Hierarchical Vertebral Body Segmentation Using Graph Cuts and Statistical Shape Modelling

INTERNATIONAL JOURNAL FOR TRENDS IN ENGINEERING & TECHNOLOGY
VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303
Hierarchical Vertebral Body Segmentation Using
Graph Cuts and Statistical Shape Modelling
Vijayalakshmi. J 1
M.E Communication and Networking
1
National Engineering College,
awesomeviji@gmail.com
Dr.S.Sankar Ganesh 2
2
Asso. Professor, Dept. of IT
1
National Engineering College,
ssganesha@yahoo.com
Abstract— Bone Mineral Density (BMD) estimations and fracture investigation of the spine bones are retrained to the
vertebral bodies (VBs).A contemporary shape and appearance based method is proposed to segment VBs in clinical
Computed Tomography (CT) images without any user arbitration. The proposed approach depends on both image
appearance and shape information. Shape knowledge is aggregated from a set of training shapes. Then shape variations are
estimated using statistical shape model which approximates the shape variations of the vertebral bodies and its background
in the variability region. To segment a VB, the graph cut method used to detect the VB region automatically. Detected
contours are aligned and mean shape model is created. The spatial interaction between the neighboring pixels is identified.
The statistical shape model is used to produce the deformable shape model and all instances of the shape lies with the
current estimate of the mean shape.
.Index Terms— ASM, BMD, Graph cuts, Modelling, VB.
——————————  ——————————
1 INTRODUCTION
OCTORS use the BMD measurements of vertebral bodies in
order to diagnose and treat osteoporosis precisely. Correct VB
segmentation takes an important step for measuring and BMD
and vertebral fractures which are used in evaluating new
osteoporosis therapies [1].The spine bone includes vertebral body
and processes as shown in Fig.1, anyhow, spinal BMD
measurements and Fracture Analysis are confined to the vertebral
bodies. Finite approaches have been made known to gear the
segmentation of spine bones.
The main goal of the proposed work is the segmentation of
vertebral bodies from computed tomography (CT) images and
increases the accuracy of the BMD measurements and fracture
analysis. Factually segmenting a vertebral body (VB) from its
background is not a simple work due to threats in spinal CT images.
These consists inner boundaries, osteophytes, bone degenerative
disease, double boundary, and weak edges of spine bones. Also,
exposure levels slice thickness, and volume. Most methods
developed for general medical image applications cannot produce
accurate results for vertebral body segmentation because a vertebral
body has an ambiguous edge boundary and it does not contain a
homogeneous region. Most methods developed for general medical
image applications they cannot produce accurate results for VB
segmentation. The vertebral body has an inexplicit edge boundary
and it does not contain a homogeneous region.
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129
D
Fig. 1. Vertebral body and processes
(a) (b) (c) (d)
Fig. 2.Typical challenges for vertebrae segmentation. (a) Inner
boundaries. (b) Osteophytes. (c) Bone degenerative disease. (d)
Double boundary.

Most of the previous works construct a shape model for each
vertebrae type which needs a strong boundary. To avoid this
drawback global shape model is required. This model can be deform
and fits to each vertebral body type.Various approaches have been
introduced to tackle the segmentation of spine bones. For instance,
Mastmeyer et al. [4] presented a hierarchical segmentation approach
for the lumbar spine in order to measure bone mineral density. They
reported that their algorithm can be used to analyze three vertebrae
in less than 10min. This timing is far from the real time required for
clinical applications but it is a huge improvement when compared to
the timing of 1 - 2h reported in [5].
Klinder et al. [6] developed automated model-based vertebra
detection, identification. The authors reported that the elapsed time
for the identification of 12 CT vertebrae is 2192 seconds (36.5 min)
on average. Other techniques have been developed to segment
skeletal structures and can be found for instance in [7, 8, 9] and the
references therein. In this paper, we propose vertebral body
segmentation approach that uses subsequently; i) graph cut
segmentation approach to extracts the boundary of vertebral body. ii)
Statistical shape model based on the graph cut segmented image to
model the shape variations of vertebral body. The graph cut
segmentation approach explained briefly at section 2 and statistical
shape modeling is explained briefly at section 3.
2 GRAPH CUT SEGMENTATION
2.1 Pre-Processing
The input images are vertebrae CT (computed tomography) images.
Radiation exposure is between 200-400 µs totally ten datasets are
tested and number of visible VBs changes from 2 to 11 for each data
set. The input images are noisy. To accurately segment the vertebrae
region the contrast of image should be increased .In the first step,
histogram equalization is performed to enhance the contrast of
images. By transforming the values in an intensity image, histogram
of the output image approximately matches a specified histogram.
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2.2 Normalized Graphcut
All After preprocessing, graph cut segmentation is used the extract
the boundary of vertebral body. In this step, the graph cut is used as a
global optimization algorithm to find the segmented VB. A graph can
be partitioned into two disjoint sets by simply removing edges
connecting the two parts. The degree of dissimilarity between these
two pieces can be computed as total weight W of the. In graph
theoretic language, it is called the cut.
Given a partition of nodes of a graph, V, into two sets A and B, let
x be a dimensional indicator vector also called feature vector, xi =1 if
node is in A and -1 otherwise. Let d(i) be the total connection from
node i to all other nodes. To separate an image I with size M-by-N
into two parts, have to define two matrices: W and D, both of size
(MXN) - by - (MXN). The matrix W is the similarity matrix with
element Wij as the similarity between the ith
pixel and the jth
pixel.
The dissimilarity between VB and other organs is based on this index
at each pixel it is also called spatial location distance di The matrix D
is a diagonal matrix and each diagonal element di contains the sum of
all the elements in the ith
row. The second step is solving a
generalized Eigen system
(1)
However, the two constraints on y which come from the condition
on the corresponding indicator vector x. First, consider the constraint
YD1 = 0. The Eigen vector y with the second smallest Eigen value is
selected for the image segmentation. If the element values in y have
all real numbers, On the basis of the eigenvector by taking the signs
into consideration we can divide the image into segments. The next
step is use the eigenvector to bipartition the graph. In the ideal case,
the eigenvector should only take on two discrete values the feature
vector sign tell us exactly how to partition the graph. The current
partitions are divided based on the threshold value called ncut.
130
(a) (b) (c) (d)
Fig. 3. (a) Input CT image (b) Pre-processed image (c) Detected vertebrae region (d) Segmented vertebrae region
Fig. 4. Block diagram of graph cut segmentation
yDYWD  )(

2.3 Grouping Algorithm
Graph partitioning has the following properties:
1. The graphs are often only locally connected and the
resulting Eigen systems are very sparse
2. Only the top few eigenvectors are needed for graph
partitioning.The second Eigen vector is used to bipartion
the graph
3. The precision requirement for the eigenvectors is low
Given an image sequence I. Construct a weighted graph G =
(V,E) where each node is each pixel of the image I. Let N be the
number of nodes (pixels), i.e., |V|.Construct an N × N symmetric
similarity matrix W as:
(2)
Where X(i) is the spatial location of node i, i.e., the coordinates in
the original image I, and F(i) is a feature vector defined as F(i) =
I(i), the intensity value, for segmenting brightness (gray scale)
images.
1. Solve a generalized Eigen system Use the eigenvector to
bipartition the graph.
2. Repeat bipartition recursively. Stop if Ncut value is larger
than a pre-specified threshold value (Large Ncut value
means that there is no clear partition point any more).
3. Furthermore, stop if the total number of nodes in the
partition (Area) is smaller than a pre-specified threshold
value.
3 STATISTICAL SHAPE MODELLING
This section briefly reviews the ASM segmentation scheme. Several
comparable approaches are found in the literature. ASMs have been
used for several segmentation tasks in medical images. Shapes and
objects have been modeled by landmarks, finite-element methods
and Fourier descriptors and by expansion in. While there are
differences, the general layout of these schemes is similar in that
there are: 1) a shape model that ensures that the segmentation can
only produce plausible shapes; 2) a gray-level appearance model that
ensures that the segmentation places the object at a location where
the image structure around the border or within the object is similar
to what is expected from the training images. In previous works filter
bank of Gaussian derivatives used.
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Subsequently a statistical analysis is performed to learn which
descriptors are the most informative at each resolution, and at each
landmark.and 3) an algorithm for fitting the model by minimizing
some cost function.
3.1 Active Shape Models
An object is described by n points, referred to as landmark
points. The landmark points are determined in a set of s training
images. From these collections of landmark points, a point
distribution model is constructed as follows (x1,y1)…(xn,yn). The
landmark points are stacked in shape vectors
(2)
(3)
(4)
The covariance
T
ii
s
i
xxxxs )()(1
 
(5)
The eigenvectors corresponding to the largest Eigen values i
are retained in a shape can now be approximated by
bxx  (6)
Where b is a vector of elements containing the model parameters,
computed by
)()( xxb T
 (7)
When fitting the model to a set of points, the values of b are
constrained to lie within the range j-1 where m usually has a value
between two and three. The number of Eigen values to retain is
chosen so as to explain a certain proportion of the variance in the
training shapes, usually ranging from 90% to 99.5%. The desired
number of modes is given by the smallest for which before PCA is
applied to the shapes, the shapes can be aligned by translating,
rotating and scaling them so as to minimize the sum of squared
distances between the landmark points.
(8)
131
(a) (b) (c)
Fig. 5. (a) Removed spinal process (b) Segmented vertebral
body (c) Extracted boundaries of vertebral body
v
Tij
Dy
rjxiXif
jxix
jFiF
w








)()(
)()(
exp*)()(
exp
2

),( ,,......11 ccc yxyxx 
 

s
i ixx 1
T
ii
s
i
xxxxs )()(1
 
  

t
i
n
i ii1
2
1

Fig. 6. Block diagram of statistical Shape Modelling

An iterative scheme known as Procrustes analysis is used to
align the shapes. This transformation and its inverse are also applied
before and after the projection of the shape model. This alignment
procedure makes the shape model independent of the size, position,
and orientation of the objects. Alignment can also help to better
fulfill the requirement that the family of point distributions is
Gaussian, which is an underlying assumption of the PCA model.
3.2 Gray-Level Appearance Model
The gray-level appearance model that describes the typical image
structure around each landmark is obtained from pixel profiles,
sampled (using linear interpolation).Each landmark is perpendicular
to the contour. The direction is perpendicular to a landmark (xn,yn)
vector that runs from (xn-1,yn-1) to (xn+1,yn+1) over 90o
in the
applications presented in this paper, all objects are closed contours,
so for the first landmark, the last landmark and the second landmark
are the points from which a perpendicular direction is computed; for
the last landmark, the second to last landmark and the first landmark
are used.
On either side k pixels are sampled using a fixed step size, which
gives profiles of length 2K+1 Cootes and Taylor [16] propose to use
the normalized first derivatives of these profiles to build the gray-
level appearance model. The derivatives are computed using finite
differences between the (j-1) th and the (j+1) th point. The
normalization is such that the sum of absolute values of the elements
in the derivative profile is 1. Denoting these normalized derivative
profiles as g1…gs the mean profile and the covariance matrix are
computed for each landmark
3.3 Multiresolution Framework
These profile models, given by j-1and j+1 are constructed for
multiple resolutions. The number of resolutions is denoted by Lmax.
The finest resolution uses the original image and a step size of one
pixel when sampling the profiles. The next resolution is the image
observed at scale and a step size of two pixels
Subsequent levels are constructed by doubling the image scale
and the step size 1 the doubling of the step size means that
landmarks are displaced over larger distances at coarser resolutions.
(9)
The result is that the fitting at coarse resolution allows the model
to find a good approximate location based on global images
structures, while the later stages at fine resolutions allow for
refinement of the segmentation result.
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3.4 Optimization Algorithm
Shapes are fitted in an iterative manner, starting from the mean
shape. Each landmark is moved along the direction perpendicular to
the contour to positions on either side. Evaluating a total of positions
the step size is, again, pixels for the (j-1) th resolution level. The
landmark is put at the position with the lowest Mahalanobis distance.
After moving all landmarks, the shape model is fitted to the
displaced points, yielding an updated segmentation. This is repeated
times at each resolution, in a coarse-to-fine fashion. There is no
guarantee that the procedure will converge
3.5 Summary of Segmentation Algorithm
1. Construct shape model .
2. Training the gray-level appearance model.
3. For each landmark, at each resolution, construct a set of
training samples with as input the 60 features and as output
zero or one depending on whether the sample is in or
outside the object. Samples are taken from an grid around
the landmark in each training image.
4. Initialize with the mean shape.
5. Start the coarsest resolution level.
6. For each landmark, put it at new locations move landmark
to best new position
7. Fit the shape model to displaced landmarks.
8. Iterate steps 3 and 4 times
9. If the current resolution is not the finest resolution, move to
a finer resolution and go to Step 3
132
(a) (b) (c) (d)
Fig. 8.(a) – (d) Labelling of the extracted boundaries of
vertebral bodies of data set
  

t
i
n
i ii1
2
1

(a) (b) (c)
Fig. 9.(a) – (c) LModes of variations of the Mean shape of data
set

4.Results And Discussions
To assess the accuracy and robustness of our proposed framework,
the test results were achieved for 11 data sets. All algorithms are run
on a PC 3 GHz Intel icore5 and 2GB RAM. All implementations are
in Matlab. To compare the proposed method with other alternatives,
VBs are subsequently segmented using the b-spline based
interpolation and statistical level sets methods. Finally, segmentation
accuracy is measured for each method S1 represents the proposed
algorithm. The alternative methods used in the experiments are
represented as S2 (for b-spline-based interpolation), and M3 (for
statistical level sets
TABLE. 1. ACCURACY AND TIME PERFORMANCE OF OUR VB
SEGMENTATION ON 11 DATA SETS.
S1 S2 S3
Min. error %
Max. error%
Mean error%
Stand. dev%
2.8
9.7
6.7
1.7
3.1
7.7
6.4
2.1
8.1
43.5
14.4
14.5
Average time, sec 60.2 35.9 7.8
To evaluate the results we calculate the percentage segmentation
error as follows
(10)
Total number of misclassified pixels is calculated from
subtracting the ASM output contour from the graph cut output
contour of the identical input image. Number of misclassified pixels
is calculated from the total number of pixels from total number on
pixels in the graph cut segmented image. The statistical analysis of
our method is shown in the Table 1. In this table the results of the
proposed segmentation method and other three alternatives are
shown. The average error of the VB segmentation on 10 clinical 3D
image sets is 4.7% for the proposed method.
4 CONCLUSION
In this paper, we have presented a segmentation framework for VBs
in clinical CT images the identification step is used to obtain up and
down boundaries of a VB. Experiments on the data sets show that
the proposed segmentation approach is more accurate and robust
than other known alternatives Experimental results showed that
proposed method gives better results than other alternatives since the
shape constraints overcame the gray level in homogeneities problem
and precisely guided the graph cuts to accurate VBs segmentations
(with mean error 6.7%). Moreover, from the application point of
view, the pro-posed shape based segmentation approach is helpful to
eliminate the spinal processes which are not required for BMD
analysis and FA. This leads to more accurate BMD measurements.
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IJTET©2015
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133
pixelsbodyvertebralofNumber
pixelsedmisclassifofnumberTotal
*100Error 

Hierarchical Vertebral Body Segmentation Using Graph Cuts and Statistical Shape Modelling

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