Transcript embc2007ashishu - University of British Columbia

Biomedical Signal and Image
Computing Laboratory
Invariant SPHARM Shape Descriptors for Complex
Geometry in MR Region of Interest Analysis
Ashish Uthama1
Rafeef Abugharbieh1
Anthony Traboulsee2
Martin J. McKeown1,2
Presented by Bernard Ng1
1 Biomedical
Signal and Image Computing Laboratory, Department of ECE, University of British Columbia
2 Department of Medicine, University of British Columbia
Biomedical Signal and Image
Computing Laboratory
Overview

Introduction



Background



Our earlier SPHARM approach
New SPHARM approach proposed
Method

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
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Shape analysis using ROIs in MR
Current analysis techniques
Feature extraction
Feature analysis
Validation
Results

Shape Analysis of the thalamus in PD
Biomedical Signal and Image
Computing Laboratory
Shape Analysis Using ROIs in MR

High resolution structural MR helps
in studying deep brain structures

Most neurological disease effect
the integrity of brain structures
(PD, MS, etc)

In some diseases this effect could
be a systematic change in shape

Using ROI (Region of Interest)
based shape analysis helps study
these changes locally
Manually traced Region of Interests (ROI) delineating the
left and right thalamus for further shape analysis
Introduction
Background
Method
Results
3
Biomedical Signal and Image
Computing Laboratory
Current Analysis Techniques

Voxel count to represent volume


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Template based representation
(medial, atlas, etc)



Very simplistic measure
Does not capture shape
Most require manual selection of Land Marks
Requires mutual registration
Automated feature extraction

Limited to spherical topology
Introduction
Background
Method
Results
4
Biomedical Signal and Image
Computing Laboratory
Our Earlier SPHARM Approach

Scale,
rotation
translation invariant


r
and
No mutual registration
Insensitive to subject (ROI)
orientation or brain size
F  ,   r
Cross sections of hypothetical 3D volumes

ROI surface represented
as a function of distance
from the centre of mass

Thus limited to ROIs
without self occlusions
F  ,    ??
A limitation for potential future work on arbitrarily
complex ROIs (e.g MS leison shape etc)
Introduction
Background
Method
Results
5
Biomedical Signal and Image
Computing Laboratory
New SPHARM Approach Proposed

Based on representing the ROI volume
using concentric spherical shells
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Arbitrarily shaped ROIs can be analyzed
Earlier such representations were not unique
Novel implementation of a radial transform

Ensures unique feature vectors
Introduction
Background
Method
Results
6
Biomedical Signal and Image
Computing Laboratory
Feature Extraction 1
A

Determine the maximum
radius Rmax (in voxels)

Obtain the bandwidth (L)
C
2
4Rmax
 2L  2L
L  Rmax 
A
B
B
Introduction
Background
C

Obtain 2Rmax number of
shells with radius equally
spaced between 1 and Ri,

Intersect these shells with
the binary ROI mask,
interpolating as required
Method
Results
7
Biomedical Signal and Image
Computing Laboratory
Feature Extraction 2
Shell 1

Obtain
the
basic
SPHARM
representation for each shell
2

0
0
Shell r
Shell 2Rmax
L
L
…
…
L
L
crlm   d  Ylm*  ,  r , ,  sin  d

c 
m
kl

2 Rmax
r2 2
r 1
sin kr m
crl
r
Obtain the final invariants
N  p, q  
k  2 Rmax m l
 c
k l
Introduction
ml
cm1l
cmrl
cm2R
max
.
.
.
.
.
.
Radial transform
To obtain unique representation
under independent rotations of the
ROI section contained in each
shell, use a radial transform
cmrl
cm1l
cm2R
l
max
cm1l
cmkl
cm2R
l
.
.
.
.
.
.
l
max
m m*
kl kl
c
Background
Method
Results
8
Biomedical Signal and Image
Computing Laboratory
Feature Analysis

Obtain features for both groups
(e.g. PD vs. Healthy controls)
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Reshape each feature into a vector
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Use a permutation test to determine if the two
groups have a significant difference
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Does not need a generating probability distribution
Best suited for long feature vectors seen in biomedical
applications
Introduction
Background
Method
Results
9
Biomedical Signal and Image
Computing Laboratory
Validation

Two groups with 20 3D ellipsoidal
volumes each
were generated
using:
x  xc  n  y  yc  n  z  zc  n 
x, y, z  
(a) Real data (b) and (c) are the two synthetic
groups created

2
2
xi
2
a  nai 

yi
2
b  nbi 
2

zi
2
cX  nci 
Realistic intersubject variability was
introduced by:

Random shifts of the centroid
 Random rotations about all 3 axes
 Gaussian noise on the surface

With fixed a and b, c was varied
over a range to study the
performance of the method
As the graph approaches cb=10 the group difference in
shape reduces
Introduction
Background
Method
Results
10
Biomedical Signal and Image
Computing Laboratory
Shape Analysis of the PD Thalami

21 controls and 19 PD patients
were scanned twice. Once before
and once two hours after the
administration of a drug

Rmax
for both thalamus was
found to be 20 voxels, 40 shells
with a bandwidth of 36 were used

Obtained feature length was 1440

Pre and Post drug analysis yielded
no significance

Significant differences observed in
both the left and the right thalamus
between healthy controls and PD
Introduction
Background
Method
Results
11
Biomedical Signal and Image
Computing Laboratory
Conclusion

SPHARM based invariant feature vectors for a
3D volume
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Unique radial transform to obtain unique vectors
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Validated with synthetic data
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Application to real data

Significant shape changes were observed in addition to
volumetric changes indicating that atrophy is not isotropic
Introduction
Background
Method
Results
12
Biomedical Signal and Image
Computing Laboratory
Questions and Comments
[email protected]