Page 1
Abstract
This paper
symmetryintegrated brain injury detection method for
magnetic resonance imaging (MRI) sequences. One of the
limitations of current injury detection methods often
involves a large amount of training data or a prior model
that is only applicable to a limited domain of brain slices,
with low computational efficiency and robustness. Our
proposed approach can detect injuries from a wide variety
of brain images since it makes use of symmetry as a
dominant feature, and does not rely on any prior models
and training phases. The approach consists of the following
steps: (a) symmetry integrated segmentation of brain slices
based on symmetry affinity matrix, (b) computation of
kurtosis and skewness of symmetry affinity matrix to find
potential asymmetric regions, (c) clustering of the pixels in
symmetry affinity matrix using a 3D relaxation algorithm,
(d) fusion of the results of (b) and (c) to obtain refined
asymmetric regions, (e) Gaussian mixture model for
unsupervised classification of potential asymmetric regions
as the set of regions corresponding to brain injuries.
Experimental results are carried out to demonstrate the
efficacy of the approach.
presents a fully automated
1. Introduction
Magnetic resonance imaging (MRI) is a medical imaging
technique most commonly used in radiology to visualize
the structure and function of the body. It provides detailed
images of the body in any plane with higher discrimination
than other radiology imaging methods such as CT, SPECT,
etc. Specifically, mining of brain injuries that appear in an
MRI sequence is an important task that assists medical
professionals to describe the appropriate treatment.
Traditionally, the boundary or region of an injury in
magnetic resonance imaging is usually traced by hand. This
manual approach is time consuming, subjective and error
prone. The computeraided diagnosis on brain MRI reduces
the manual workload by a combination of image processing
and pattern recognition techniques. An efficient injury
detection algorithm is important for diagnosis, planning
and treatment. Currently in many computeraided
applications,
segmentation or detection methods are recommended for
clinical treatment that can significantly reduce the time and
make such methods practical. Previous works [16], based
on 2D and 3D image analysis, detect brain injuries
reasonably well by using training sets and prior models, as
well as using efficient preprocessing like registration, with
injury boundary outlined. Numerous features are used in
model matching schemes, like image intensity, texture,
shape, etc. In this paper, symmetry is integrated with image
analysis as a new kind of feature. The integration allows
fully automatic brain injury detection, without training and
prior modeling, and it is applicable to a wider range of MRI
data with different ages and injury characteristics.
The rest of this paper is organized as follows. In section
2, we give an overview of related work and our
contributions. In section 3, the technical details of our work
are provided. Section 4 gives experimental results. Finally,
conclusions are given in section 5.
automatic or semiautomatic image
2. Related Works and Our Contributions
2.1. Related Works
There are many challenges associated with automated
detection of brain injuries. The brain injuries are always
different in size, shape, and may appear in any location with
different image intensities. Some injuries also deform other
normal and healthy tissue structures. In order to solve those
challenges, stateoftheart
extraction techniques basically use two kinds of methods:
tissue classification/segmentation
extraction. The tissue classification approach [1, 2] starts
with brain segmentation based on a prior model of tissue,
and extracts ROIs from classified clusters. Unfortunately,
in order to obtain satisfactory classification results, large
amounts of training data or a complex prior model is
required, and the range of application is strictly restricted
by the domain of training phase. The abnormality/target
extraction approach [3, 4] generally builds a stochastic
model for normal brain tissues, and simultaneously detects
abnormality that is not a well fit into the model. However, it
regionofinterest (ROI)
and abnormality
Automatic Symmetryintegrated Brain Injury Detection in MRI Sequences
Yu Sun1, Bir Bhanu1, Shiv Bhanu2
1. Center for Research in Intelligent Systems, University of California, Riverside, CA 92521.
2. School of Medicine, University of California, San Francisco, CA 94122.
ysun@ee.ucr.edu, bhanu@ee.ucr.edu, shiv.bhanu@ucsf.edu
799781424439935/09/$25.00 ©2009 IEEE
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Table 1. Comparison of related symmetry integration methods and this paper
Authors
Saha et al.
[12]
Principle of Techniques
Brain MRI segmentation
using a fuzzy point
symmetry based genetic
clustering technique.
Datasets and Results
Datasets: Totally 181 MRI slices,
shows seven slices in results.
Results: Segmentation results in
2D; Minkowski Score to measure
the quality of clustering compared
with groundtruth.
Datasets: Five images from five
patients.
Results: Lesion
results in 2D and 3D, with
groundtruth.
Datasets: Six images  no source.
Results: Abnormality detection
results in 2D; no groundtruth; Dice
Coefficient to
abnormality detection performance.
Datasets: MRI sequences of 2
patients, with 16 slices for each;
shows results on 4 slices of each
patient;
Results: Both segmentation and
injury detection results in 2D with
groundtruth; Error rate to measure
the detection accuracy compared to
groundtruth in 2D and 3D.
Comments
+ Assignment of points to clusters in genetic
algorithm by point symmetry based distance
rather than Euclidean distance; no a priori info.
 Time consuming; many noisy regions in
results; cope with internal symmetry within a
region only.
+ Not rely on a template; good generality;
enhance texture symmetry.
 Not robust to changes in parameters; uses
only local symmetry.
Bergo
al. [13]
et
MRI segmentation based
on the analysis of texture
symmetry.
segmentation
Ray et al.
[14]
Locate brain abnormality
by finding a bounding
box around it using the
symmetry analysis.
measure the
+ No registration; no training image; can be
implemented in realtime.
 Need the reference (template) image;
abnormality boundary in segmentation result is
not well outlined.
+ Integrates symmetry in all steps; no prior
model or template; no training data; good
generality; efficient segmentation algorithm;
uses global symmetry rather than local or
internal symmetry.
 Some very low contrast injured regions are
missed.
Sun,
Bhanu and
Bhanu
This paper

Detect brain injury in
MRI by
integration in several
steps associated
segmentation, clustering
and classification.
symmetry
with
is always challenging to build a complete prior model in
order to cover enough tissue information. Another
abnormality extraction method is called digital subtraction
[5], which is useful to track structure or volume changes of
brain collected at different times. The accurate subtraction
relies highly on normalization and registration [6]. As a
result, most of the current ROI extraction methods highly
depend on the quality of preprocessing and prior
knowledge. Our method overcomes the above limitations
to a great extent by integrating symmetry information in
segmentation and abnormality extraction.
2.2. Our Contributions
Related works in [12, 13, 14] basically integrate
symmetry information into brain MRI segmentation in only
a single step, whereas our method integrates symmetry in
all the steps of segmentation, clustering and classification
in the whole system. The limitations of these techniques
compared to our method are shown in Table 1. We
formulate the proposed new idea based on the observation
that for most abnormality detection methods, though
different in principle, accept a common criterion that
abnormal regions are detected by their properties that
deviate from the expected normal and healthy tissue
properties. Specified to our case, since most of the injuries
are asymmetric with their mirror regions against the
symmetry axis, while the other healthy brain structures are
highly symmetric, we are able to detect injuries by
symmetry integration. Therefore, asymmetry is regarded as
a distinct property of injuries that deviates from other
normal symmetric tissues. By integrating symmetry, we
overcome the limitations of other approaches and this paper
makes following contributions:
(a) By symmetry integration, our method does not need
prior models for injury detection. We eliminate symmetric
tissues without further classifying them by a large amount
of training data. Furthermore, symmetry information is able
to classify brain image into symmetric and asymmetric
regions, and our results show that the extracted asymmetric
regions cover almost all injuries or other abnormalities.
(b) Unsupervised classification can be used to classify
asymmetric regions into injuries and other normal regions
by features composed of image intensities and 3D brain
asymmetry volumes, without preprocessing and training.
(c) Our method integrates symmetry information in almost
all steps in approach, whereas other works only integrate
symmetry in single step.
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3. Technical Approach
The overall diagram of our method, with example
results of each step, is shown in Fig. 1. Since symmetry is
the most important feature in our method, we integrate
symmetry in several steps that can be seen in Fig 1:
(1) Symmetry affinity matrix computation in Fig 1(b);
(2) Symmetryintegrated image segmentation in Fig 1(c);
(3) Asymmetric region extraction by kurtosis and skewness
of symmetry affinity, as in Fig 1(d);
(4) Cluster and identify asymmetric groups in Fig 1(e) (f).
(5) Classify asymmetric regions into injury and noninjury
using intensity and 3D asymmetry volume as in Fig 1(h).
In step (1), a symmetry affinity matrix is obtained, that
is used frequently as a measurement of symmetry in later
steps. Step (2) enhances symmetry level of segmentation
results to make sure that most symmetric parts are
segmented appropriately. Thus it prevents misclassification
of symmetric parts into asymmetric regions in a later step.
In step (3), kurtosis and skewness of symmetry affinity
matrix are computed and they are used to extract
asymmetric regions from segmented parts. Meanwhile in
step (4), symmetry affinity matrix is also used for clustering
and identification of asymmetric groups. Results from step
(3) and (4) are fused to obtain refined asymmetric regions
in Fig 1(g). Finally, an unsupervised classifier is used to
extract injuries from the asymmetric regions.
3.1. Symmetry Extraction and the Symmetry
Affinity Matrix
In order to integrate symmetry, a symmetry
measurement scheme of MRI image is needed. We use
global symmetry constellations of features [7] to detect the
reflective symmetry axis for the brain, as in Fig 1(a). A
symmetry affinity matrix as in Fig 1(b), measuring the
symmetry level of each pixel with respect to its symmetry
counterpart pixel reflected by the axis, is computed by
curvature of gradient vector flow (CGVF) [8]:
(1)
Let the GVF of image be:
(2)
In equation (1),
/ux
=∂∂ ,
∂ are the first derivatives of pixel along x and y
x u
/
y uuy
= ∂∂
,
/
xvvx
= ∂∂
,
/
yvvy
= ∂
Fig 1. Overall system diagram
(a) Symmetry
Extraction
(b)
Symmetry
Affinity
Input
Image
(c) Image segmentation
By
Symmetryintegrated
Region Growing
(e) Symmetry Affinity
Segmentation
By 3D Gradient
Relaxation Algorithm
(d) Identify
Asymmetric
Regions
By
KurtosisSkewness
(f) Identify
Asymmetric
Groups
(g) Fusion of
Asymmetric
Regions
(h) Verify
Injury Regions
By
GMM/EM
Classifier
Potential Injury of
2D Regions & 3D Volume
[ ( , ), ( , )]u x y v x yV
=
22
3
1
(x,y)[()]

xyxy
Curvvu uvu vv u
V
=+−−
81
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Page 4
directions. Considering a pixel ( ,
symmetry affinity as:
( , ) ( ,
iii
C x yCurv x y
=
)
ii
x y
, we define its
(3)
where is the symmetric counterpart of by the
symmetry axis. If the two points have locally symmetric
fields, then values of and should be
closer. Three other symmetry conditions are stated in [8],
which can be combined with eq. (3) to build the affinity
matrix. The brighter regions in symmetry affinity matrix
indicate potential asymmetric fields in the image. The
symmetry affinity matrix is further used to outline the
symmetry constraint for pixel aggregation in a region
growing approach for image segmentation in the next
subsection.
3.2. Symmetryintegrated Image Segmentation
Region growing segmentation accepts image intensity as
a constraint for pixel aggregation, either by color or gray
scale. Recent improvements in constraint include a
combination of texture, shape, etc., to segment regions with
different properties. In order to make sure that symmetric
parts are segmented appropriately, in our work, a symmetry
constraint derived from symmetry affinity matrix is
integrated into region growing constraint as shown below:
(4)
and in equation (4) are symmetry affinities of pixel i
and neighboring region j. Equation (4) provides the
following symmetry constraints: the first term controls the
symmetry level, which means that if both patterns i and j
indicate low symmetry affinities (highly symmetric), they
are more likely to be aggregated by decreasing the
constraint; while the second term favors more similar
symmetry affinities. In our work, the symmetry constraint
is combined with gray scale intensity and texture to build an
aggregation constraint as follows:
(5)
where uses the intensity difference of i and j as
graylevel constraint, and uses texture difference,
obtained by Gabor filter, as the texture constraint. Based on
the aggregation constraint, pixel i will be aggregated into
the neighboring region j if constraint between them is
below a threshold . We call equation (5) as the symmetry
integrated multiple constraints. After segmentation, regions
with natural symmetric properties will be segmented
symmetrically. An example result is shown in Fig 1(c).
This approach will improve the performance of asymmetric
region extraction in the next section. Note that Gupta et al.
[10] applied symmetry integration (edgeweight) to
enhance the symmetry level in a graphcut segmentation
approach. This integration has very limited improvements
in segmentation results, compared to our method.
3.3. Asymmetric Region Extraction
A region growing algorithm with symmetry constraints
for pixel aggregation separates symmetric and asymmetric
parts in segmentation results by ensuring that naturally
symmetric parts are segmented symmetrically. The
asymmetric region extraction basically classifies the
segmented regions into symmetric and asymmetric regions.
We provide a new method using kurtosis and skewness of
symmetry affinity matrix to detect asymmetric regions. For
a sample of n values the sample kurtosis and skewness are
given by equations (6) and (7):
Kurtosis: (6)
Skewness: (7)
Kurtosis is a measure of the "peakiness" of the
probability distribution of a random variable. A larger
kurtosis means that the probability distribution indicates a
higher and narrower peak. Kurtosis property has been
applied in image processing to detect the abnormality based
on the reason that kurtosis measures the deviation of a
distribution from the background [9]. We use kurtosis of
symmetry affinity matrix to detect asymmetric regions,
based on the observation that the asymmetric regions
(brighter) in the symmetry affinity matrix can be regarded
as abnormal targets with background, where symmetry
affinity values of pixels are very low and smoothly
distributed. For each segmented region the kurtosis of its
symmetry affinity is computed using eq. (6), resulting in a
single kurtosis value for each region. Larger kurtosis of a
region means more deviation in its symmetry affinity
distribution, which leads to potential asymmetry.
The skewness is another cue for asymmetry detection.
Once we know the mean symmetry affinity value of a
region, the negative skewness means that the distribution is
lefttailed to the mean value. Since zero symmetry affinity
means perfect symmetry, negative skewness means that the
region affinity favors more asymmetry. The asymmetric
region detection can be expressed as follows:
4
4
1
4
2
2
2 2
) )
1
1
n
()
1
n
((
n
i
i
n
i
i
xx
g
xx
µ
δ
=
=
−
==
−
∑
∑
3
3
1
3
1.5
2
2 1.5
) )
1
1
n
()
1
n
((
n
i
i
n
i
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xx
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δ
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( , )
texturei j
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( , )
grayi j
δ
( , ) i j
δ
m
δ
( (1 )(1 ))
1 
+

2
( , )
i j
2
ij
ij
symmetry
δ
actanCC
CC
π
π
+++
−
=+
( , )i j
δ
( , )i j( , )i j( , ) i j
symmetry
δ
graytexture
δδ=++
( ,x y)
ii
( ,)
ii
Curv x y
(,)
jj
Curv xy
)(,)
ijj
Curv x y
−
i C
j
C
(,)
jj
x y
82
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Page 5
(a) Discard symmetric regions whose mean symmetry
affinity is quite low; note that highly symmetric regions
will have a low affinity.
(b) For each of the remaining regions, compute its kurtosis
minus skewness combination g = (g4g3) from eq. (6) and
(7), and build a histogram for the combination g of all
candidate regions. Larger (g4g3) indicates a more
asymmetric region. A threshold Ω is found to partition the
histogram into symmetric and asymmetric regions. Regions
with values of (g4g3) larger than the threshold are
extracted as asymmetric regions, as shown in Fig 1(d).
3.4. Symmetry Affinity Clustering
The purpose of asymmetric region extraction is to cover
all the injured regions, while at the same time allowing the
number of other normal asymmetric regions be as small as
possible. The asymmetric regions obtained in the previous
section can be combined with the results of symmetry
affinity clustering to reduce the number of normal
asymmetric regions. Symmetry affinity clustering is
realized by 3D relaxation method based on maximizing a
criterion function [11]. Basically this algorithm iteratively
separates the symmetry affinity histogram into two classes,
as symmetry and asymmetry. The original symmetry
affinity valued between 0 and 1 is assigned as probability of
each pixel. The mean neighborhood probability of the ith
pixel under consideration is denoted by the sum of the
weighted symmetry affinities of its 8neighborhood pixels
from all slices at the same 2D neighborhood position, that
build a 3D neighborhood. The mean 3D neighborhood
probability is shown as:
(8)
where n is the number of slices in MRI sequence, and 8n is
the total number of pixels in 3D neighborhood .
is equal to the symmetry affinity value of jth pixel in , and
gives weight to each affinity of jth pixel, where less
weight is assigned to pixels that belong to farther MRI
slices. And the values of satisfy the following two
constraints: and . The first constraint
ensures the normalization of the probability , and the
second constraint means that the weight of slice j+1, which
is farther from the previous slice j, is half the value of slice j.
The following iterative process will separate the
distribution of symmetry affinity histogram into symmetry
and asymmetry clusters, by updating symmetry affinity
of ith pixel:
(9)
where in iteration n is updated as:
(10)
and
(11)
where means the cluster of asymmetry. and in eq.
(10) are the control parameters constrained by ,
valued in our case. Normally, 2 iterations are
enough to cluster symmetry and asymmetry pixels in
symmetry affinity matrix, and the asymmetric clusters are
shown in Fig 1(f).
The final asymmetric regions shown in Fig 1(g) are
obtained by combing the results in Fig 1(d) and 1(f), by
using the fact that the final asymmetric regions from 1(d)
are extracted into 1(g) if the regions contain over 50%
asymmetric pixels grouped by 1(f). That means if the two
results (1(d) and 1(f)) have at least 50% overlap in common
asymmetric fields, the regions in 1(d) are extracted as
asymmetric regions into 1(g). The 50% overlap threshold is
chosen by observation of results of a few testing slices, and
it is found to be robust to MRI sequences. Lots of normal
asymmetric regions are eliminated by this overlapping; at
the same time all injuries or other abnormalities are
reserved. Basically the result in Fig 1(g) contains all the
injuries and the number of other normal asymmetric
regions is minimized.
3.5. Injury Extraction
Asymmetric regions obtained from section 3.4 are
potential candidates for
unsupervised Expectation Maximization (EM) classifier
with Gaussian Mixture Model (GMM) is used to classify
candidate asymmetric regions into two classes: injury vs.
noninjury, basically by a 2dimensional feature, composed
of gray scale intensity, and the 3D asymmetry volume. The
3D asymmetry volume is obtained by binarization of results
in Fig 1(g), where the pixel belonged to asymmetric region
is valued 1, and the pixel in other symmetric region is
valued 0. The binary results of all slices in MRI sequence
are added up to build the 3D asymmetry volume. The value
of asymmetry volume means how frequently the
asymmetric regions appear in slices at the same 2D position.
If an injury exists in 3D MRI, its asymmetry in 2D slices
will have a high value. Injuries are more likely to be
classified into one group by using 3D asymmetry volume
extracting injuries. An
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Page 6
feature. The mean value of 3D asymmetry volume of each
asymmetric region in Fig 1(g) is used as a feature for
classification, where the other feature is the mean gray
scale value. The class with larger mean 3D asymmetry
volume is identified as the injury class, and the final injury
regions belonging to the injury class is shown in Fig 1(h).
4. Experimental Results
4.1. Datasets and Parameters
We use MRI datasets provided by Loma Linda
University Medical Center at Loma Linda, CA. It is
MRI
#
composed of two sequences of MRI slices from two
patients labeled as #A and #B. Sample slices are shown in
Fig 2 and Fig 3. Slices in each MRI sequence are collected
from 2D projections of different 3D brain layers for the
same patient. Several challenging injury cases are also
obtained from the Internet, and an example is shown in Fig
4. The 2 major parameters in our algorithm are: threshold
for region growing pixel aggregation criterion in
equation (2), and the kurtosisskewness histogram cut
threshold Ω for asymmetric region detection introduced in
section 3.3. The values of the two parameters are 0.024 and
0.22 respectively. We use the same parameter setting for
running all slices in all MRI sequences.
a. Original Image b. Segmentation
c. Asymmetric
Regions
d. Injury Regions
(Computed)
e. Injury Regions
(Groundtruth)
A6
A7
A9
A11
Fig 2. Example results on slices for patient #A
( , )i j
δ
tδ
84
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Page 7
MRI
#
B7
a. Original Image b. Segmentation
c. Asymmetric
Regions
d. Injury Regions
(Computed)
e. Injury Regions
(Groundtruth)
B8
B9
B10
Fig 3. Example results on slices for patient #B
(a)
(b)
(c)
(d)
Fig 4. (a) Original image; (b) Injury detection by
region intensitybased asymmetry detection; (c) Injury
detection by our method; (d) groundtruth injuries.
Table 2. Results of MRI sequence for patient #A
Injury
area
ground
truth
(pixels)
1 1885 0
2 3271 0
3 4421 0
4 5583 66
5 6707 145
6 7839 741
7 8667 707
8 9472 583
9 10166 552
10 10013 548
11 9089 189
12 8154 108
13 9444 0
14 8825 0
15 7019 0
16 7086 0
Total
117640 3639
MRI#
Total
brain
area
(pixels)
Percent
injury
Injury
area
comput
ed
(pixels)
0
0
0
53
137
696
754
548
541
526
168
98
0
0
0
0
3452
Error
rate
0
0
0
0
0
0
1.18%
2.16%
9.45%
8.16%
6.15%
5.43%
5.47%
2.08%
1.32%
0
0
0
0
3.09%
27.3%
8.97%
7.29%
6.65%
9.43%
3.07%
6.39%
16.4%
10.2%
0
0
0
0
7.53%
85
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Page 8
4.2. Experimental Results
We run our algorithms on MRI sequences of two
patients. An example slice and the result of each step are
shown in Fig 1. Slices from patient #A and #B are shown in
Fig 2 and Fig 3. As can be seen in the example of patient #A
from Fig 2 (c) to (d), the normal asymmetric regions are
eliminated by unsupervised classifier without any training
phase or prior model, only using a 2dimensional feature
introduced in section 3.5. The final injury regions in Fig
2(d) are compared to the groundtruth injuries in 2(e), by
finding the percentage of overlap and nonoverlap area.
The percentage of nonoverlap area, also called the false
positive rate, determines the error rate, as shown in Table 2.
Fig 3 also shows some example results from patient #B.
The overall error rate of patient #A by our method is 7.53%
shown in Table 2, and 9.14% for patient #B. Comparisons
between Fig 2(d) and (e), also between Fig 3(d) and (e)
show that most of the injuries can be successfully extracted
with low error rate by our method. The error rate of
nonoverlapping area directly comes from the segmentation
results. By searching better parameters of segmentation to
improve the injury region boundary, the error rate can
further be reduced. One of our future works will be focused
on segmentation optimization by effective parameter
searching. Table 2 provides statistical results of MRI
sequence from patient #A. One challenging case in Fig 4
shows the successful detection of injury by our method in
Fig 4(c), a better result compared to the result in Fig 4(b),
which extracts asymmetric regions by directly comparing a
region’s intensity with its mirror region with respect to the
symmetric axis. The error rate by our method in Fig 4(c) is
11.4%, compared to 27.6% by the method in Fig 4(b).
5. Conclusions
This paper provides a new injury detection method for
brain MRIs. A symmetryintegrated image segmentation is
applied to ensure that the symmetry property is preserved in
the segmentation results. Kurtosis and skewness are used
with a symmetry affinity matrix to extract potential
asymmetric regions. An asymmetry grouping using 3D
relaxation algorithm is combined to further refine the
asymmetric regions. Brain injuries are finally extracted
from asymmetric regions using an unsupervised classifier
based on the Gaussian mixture model. Both qualitative and
quantitative results on the data from the two patients show
that the volume of the computed injury closely
approximates the groundtruth. In the future we will
evaluate the approach on larger scale of datasets.
Acknowledgements: The authors would like to thank
Stephen Ashwal and Andre Obenaus of LLUMC for
providing us the MRI data that has been used in this paper.
This research was supported in part by NSF grant 0641076.
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