Statistical Cerebrovascular Segmentation for Phase-Contrast
MRA Data
Mohamed Sabry 1, Charles B. Sites 1, Aly A. Farag 1, Stephen Hushek 2, Thomas Moriarty 2
1
Computer Vision and Image Processing Laboratory
University of Louisville, Louisville, KY, 40292.
{msabry, syschuck, farag}@cvip.Louisville.edu
http://www.cvip.uofl.edu
2
Dept. of Neurological Surgery, University of Louisville, KY, 40292.
Abstract-In this paper, we present a statistically based
segmentation algorithm to extract vascular tree from Phase
Contrast Magnetic Resonance Angiography, “PCMRA”.
Classification is based on the intensity distribution of the
tissues in the data volume, where voxels are classified as
either vessels or non-vessels. Our algorithm is adaptive to
reduce the bias field effect in the images by estimating the
model parameters for each slice of the data volume using the
Expectation Maximization, “EM” algorithm for finite
mixture of densities. A connectivity filter is designed taking
into account the topology of the vascular tree to remove nonvessel tissues that appear after statistical segmentation in the
form of small islands. We also implemented the Maximum
Intensity Projection algorithm, “MIP” to validate the results
by projecting both the segmented and original data volumes
at different angles. Hence, the resultant images from both
volumes can be compared side by side, which facilitates the
validation process. Finally, the segmented tree is visualized in
3D using Visualization Toolkit, “VTK”, which can be viewed
on a stereo graphics workstation or in a virtual reality
environment. The results are validated by our medical
research team and successfully showed small MRA vessels
down to the limit of the scanner resolution.
Keywords - Statistical segmentation, Vascular Tree, PCMRA.
is extracted based on the tubular shape of vessels [5]. Other
approaches for MRA vessel segmentation is the manually
defined seed locations for segmentation [6].
Validating the model is very tedious and difficult process since
practitioners usually rotate the visualized 3D model by certain
angles in order that the views at these angles agrees with the
available 2-D images taken by digital subtraction angiography
(DSA) or MIP. MIP algorithm is the most common way of
displaying 3-D MRA although it is sensitive to high intensity
values that obscure regions of slow flow. The MIP image is
similar in appearance to traditional X-ray but has some
characteristics that make it easy to process digitally.
In this paper, we present an automatic statistically based
segmentation algorithm to extract vascular system from phasecontrast MRA, where voxels are classified as either arteries or
non-arteries. Our algorithm is adaptive to reduce MRA
inhomogenities caused by the bias field by estimating the model
parameters for each slice of the data volume using expectation
maximization (EM). A connectivity metric (filter) is developed
to authenticate the cerebrovascular tissues. Finally, we validated
the results using the technique presented in [7].
II. RELATED WORK
I. INTODUCTION
The human cerebrovascular system is a complex threedimensional anatomical structure. Serious types of vascular
diseases such as carotid stenosis, aneurysm, and vascular
malformation may lead to brain stroke, which is the third leading
cause of death and the number one cause of disability. An
accurate model of the vascular system from MRA data volume is
needed to detect these diseases at early stages and hence may
prevent invasive treatments. A variety of methods have been
developed for segmenting vessels within MRA. One class of
methods is based on a statistical model, which classifies voxels
within the image volume into either vascular or non-vascular
class for time-of-flight MRA [1]. Another class of segmentation
is based on intensity threshold where points are classified as
either greater or less than a given intensity. This is the basis of
the iso-intensity surface reconstruction method [2]–[4]. This
method suffers from errors due to image inhomogenities in
addition; the choice of the threshold level is subjective. An
alternative to segmentation is axis detection known as
skeletonization process, where the central line of the tree vessels
The most frequently used methods of acquisition in MRA are the
‘bright blood’ sequences TOF (time-of-flight) and PCA (phase
contrast angiography), which rely on suppression of background
stationary tissue and increased vessel-to-soft-tissue contrast from
the flow of moving spins. Wilson and Noble [1] showed that the
histogram of TOF data volume could be classified into three
intensity regions. The lowest intensity region corresponds mainly
to cerebrospinal fluid (CSF) surrounding the brain tissue, bone
and the background air. The middle intensity region corresponds
to brain tissue, including both the gray and white matter. The
high-intensity region consists of fat, which is found adjacent to
the skin, and arteries. They modeled the low and middle intensity
regions (CSF and brain tissues) by Gaussian distribution. The
high intensity region (arteries) is modeled by a uniform
distribution over the whole intensity range. Fig. 1, shows a
typical TOF data volume histogram, where the dotted line,
represent the actual data volume and the solid line represents the
fit of two Gaussian and a uniform distribution. They estimated
the distribution parameters using EM algorithm and classified
voxels using Bayes classifier.
Fig. 2. PCA volume histogram
Fig. 1. TOF volume histogram
III. STASTICAL CLASSIFICATION ANALYSIS
In case of PCA, our studies showed that the situation is different.
We analyzed different PCA data sets and found that the volume
histogram always has one peak near the low intensity region,
which is not surprising since PCA is known to have good
suppression of stationary tissues over TOF. We proposed the
following model; we will assume that our data volume consists
of two classes, vessel and non-vessel. Non-vessel class includes
both the low and middle intensity regions (CSF, WM, and GM)
and is modeled by a Gaussian distribution. The vessel class
includes arteries and is modeled by a uniform distribution. Fig. 2,
shows a typical PCA data volume histogram, where the dotted
line, represent the actual PCA data volume and the solid line
represents the fit of a Gaussian and a uniform distribution. The
total distribution of the PCA data can be expressed as a finite
mixture
of
two
classes;
vessel
and
non-vessel.
p( x)  p( x | 1 ) P(1 )  p( x | 2 ) P(2 )
Where, p (x ) is the total distribution of PCA data,
(1)
x is the
p( x | 1 ) is the posterior distribution of nonvessel class, p( x |  2 ) is the posterior distribution of vessel
class, P(1 ) and P( 2 ) are the proportions of non-vessel and
voxel intensity,
vessel classes in data volume respectively. A Gaussian
distribution models non-vessel class as follows:
p( x | 1 ) 
 ( x   )2 

exp  
2 2 
2 2

1
(2)
p(x i|ω2 )P(ω2 )  p(x i|ω1 )P(ω1 )
 ( x   )2 
exp   i 2  P(ω1 )
2
2 2


1
P(ω2 ) 
I
1
 P(1 ) I
xi*     2 ln 
 P( 2 ) 2
we should estimate the parameters of each class distribution.
Four parameters need to be estimated
IV. PARAMETERS ESTIMATION
EM is a general method of finding the maximum-likelihood
estimate of the parameters of an underlying distribution from a
given data set when the data is incomplete or has missing values
[8]. The mixture-density parameter estimation problem is
probably one of the most widely used applications of the EM
algorithm in the computational pattern recognition community,
where parameters are iteratively estimated by updating the initial
estimates of the parameters. When the distribution is Gaussian,
the parameters of the distribution can be directly estimated from
the following equations.
N
new
(3)

p
old
i 1
N
p
N

new 2

p
i 1
old
P(ω2 | xi )  P(ω1 | xi )
(4)
(1 | xi ) xi
old
N
p
(8)
(1 | xi )
(1 | xi )( xi   new ) 2
i 1
vessel class if:
 ,  2 , P(1 ) for non-
vessel class and P( 2 ) for vessel class, which can be achieved
by EM algorithm.
i 1
Where, I is the maximum intensity in the data volume.
According to Bayes classifier, a voxel x i is said to belong to
(7)
*
A uniform distribution models vessel class as follows:
1
I
(6)
Where, x i is the decision level. Before classification takes place,

p( x |  2 ) 




(5)
old
(1 | xi )
(9)
1
N
P new (1 ) 
N
p
old
i 1
(1 | xi )
P new ( 2 )  1  P new (1 )
p
old
(10)
Table 1, shows the initial and final estimates of the parameters
estimated by EM for patient1 and patient2 respectively.
(11)
TABLE 1
RESULTS OF EM ALGORITHM FOR PATIENT1 AND PATIENT2.
p old ( xi |  k ) P( k )
(12)
( k | xi )  old
p ( xi | 1 ) P(1 )  p old ( xi |  2 ) P( 2 )
N is the total number of voxels in the PCA volume and
xi is the intensity of voxel i .
Where,
0
Patient 1
Initial
Final
Est.
Est.
19
25
Patient 2
Initial
Final
Est.
Est.
4
16
2
168.5
223.9
35
128.78
P0 (1 )
0.9
0.1
0.9812
0.0188
0.9
0.1
0.9224
0.0776
0
P0 ( 2 )
V. PARAMETERS INITIALIZATION
Convergence of EM algorithm is critically dependent on the
initial guess of the parameters. The mean  0 is chosen to be the
Fig. 4 and Fig. 5, show the fit of a Gaussian and uniform
distribution by EM algorithm versus the total distribution of the
whole MRA volume for patient1 and patient2 respectively.
intensity corresponding to the histogram maximum value as
 02 can be estimated as follows:
p( x)  p( x | 1 ) P(1 )  p( x | 2 ) P(2 )
(13)
shown in Fig 3. The variance
p ( x) 
1
2 02
( x  0 )2
1
) P0 (1 )  P0 ( 2 )
2
2 0
I
(14)
P0 (1 )
(15)
exp( 
p(  0 ) 
2 
0
2
2
0

P0 ( 2 )
I
P02 (1 )
P ( ) 

2  p(  0 )  0 2 
I 

2
Fit of Mixture Dist. By EM
PCA Volume Histogram
(16) Fig. 4. Fit of a Gaussian and uniform distribution by EM algorithm versus the
It is a fact that arteries constitute a small percentage of the human
brain, hence the initial estimates for P0 ( 2 ) and P0 (1 ) are
0.1 and 0.9 respectively. EM steps are repeated iteratively until
no further changes in the parameter values or difference between
them is very small. EM is found to converge for many data sets
after 15 iterations. We did not approximate the EM parameter
estimation equations as in [1] to speed up the processing time.
total distribution of the whole PCA volume for patient1.
Fit of Mixture Dist. By EM
PCA Volume Histogram
Fig. 5. Fit of a Gaussian and uniform distribution by EM algorithm versus the
total distribution of the whole PCA volume for patient2.
VI. ADAPTIVE SEGMENTATION
Segmenting the whole data volume based on a single decision
level x * is not an accurate model and is prone to error.

Fig. 3. Estimating
0
Fig. 6. Typical seed image
Fig. 5. Dotted curve is the total volume
histogram. Each solid line is a slice histogram.
The histogram of each volume slice is studied independently. It
is found that, having a single decision level for each slice to
adapt the changes of arteries intensity from slice to another is a
better model. The solid lines of Fig. 5, shows the independent
histograms of the first four slices of the PCA volume. The dotted
line represents the histogram of the whole data volume. Classifier
parameters are then estimated for each slice independently and a
new decision level is calculated for each slice. This adaptation
will reduce the effect of MRA inhomogenities caused by bias
field. As a generalization, the whole volume can be divided into
n sub-volumes of m slices. Our case occurs when m equals one.
VII. CONNECTIVITY FILTER
Some non-cerebrovascular tissues appear in the final segmented
volume. A connectivity metric (filter) is developed to
authenticate the cerebrovascular tissues. The filter exploits the
fact that the vascular system is a tree-like structure and makes
use of the 3D computer graphics region-filling algorithm to
extract the vascular tree. The algorithm needs for a start a point
that belongs to the tree. That can be achieved by searching the
data volume for the slice that has the largest brightest spots
which corresponds to the carotid arteries cross section voxels.
Those voxels are marked as parents, and are pushed into a stack
data structure. Let vessel_array is a 3D empty array that will
store the connected vessel tree extracted by the filter. Each parent
voxel is popped from the stack and is inserted into vessel_array,
then it is compared with the 26-adjacent neighbour voxels
(children) that form a small cube whose center is the parent. If
the child is adjacent to its parent, it is marked as parent too and is
pushed into the stack. The process is repeated until the stack is
empty. vessel_array now contains our connected tree. Since our
algorithm investigates only those neighbours (children)
surrounding the current voxel (parent), hence, we eliminate the
possibility of having unconnected tissues in the final volume.
Fig. 6 shows a typical seed image for carotid voxels, where
arrows point to carotid cross sections.
VIII. VALIDATION
One of the crucial issues with 3D volumes generated from MRA
scans is the validation with respect to the known structures.
It is quite difficult to devise validation criteria because of the
extent and complexity of the vascular tree. While basic arteries
and veins are of known size and significance, the rest of the
vascular tree does not have distinct landmarks to recognize.
Basic evaluations of these models using phantoms can be
employed but there exists no such phantom that mimics the
complexity of the vascular tree especially those vessels whose
diameters less than 1mm. Practitioners usually validate the
resulting cerebrovascular volume by rotating the visualized 3-D
model by certain angles in order that the views at these angles
agree with the available 2-D images taken by DSA or MIP.
In [7], we implemented the MIP algorithm such that we can
generate any projection of the data volume at any angle. We
applied the algorithm to both the original and segmented
volumes. The generated projected images from all directions at
different angles to both volumes can then be compared to each
other side by side. This technique will help practitioners to
evaluate visually the quality of the MRA results fast when
compared with traditional methods.
IX. RESULTS
The MRA data sets were collected using GE MEDICAL
SYSTEMS Genesis Signa MRI system. MRA data set consists of
256x256x117 axial slices from Nasal Cavity to the top of the
skull with 1mm thickness. The first row of Fig. 7 and 8 show the
MRA volume of patient1 and patient2, respectively, projected by
the MIP algorithm at angles 0, 25, 45, 90 before segmentation,
while the second row of both figures show the resultant images at
the same angles after applying our segmentation technique. First
row of Fig. 9 shows some selected row data slices numbered (1,
7, 98, 101, and 117) for patient1. The second row shows the
segmented slices before applying the connectivity filter. The
third row shows the segmented slices after the application of the
connectivity filter. Note that the filter removed all the nonvessels that formed small islands in the data volume. The last
column of the same figure shows the 3D visualization for each
mentioned case. This patient suffers from a severe artery
malformation, which is apparent in the images of second column
from left. Left and Right images of Fig.10 show the 3-D visualization
of patient1 and patient2 respectively. Fig. 11 shows the 3D volume
of patient2 before and after applying the connectivity filter. Since
stereo viewing is recommended for highly complex 3D vascular
structure, we used VTK as a visualization toolkit because of its
capability in rendering the results in stereo, besides it can be used
with virtual reality display environments such as Immersa-Desk system, where our 3-D results are displayed. Speed wise, the
proposed segmentation algorithm is very fast compared with other algorithms. 256x256x117 slices takes 2 minutes over Onyx-II
supercomputer
Fig. 7. First row shows the MIP images of the MRA volume of patient1 projected at angles 0, 25, 45, 90 respectively before segmentation.
Second row shows the resultant MIP images generated at the same angles after applying our segmentation technique
Fig. 8. First row shows the MIP images of the MRA volume of patient2 projected at angles 0, 25, 45, 90 respectively before segmentation.
Second row shows the resultant MIP images generated at the same angles after applying our segmentation technique
#1
#37
#98
#101
#117
Fig. 9. Patient1 (1st row) selected raw data slices numbered (1, 7, 98, 101, and 117). (2nd row) segmented slices by our algorithm before connectivity filter.
(3rd row) segmented slices by our algorithm after connectivity filter. (last column) from top to bottom, 3D visualization for the un-segmented volume,
segmented volume without connectivity filter, and segmented volume with connectivity filter.
Fig. 10. 3-D visualization of patient1 and patient2 respectively.
Fig. 11. 3-D visualization before and after applying connectivity filter for patient2.
X. CONCLUSION
We have presented a fast automatic statistically based
segmentation algorithm to extract the cerebrovascular system
from phase contrast MR angiography. Our algorithm is adaptive
by finding an intensity decision level for each data slice to
overcome MRA inhomogenities. We designed a parent/child
connectivity filter to remove tissues that form small islands in the
segmented volume.
XI. FUTURE WORK
Investigate the application of MRF to segmentation process to
take into account the spatial distribution of voxels in data volume
and also improve the statistical model by taking into account
geometrical features beside the intensity level.
ACKNOWLEDGMENT
The Whitaker Foundation Research Grant No. 98-009 has funded
this project. The generous support of Norton Healthcare
Organization for our medical research through Grants 97-72 and
97-73 is greatly appreciated.
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