEE.
(d) Rhee et al. [28]. © 2010 IEEE. (e) Wang et al. 2019 [33].
Figure 3.2: Examples of volume rendering from related work. Reprinted with permission.
constant red color for bones, plus semi-transparent skin (Figure 3.2d top); and the other is employs the
volume-rendering program developed by Kniss et al. [14] (Figure 3.2d bottom).
Wang et al. (2019) [33] proposed a system to model and simulate the hand using MRI. They first seg-
mented hand bone anatomy (meshes) in multiple poses from MRI, interpolated and extrapolated them to
the entire range of motion, essentially producing an accurate data-driven animation rig for bones. Then,
they simulated soft tissues using finite element methods (FEM) driven by the bone animation. They visu-
alized their results by compositing the surface renders of the bones and skin together with transparency,
as illustrated in Figure 3.2e. They also published their dataset [34], which is the world’s first dataset of
MRI scans of the human hand in multiple poses.
23
Chapter4
VolumeRenderingPipelineforHandAnatomy
In this section, we give a structural overview of our anatomy volume-rendering pipeline based on the
volume ray-casting algorithm. We propose an extension to this algorithm: given the geometry of the
internal structures, the camera ray can be decomposed into several segments, depending on what objects
are intersected by the ray; individual transfer functions can then be used for different segments, depending
on what objects are traversed. The evaluation of the optical model for volume rendering can be separated
into the following stages: data acquisition, volume traversal, interpolation, classification, and compositing.
4.1 DataAcquisition
Our hand MRI data in the neutral pose (Figure 4.1a) was acquired from the existing dataset created by Wang
et al. (2019) [34]. They used lifecasting materials to generate hand molds to prevent hand movement during
the scanning. The noise outside of the hand regions in their MRI images is actually the air bubbles of the
mold. The neutral pose corresponds to "pose01" in the dataset. In addition, we use their geometry meshes
corresponding to the internal structures. These meshes were segmented from the MRI using the method
described in [33].
The geometry corresponds to the following structures of hand anatomy: skin, bones, muscles, tendons,
and ligaments. All hand bones, including phalanges, metacarpals, and carpals, except the proximal row of
24
(a)MRIslices. Hand has several tissues represented by different MRI intensities.
The image quality in the wrist region is lower than in other regions.
(b) skin: 1 mesh
(c) bones: 23 meshes (d) muscles: 17 meshes (e) tendons: 10 meshes (f) ligaments: 6 meshes
Figure 4.1: MRI slices (a) and corresponding mesh geometry (b-f) in the neutral pose.
carpals were segmented, this is due to the low MRI quality at the wrist region (Figure 4.1a, Figure 4.1c). All
muscles of the hand were segmented (Figure 4.1d). All tendons (except extensor pollicis brevis and abductor
pollicis longus located at the medial side of the thumb) were paired and simplified into rod shapes (Figure
4.1e). Similarly, the ligaments (Figure 4.1f) at 4 MP joints of the index, middle, ring and pinky finger, and
2 PIP joints of the index and middle finger, were segmented and combined into six "capsules" that wrap
around these joints. The numbers of segmented meshes are: 1 for the skin, 23 for bones, 17 for muscles, 10
for tendons, and 6 for ligaments. The extracted geometry closely matches the MRI data: Figure 4.1 shows
the MRI slices and corresponding mesh geometry in the neutral pose.
25
4.2 VolumeTraversal
Following the volume ray casting algorithm, for each pixel of the final image, a viewing ray is cast into
the volume. Ray-object intersections are performed to find a list of all intersections between this ray and
meshes in the scene. These intersections are then sorted by their distances to the camera. After the sorting
is done, the positions of the first and last intersection define the starting and ending point of the sampling,
respectively. If there is no intersections along the ray, no further computation is need and the value of the
corresponding pixel will be the background color. Since empty space outside the hand does not contribute
to the final image, sampling points between outermost intersections of viewing ray and mesh groups is a
reasonable decision, and by doing so: (1) the workload for each pixel is reduced, and hence increasing the
rendering speed; (2) any MRI noise outside the hand caused by the air bubbles in the hand mold (Figure
4.1a) are ignored, improving the image quality.
Figure 4.2: Volume rendering without (left) and with (right) stochastic jittering of the sampling
positions. Wood-grain artifacts can be observed in the left image.
Along the path of the ray, equidistant sampling points can be selected. However, the approximate
discretization of Equation 2.1 into Equation 2.7 may lead to sampling artifacts when the sampling rate is
26
Figure 4.3: Tri-linear interpolation.
too low. This can manifest as “wood-grain artifacts” (Figure 4.2 left). This issue can be alleviated with two
solutions: (1) decrease the distance between sample points, which will also decrease the rendering speed;
(2) add random small offsets to the sampling positions of rays in the viewing direction using stochastic
jittering. We adopted the second solution in our pipeline. Figure 4.2 shows a comparison of two renders
without and with stochastic jittering.
4.3 Interpolation
Since the sampling positions are usually different from grid points, a continuous 3D field needs to be
reconstructed from the discrete grid in order to obtain the data values at the sample positions.
We adopted tri-linear interpolation to interpolate grid MRI values to the entire volume (Figure 4.3).
This is the most common reconstruction method for uniform grids, as it is fast to compute. To simplify the
notation, the following discussion assumes normalized coordinate valuesx,y, andz that are in the interval
27
[0,1] for points within the voxel. Normalized coordinates can be obtained from arbitrary coordinates by
scaling and translation. Tri-linear interpolation between eight pointsv
000
tov
111
is given by:
f(p)=(1− z)(1− y)(1− x)f(v
000
)
+(1− z)(1− y)xf(v
001
)
+(1− z)y(1− x)f(v
010
)
+(1− z)yxf(v
011
)
+z(1− y)(1− x)f(v
100
)
+z(1− y)xf(v
101
)
+zy(1− x)f(v
110
)
+zyxf(v
111
),
where f(v
000
) to f(v
111
) are the function values at the sample points v
000
to v
111
, respectively. The
result is the interpolated function value at pointp.
4.4 Classification
Classification maps scalar values of the dataset to optical properties for the volume-rendering integral
(Equation 2.1). It allows us to distinguish different materials in a volume. In our method, a material or
tissue type is assigned to each sample position. Each material stores a transfer function that maps from
scalar values(x(t)) to colorC(t) and opacityα (t).
4.4.1 MaterialAssignment
We first classify each sample position based on its spatial relation to the following mesh groups: bones,
muscles, tendons, ligaments, and skin. That is, if a sample point is inside a mesh group, it belongs to
28
the category represented by the mesh group. The category of materials includes bone, muscle, tendon,
ligament, and fat (inside the skin mesh). Since meshes overlap with each other, e.g., every internal mesh is
inside the skin mesh, joint ligaments intersect with the end of the phalanges, etc., we assign the following
priority to these categories:
bone>tendon>muscle>ligament>fat. (4.1)
Specifically, our method works as follow: (1) for each pixel, we compute a sorted list of intersections
between the viewing ray and all meshes in the scene; (2) create equidistant sampling points between
the closest and furthest intersections, with stochastic jittering, in a front-to-back manner; (3) maintain a
priority queue of (geometry id, material id) pairs that can be directly used for material assignment; the
priority depends on the material id (Equation 4.1); (4) if we encounter a new mesh that is not in the queue,
this implies that it is an entry point of an interval whereby all interior sampling points share the same
material; a pair (geometry id, material id) for this mesh is inserted into the queue; (5) if we encounter an
old mesh that is already in the queue, this implies an exit point of a material interval; the corresponding
pair in the queue should be removed; (6) during volume traversal, the material with highest priority in the
queue is assigned to the sample point. In Figure 4.1, we demonstrate an example of the material assignment.
It is evident that without priority, the material assignment of a sample point can be ambiguous because
this sample point can belong to more than one category. With priority assignment, a sample point will be
classified as the one that has the highest priority among all the categories that it could belong to. Figure 4.5
shows a comparison of the renders of bones, tendons, muscles, and ligaments without and with priority
assignment using constant color and opacity as transfer functions (i.e., without MRI data).
Traditionally, segmentation is performed prior to the volume traversal. The segmentation information
can be represented in an object ID volume, where each voxel contains the ID of the object it belongs to.
Then the segmented volume data can be rendered using basic ray casting, with the knowledge of the object
29
Figure 4.4: An example of material assignment. A single ray corresponding to a given image pixel is
intersected with all meshes in the scene (skin, bone and ligament in this example). Sampling points that lie
inside the interval between two neighboring intersections are identified as the same material. In the first
and fifth intervals, only skin is present in the queue, and so every sampling point in these two segments
is classified as fat tissue. In the second interval, both bone and skin are present in the queue. However,
the bone has higher priority than the skin, so sample points in this region are classified as bone tissue.
Similarly, sample points in the fourth interval are classified as ligament tissue. In the third interval, all
tissues are present, hence the bone material is assigned because the bone has the highest priority.
Figure 4.5: Comparison of renders without (left) and with (right) priority assignment. Artifacts
marked with red squares are caused by wrong material assignments between bones and joint ligaments.
30
Figure 4.6: Comparison of segmented bone renders between “3D slicer” (left) and our method
(right). Our result is free from staircase/voxelization artifacts that can be observed on the left.
ID of each voxel. However, staircase/voxelization artifacts caused by partial volume effects will appear at
the boundaries of two objects. This approach of performing ray-object intersections and sampling within
the segments between intersections produces higher image quality than the above-mentioned voxel ap-
proach. With our method, the boundary between two materials is the smooth surface of a mesh, instead
of the irregular outer surface of a discretized grid. Therefore, our results are free of staircase artifacts. In
Figure 4.6, we give the comparison of volume rendering of a segmented bone between “3D slicer” (a free
and open-source software capable of segmentation and volume ray casting), and our renderer.
4.4.2 TransferFunctions
With material assignment, we can selectively use different transfer functions for different objects within
the dataset. Previously, Hadwiger et al. (2003) [11] and Bruckner et al. (2006) [3] utilized focus-plus-
context (F+C) to better visualize the 3D information: depending on whether objects are selected to be “in
focus” or not, their visual appearance can be different. Whereas objects “in focus” may feature significant
opacity, objects which are considered to be “context” act as a semitransparent reference. Inspired by this
31
Figure 4.7: Volumerenderingwithinterior-emphasizedstyle. Internal organs are clearly shown (on
both sides), boundaries between tissues are smooth and clear, and semi-transparent skin provides the
context of the hand shape. In particular, on the palmar side (left), rich muscle textures can be observed; on
the dorsal side (right), bone marrow, compact bone, and spongy bone of metacarpals can be recognized.
concept, we devised two styles/groups of transfer functions to individually emphasize the inner structures
(bones, muscles, tendons, and ligaments) and outer subcutaneous fat tissue that lies beneath the skin.
We named these two styles “interior-emphasized” and “fat-emphasized.” A style is given by specifying a
transfer function for each material. Hence, for each style, once a sample point’s material is determined,
the associated transfer function is also determined.
4.4.2.1 Interior-EmphasizedStyle
In the interior-emphasized style, the skin looks like a semi-transparent membrane, and internal organs
(such as bones and muscles) under the skin are clearly shown with significant opacity and contrasting
colors (Figure 4.7).
The interior-emphasized style is achieved as follows. (1) Divide objects into two major groups: non-fat
(bones, muscles, ligaments, tendons) and fat tissues. (2) Assign each non-fat tissue color that is the product
of a scale factor and a custom colorC
material
. The scale factor can be computed by first modulating the
32
Material Transfer Function C
material
α material
bone (244, 214, 145) 1.0
muscle C(t)=max(min(a(s(x(t))/s
max
)
b
,0.0),1.0)∗ C
material
, (255, 98, 56) 1.0
ligament α (t)=α material
. (170, 170, 170) 1.0
tendon (255, 255, 255) 1.0
fat
C(t)=ρ fat
(s(x(t)))/ρ
fat_max
∗ C
material
,
0.6
α (t)=ρ fat
(s(x(t)))/ρ
fat_max
∗ α material
.
(177, 122, 101)
Table 4.1: Transfer functions for interior-emphasized style. t denotes the distance to the camera;
x(t) denotes the sampling position at distancet;s(x) denotes the MRI scalar value at sample positionx;
s
max
denotes the maximum MRI value; ρ fat
(s) denotes the frequency of MRI value s within fat region;
ρ fat_max
denotes the maximum frequency of MRI values in the fat region. Column "Transfer Function"
gives the formula to compute color C(t) and opacity α (t) at sample position. Columns C
material
and
α material
define the custom color and opacity for each material. All values are carefully chosen to best
visualize the data.
normalized MRI value s(x(t))/s
max
at sample point x(t) with a multiplier a and an exponent b, where
s
max
denotes the maximum MRI value in the dataset. Then, the scale factor is clamped to[0,1]. (3) Assign
non-fat tissue constant opacity α material
. (4) Assign the fat tissue color that equals the product of the
normalized frequency of the MRI values within the fat regionρ fat
(s(x(t)))/ρ
fat_max
and a custom color,
whereρ fat_max
denotes the maximum frequency of MRI values in the fat region. (5) Assign the fat tissue
opacity that equals the product of the normalized frequency of the MRI values within the fat region and a
custom opacity. Table 4.1 listed the transfer function for each material; all values are carefully chosen to
best visualize the data.
For internal organs, MRI values in these regions play an important part in the color transfer function,
and hence internal organs are highlighted with MRI intensity. The reasons to use the frequency of MRI
values are twofold. First, in the past, histogram analysis has been utilized to extract tissue features [19][23],
and it is also intuitive to highlight the data in regions where the peak of the frequency histogram is reached.
Second, in particular for fat tissue, we found that in the wrist region, the MRI intensity in the dataset has
lower quality than in other regions (Figure 4.1a). This introduces a substantial amount of low MRI values
in this region, and the MRI values of the skin happen to be in the same range. Therefore, by utilizing the
33
Figure 4.8: Frequency histogram of MRI values in the neutral pose.
frequency of the MRI values within fat to scale its color and opacity, we highlight the skin and partially
hide the subcutaneous fat tissue, which has higher MRI intensity. Note that low intensity voxels in the
wrist area are also emphasized, but they do not occlude the internal organs. Figure 4.8 shows the frequency
histogram of the MRI value in all regions.
4.4.2.2 Fat-EmphasizedStyle
In the “fat-emphasized” style, the subcutaneous fat tissue is no longer translucent. Instead, it is “in focus”
and features significant opacity. Other tissues have constant but contrasting colors, which provides the
context of shape and spatial relation and highlights the black superficial veins presented in the fat layer,
such as the traverse natatory veins, palmar digital veins, the superficial venous palmar arch, and dorsal
metacarpal vein, as illustrated in Figure 4.9. These effects are more obvious on the dorsal side because the
dorsal veins are closer to the skin. We highlight the corresponding veins in Figure 4.10 for reference.
34
Figure 4.9: Volume rendering with fat-emphasized style. Fat layer is “in focus” and has significant
opacity, while internal organs provide the “context” of shape and spatial relations. Several superficial
veins underneath the skin are visible and annotated, such as the traverse natatory veins, palmar digital
veins, superficial venous palmar arch, and dorsal metacarpal veins.
Figure 4.10: Venous system of the hand with annotation. © 2022 Elsevier. Image adapted, with per-
mission, from https://3d4medical.com under student license.
35
Material Transfer Function C
material
α material
bone (244, 214, 145) 1.0
muscle C(t)=C
material
, (255, 98, 56) 1.0
ligament α (t)=α material
. (170, 170, 170) 1.0
tendon (255, 255, 255) 1.0
fat
C(t)=max(min(a(s(x(t))/s
max
)
b
,0.0),1.0)∗ C
material
,
0.6
α (t)=α material
.
(177, 122, 101)
Table 4.2: Transferfunctionsforthefat-emphasizedstyle.t denotes the distance to the camera;x(t)
denotes the sampling position at distancet; s(x) denotes the MRI scalar value at sample positionx; and
s
max
denotes the maximum MRI value. The column “Transfer Function” gives the formula to compute
colorC(t) and opacityα (t) at a sample position. ColumnsC
material
andα material
define the custom color
and opacity for each material. All values are carefully chosen to best visualize the data.
The “fat-emphasized” appearance style is achieved as follows. (1) Divide objects into two groups: non-
fat tissues and fat tissue. (2) Assign each non-fat tissue a constant color and a constant opacity. (3) Similar
to the non-fat tissue in the “interior-emphasized” style, assign the fat tissue color that is the product of
a scale factor and a custom color. The scale factor is the same as before, and can be computed by first
modulating the normalized MRI value at the sample point with a multiplier and an exponent. Then, the
scale factor is clamped to [0,1]. (4) Assign the fat tissue a constant opacity. Table 4.2 gives the transfer
function for each category.
It is important to note that no contrasting media such as those utilized in magnetic resonance angiog-
raphy (MRA) are involved during the scanning, nor do we have segmented the veins. The veins are present
because veins have lower MRI intensity compared to other tissues in the fat layer. For future work, more
advanced transfer functions can be devised to utilize gradient magnitude (proposed by Leovy et al. [20]),
in order to visualize the boundary surfaces of veins, possibly also arteries and nerves, and de-emphasize
the homogeneous tissue in the fat layer.
36
4.5 Pre-MultiplicationwithOpacity,andFinalCompositionEquations
In Chapter 2, associated colors [36] were assumed, which consist of color components that are already
weighted by their corresponding opacity. An alternative description uses color components that have not
been pre-multiplied with opacity, i.e., non-associated colors. The colors given in Table 4.1 and Table 4.2
are non-associated colors. Hence, the previous equations have to be modified to allow for non-associated
colors: original color terms have to be replaced by color terms that are explicitly weighted by opacity.
For example, C
i
needs to be substituted by α i
C
i
in the iterative compositing equations. With non-
associated colors, the front-to-back compositing Equation 2.8 is replaced by
C
′
i
=C
′
i− 1
+(1− α ′
i− 1
)α i
C
i
,
α ′
i
=α ′
i− 1
+(1− α ′
i− 1
)α i
.
(4.2)
Similarly, the back-to-front compositing scheme is changed from Equation 2.9 to
C
′
i
=α i
C
i
+(1− α i
)C
′
i+1
.
(4.3)
We implemented front-to-back composition for non-associated colors using Equation 4.2. This yields
a color and an opacity value for a single pixel of the final image. Multi-threading was utilized to calculate
multiple pixels in parallel since the computations of different pixels are independent.
37
Chapter5
Results
In this chapter, we evaluate our volume renderings method using animated sequences of MRIs. We compare
the results with standard surface rendering, as well as volume rendering methods of related work.
5.1 Performance
All experiments were performed using the computing environment described in Table 5.1. Our CPU vol-
ume renderer was written in C++ and built and tested on Linux. We used Intel
®
Embree library for calcu-
lating ray-object intersections and oneTBB for computing multiple pixels in parallel. Python scripts were
used to automate batch rendering of testing sequences.
Our animated hand MRI data and mesh geometry for testing was acquired from Mianlun Zheng, Bohan
Wang, and Jernej Barbič [33][34]. These animated MRIs come from layered FEM simulation driven by five
input joint animations: "close the fist" (keyframed, 132 frames), "opposition of the thumb" (keyframed, 996
frames), "performance animation" (motion-captured, 653 frames), "numbers 1-5" (motion-captured, 360
frames) and "American Sign Language" (keyframed, 732 frames).
The resolution of the input MRI volume data is 400× 400× 400 and the voxel size is 0.64mm× 0.64mm× 0.64mm. Table 5.2 shows the specifications of mesh geometry used for classification. We
38
Software Environment
name version
Operating system Ubuntu 20.04
Linux kernel 5.13.0-44-generic
g++ 12.0.1
Embree 3.4.0
oneTBB 2021.5.1
Python 3.8.10
CPU Specifications
Number of CPUs 1
CPU model Intel® Core™ i7-7700K
Number of cores 8
Processor base frequency 4.2 GHz
Max turbo frequency 4.5 GHz
Memory Specifications
Memory size 40 GB
Memory speed 2400 MHz DDR4
Table 5.1: Software environment and hardware specification.
rendered these five motion sequences with two types of transfer functions (fat-emphasized, interior-
emphasized) with three camera configurations (front, back, side), thus generating 5× 2× 3 = 30 image
sequences in total. On average, it takes 3.7 seconds and 4.7 seconds to render an image of 1024× 1024
resolution with fat-emphasized and interior-emphasized style of transfer functions, respectively. Table 5.3
gives the time cost for each sequence. The maximum memory usage was 612.3 MB.
tissue type # meshes # vertices # triangles
bones 23 788/8,291/3,353/77,111 1,572/17,838/6,764/15,576
muscles 17 1,089/10,924/3,247/55,205 2,174/21,844/6,442/109,506
tendons 10 3,000/9,032/7,613/76,129 5,996/18,060/15,222/152,218
ligaments 6 663/1,658/1,051/6,305 1,322/3,312/2,098/12,586
skin 1 18,105 36,206
Table 5.2: Specifications of meshes of all hand tissues. Column "# meshes" shows the number of
meshes. Columns "# vertices" and "# triangles" give the minimum/maximum/average/total numbers of
vertices and triangles for each mesh group, and numbers of vertices and triangles for the skin mesh.
39
sequences
fat-emphasized interior-emphasized
n
f
t (hr)
t
ff
(s) t
fb
(s) t
fs
(s) t
if
(s) t
ib
(s) t
is
(s)
"Close the fist" 3.60 3.54 3.45 4.68 5.24 4.05 132 0.9
"Opposition of the thumb" 3.87 3.82 3.76 4.81 5.04 4.49 996 7.1
"Performance animation" 3.65 3.66 3.50 4.52 5.14 4.14 653 4.5
"Numbers 1-5" 3.79 3.79 3.63 4.68 5.12 4.54 360 2.6
"American Sign Language" 3.67 3.64 3.50 4.49 4.85 4.44 732 5.0
Table 5.3: Thetimecostforeachanimationsequence. In the "fat-emphasized style" column, we give
the average rendering time per frame for this style with front view (t
ff
), back view (t
fb
), and side view
(t
fs
). Similarly, in the column "interior-emphasized style", we show the same for this style with front view
(t
if
), back view (t
ib
), and side view (t
is
). Columnn
f
andt give the total number of frames and total render
time for each sequence.
5.2 ResultsandComparisons
Figure 5.1 gives the volume rendering results of the sequence “American Sign Language” with the interior-
emphasized style. The hand was posed into letters A-E and rendered from both front and back views.
In these renderings, color and opacity are consistent across the range of motion. The internal structures
are clearly shown, the boundaries between tissues are smooth and clear, and the semitransparent skin
provides the context of hand shape. On the palmar side, muscles are shown with rich texture due to the
usage of MRI values in its transfer function; on the dorsal side, the anatomy of metacarpals can be easily
identified for the same reason. The outer bone layer (compact bone) is shown in black, the bone center
(bone marrow) is shown in yellow, and the two bone ends are shown in dark yellow.
Figure 5.2 shows the results of sequence “numbers 1-5” with the fat-emphasized style, in which the
hand was posed into numbers 1 to 5 and rendered from the front and back views. The appearance of the
hand and internal organs are consistent across the range of motion. Constant but contrasting colors of
the internal tissues provide shape cues for all the inner structures. The superficial veins beneath the skin
are clearly shown in black, and are nicely animated across the range of motion. One particular advantage
we have gathered from our experiments is that using the "fat-emphasized" style, any FEM simulation
instabilities in the fat layer are much easier to identify, compared to the surface rendering of the skin.
40
Figure 5.1: “American Sign Language”: Letters A to E, rendered with interior-emphasized style; front
view (top row) and back view (bottom row). The internal structures are clearly shown, the boundaries
between tissues are smooth and clear, and the semi-transparent skin provides the context of the hand
shape.
41
Figure 5.2: "Numbers1-5", rendered with fat-emphasized style from front view (top) and back view (bot-
tom). The appearance of the hand and internal organs are consistent across the range of motion. Constant
but contrasting colors of the internal tissues provide shape cues; the superficial veins beneath the skin are
clearly shown in black and are nicely animated across the range of motion.
42
Figure 5.3 shows a comparison of fat-emphasized style and interior-emphasized styles, using the se-
quence "opposition of the thumb" (side view). It is important to note that these two styles are designed
to emphasize different structures while preserving overall context, not to compete with each other. The
visual difference between the two styles are mainly: (1) the anatomy of the bone is clearly shown in the
interior-emphasized style, especially in middle and proximal phalanges and metacarpals, whereas the bone
tissue in the fat-emphasized style merely provides the shape of its outer surface; (2) The shapes and spatial
relation of tendons and ligaments can be recognized in the interior-emphasized style, but not as easily as in
the fat-emphasized style, due to low MRI densities in these regions; (3) in interior-emphasized style, skin
and wrist region have significant color and opacity, and the subcutaneous fat tissue is partially hidden,
whereas in the fat-emphasized style, subcutaneous fat tissue has significant color and opacity, and skin
and wrist region are close to black; (4) superficial veins are easier to be identified in the fat-emphasized
style compared to the other style.
In terms of camera extrinsics (position and orientation), different views provide insight into differ-
ent aspects of the hand. Specifically, in the interior-emphasized style, the front view emphasizes palmar
muscles and phalanges due to the spatial relations between muscles and bones. In the back view, the
metacarpals and carpals that were occluded in the front view, are now visible. In addition, the side view
provides insights into the spatial relationships between tendons, ligaments, and interphalangeal joints.
Similarly, the fat-emphasized style not only provides the shape cues for the above-mentioned structures,
but also displays the variation of densities and superficial veins within fat tissue.
Figure 5.4 shows the comparison between surface rendering and our volume rendering in the “Close
the fist” motion. The skin surface is rendered with Pixar RenderMan. Albedo and displacement textures are
acquired from [33]. Although these images looks appealing due to the usage of textures and illumination,
they do not show the internal anatomy. In addition, superficial veins that are visible in our fat-emphasized
renders cannot be shown easily with surface rendering. Surface rendering of internal structures was done
43
Figure 5.3: “Opposition of the thumb”, rendered from the side view in the interior-emphasized (top)
and fat-emphasized (bottom) styles. The visual difference between the two styles are mainly: (1) the bone
anatomies are clearly shown in the interior-emphasized style; (2) The shapes and spatial relations of ten-
dons and ligaments are easier to identify in the fat-emphasized styles; (3) in the interior-emphasized style,
skin and wrist regions have significant color and opacity, and the subcutaneous fat tissue is partially hid-
den; in contrast, in the fat-emphasized style, subcutaneous fat tissue has significant color and opacity, and
the skin and wrist regions are close to black; (4) superficial veins are easier to identify in the fat-emphasized
style.
44
Figure 5.4: Comparison between standard surface rendering (left) and our volume rendering
(right) in the “close the fist” motion. Surface renderings of the skin mesh and internal organs were
created using Pixar RenderMan and Maya Arnold, respectively. Compared to surface rendering, our results
are not photo-realistic due to the lack of textures, scattering, and global illumination. However, surface
rendering cannot show the outer surface and internal structures simultaneously unless transparency is
used, which will diminish the benefit of textures. Furthermore, surface rendering suffers from artifacts
introduced by interpenetration between internal structures.
45
using Maya Arnold. Compared to our results, the surface rendering of the internal organs looks more
photo-realistic, but does not show the outer surface of the hand. In addition, the textures of the muscles
do not correspond to any real data. Moreover, surface rendering suffers from artifacts due to penetrations
between different structures, e.g., ligaments and bones, tendons and muscles. These problems are solved
in our MRI rendering method, thanks to our priority assignment of different tissues. It is important to note
that not only single material assignment is possible, but a linear combination of different materials is also
easily achievable in volume rendering.
We also compared our renders to related work. In Figure 5.5, we visually compared our results with
[Rhee et al. 2010] [28], in similar poses. Similar to our method, they also have two rendering styles, one
emphasizing the internal organs and the other emphasizing the fat tissue. Compared to them, in the first
style, the bones and other important organs, such as tendons and muscles, are highlighted in our results
with clear boundaries. In the second style, in their results, the bones and some superficial veins (above the
thumb’s metacarpal) are visible, but the boundaries between different tissues are not as clear as ours.
46
Figure 5.5: Comparison of volume renders of [Rhee et al. 2010] (left) and our method (right). ©
2010 IEEE. Reprinted, with permission, from Rhee et al.[28].
47
Chapter6
Conclusion
6.1 Summary
The main contributions of this master thesis are:
• The development of a volume rendering pipeline that implements the state-of-the-art volume ren-
dering method, namely the volume ray casting algorithm.
• Demonstrating how the geometric shape of interior structures can be utilized to define the transfer
function at each sample point, in a manner that resolves the ambiguities in areas of intersection, and
removes staircasing artifacts.
• The design of two groups of transfer functions capable of emphasizing different aspects of the hand
anatomy.
• The evaluation of the pipeline both in terms of rendering performance and image quality.
48
6.2 FutureWork
We would like to improve the rendering performance of the pipeline and achieve interactive rendering by
converting our CPU implementation to the GPU, so that the process of iterative design of transfer functions
can be more efficient.
In addition, to improve volume rendering quality, it would be beneficial to include scattering into our
optical model and implement photo-realistic Monte-Carlo ray casting, such as [29], [16], [10].
Finally, it would be interesting to explore more advanced transfer functions, and combine them with
other rendering techniques, such as surface rendering, non-photorealistic rendering, or maximum inten-
sity projection.
49
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52
Abstract (if available)
Abstract
This thesis investigates volume rendering techniques and the design of transfer functions to improve the visualization of human hand anatomy using medical resonance imaging (MRI). Volume rendering of the human hand is a challenging but crucial problem for understanding hand anatomy in three dimensions. The hand is inherently complex, and it is difficult to design volume rendering transfer functions that are suitable for each specific application. We first introduce the fundamentals of volume rendering and hand anatomy, and discuss the related work on hand anatomy visualization. Then, we propose a ray-casting pipeline that uses both the hand MRI volume data, and the geometry of its inner structures and their known segmentation, permitting fine control over the appearance of each tissue. Additionally, we devise two sets of transfer functions to emphasize different hand tissues of interest, while preserving the visual context of the hand, inspired by the concept of "focus-plus-context." We also present pipeline extensions to tackle several artifacts of standard volume ray-casting. We evaluate our volumetric rendering on five challenging hand motion sequences. Finally, our experimental results show that our volumetric rendering improves hand anatomy visualization, compared to standard surface and volume rendering techniques.
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Asset Metadata
Creator
Huang, Jingtao
(author)
Core Title
Volume rendering of human hand anatomy
School
Viterbi School of Engineering
Degree
Master of Science
Degree Program
Computer Science
Degree Conferral Date
2022-08
Publication Date
07/06/2022
Defense Date
06/17/2022
Publisher
University of Southern California
(original),
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Tag
hand anatomy,medical applications,MRI,OAI-PMH Harvest,transfer function,volume rendering
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Barbič, Jernej (
committee chair
), Gupta, Satyandra K. (
committee member
), Raghavachary, Saty (
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)
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ishuang.jt@gmail.com,jingtaoh@usc.edu
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Tags
hand anatomy
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