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 Dr.S.Sankar Ganesh 2 2

Vijayalakshmi. J 1

Asso. Professor, Dept. of IT

M.E Communication and Networking 1 National Engineering College, awesomeviji@gmail.com

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

D

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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Fig. 1. Vertebral body and processes

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Fig. 2.Typical challenges for vertebrae segmentation. (a) Inner boundaries. (b) edit Osteophytes. (c) Bone degenerative IJTET staff will and complete the final formatting disease. of your (d) Double boundary.

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VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303 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

(a)

(b)

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].

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Normalized Graphcut Fig. 3. (a) Input CT image (b) Pre-processed image (c) Detected2.2 vertebrae region (d) Segmented vertebrae region

Fig. 4. Block diagram of graph cut segmentation

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.

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 d i The matrix D is a diagonal matrix and each diagonal element d i contains the sum of all the elements in the ith row. The second step is solving a generalized Eigen system

( D  W )Y  Dy

(1)

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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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.

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VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303 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: wij  exp

 x(i )  x( j )  F (i )  F ( j ) * exp if X (i )  x( j )  r 2   y T Dv

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

xc  ( x1 , y1,......xc, yc )

(2)



(3)

(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).

x 

s

i 1

xi

s  i 1 ( x i  x)( xi  x)T s

(4)

The covariance

s  i 1 ( x i  x)( xi  x)T s

(5)

The eigenvectors corresponding to the largest Eigen values are retained in a shape can now be approximated by

x  x  b

i (6)

Where b is a vector of elements containing the model parameters, computed by

(a) (b) (c) Fig. 5. (a) Removed spinal process (b) Segmented vertebral body (c) Extracted boundaries of vertebral body

3.

3

Furthermore, stop if the total number of nodes in the partition (Area) is smaller than a pre-specified threshold value.

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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Fig. 6. Block diagram of statistical Shape Modelling

b  ()T ( x  x)

(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.



t i 1

i  i1 i 2n

(8)

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VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303 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 (x n,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.

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Fig. 8.(a) – (d) Labelling of the extracted boundaries of vertebral bodies of data set

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Fig. 9.(a) – (c) LModes of variations of the Mean shape of data set



t i 1

i  i 1 i 2n

(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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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 graylevel 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 L max.

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.

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

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VOLUME 3 ISSUE 1 –JANUARY 2015 - ISSN: 2349 - 9303 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 %

2.8

3.1

8.1

Max. error%

9.7

7.7

43.5

Mean error%

6.7

6.4

14.4

Stand. dev%

1.7

2.1

14.5

Average time, sec

60.2

35.9

7.8

To evaluate the results we calculate the percentage segmentation error as follows Error  100 *

Total number of misclassifed pixels Number of vertebral body pixels

(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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