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International Journal of Computer Engineering & Technology (IJCET) Volume 8, Issue 3, May-June 2017, pp. 36–55, Article ID: IJCET_08_03_005 Available online at http://www.iaeme.com/ijcet/issues.asp?JType=IJCET&VType=8&IType=3 Journal Impact Factor (2016): 9.3590(Calculated by GISI) www.jifactor.com ISSN Print: 0976-6367 and ISSN Online: 0976–6375 © IAEME Publication

REVIEW OF MEDICAL IMAGE

SEGMENTATION WITH STATISTICAL

APPROACH- STATE OF THE ART AND

ANALYSIS

Regonda Nagaraju and M. Janga Reddy

Research Scholar, SJJT University, Chudela

ABSTRACT

In recent years, there are many image segmentation algorithms based on level set

method have been suggested by the research community in-accordance with the

different applications of image processing. At the same time the research communities

have put forward the corresponding solutions and continue to improve and enhance

the efficiency and effectiveness of these algorithms. In this article, according to the

development of the image segmentation methods based on level set, ASM and AAM

(statistical methods) overview and analysis is given for readers of different

backgrounds in this field to use. These algorithms are summarized from three aspects,

i.e., efficiency, discrimination, and robustness. Additionally, some applications and

direction for future implementations of SVD based AAM along with level set method is

enumerated. The main purpose of this paper is to serve as a guide for further

research.

Keyword: SVD, AMM, Statistical method, Image processing.

Cite this Article: Regonda Nagaraju and M. Janga Reddy, Review of Medical Image Segmentation with Statistical Approach - State of the Art and Analysis. International

Journal of Computer Engineering & Technology, 8(2), 2017, pp.36–55. http://www.iaeme.com/ijcet/issues.asp?JType=IJCET&VType=8&IType=3

1. INTRODUCTION

Image segmentation is a process of dividing the images into meaningful subsets and always been perceived as one of the most difficult task in the field of image processing and computer vision. The biggest challenge that often encounter during the medical image segmentation is caused due the image noise. In medical imaging, the source of imaging modalities includes CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography) etc. These modalities generate a huge amount of image information useful to rule out the medical related issues. Due to the varying artifacts and quality of the image capturing devices, we not only find the variation in size of the captured images but also changes into the resolution of the images caused due to intensity in homogeneity or non-

Review of Medical Image Segmentation with Statistical Approach - State of the Art and Analysis


uniformity of the image intensities due to the noise and hence causes the technical challenges during segmentation. Model-based segmentation approaches have been established as one of the most successful methods for image analysis. By matching a model which contains information about the expected shape and appearance of the structure of interest to new images.

In recent years, active contour models (ACM) implemented via level set methods have been successfully used in image segmentation [1-4]. The basic idea of ACM is to implicitly represent a contour as the zero level set of higher dimensional level set function, and formulate the evolution of the contour through the evolution of the level set function [5]. The pioneer work about ACM can be traced to Kass in 1988 [6], after which the approaches have developed in a variety of directions. Generally, the existing ACM can be broadly classified as either edged based models [1,6–9] or region based models [1,10–16].Edged based models [1–4] utilize image gradient information to stop the curve evolution. For this kind of models, it is not necessary to place a global constraint on the level set. The Geodesic active contour (GAC) model is one of the famous models in this class [17].However, for some type of images, which object boundaries are weak or corrupted by noise, the edge-based models are likely to pass through the object boundary or produce spurious boundaries.

The intent of this article is to provide the summary of the current state of the art with regard to statistical shape models and to demonstrate work done until now in this domain. A successful attempt also done in present scenario what might yet be done. To ensure comprehensive coverage, we have screened at-most publication s including IEEE Transactions PubMed, IEEE-Xplore, Citeseer and Google on Medical Imaging and Medical Image during the last 10 years for articles related to shape models. In addition, we have included a large number of articles from other international journals, but also numerous conference and workshop papers which present good ideas, but which have not been published in any journal yet. Our main source of references was the Internet; we have searched for the terms shape model and statistical model and level set based active contour.

In this paper, we will review methods and procedures for generating, training and employing statistical models of shape and appearance for 3D medical image segmentation. Specifically, we will discuss work on discrete, parametric models which can be trained from a set of example data. Probably the best-known methods in that area are the Active Shape models (Cootes et al., 1995) and Active Appearance models (Cootes et al., 2001) by Cootes et al. In addition, we will discuss related concepts and alternative approaches, all within the context of statistical shape models.

The remainder of this paper is organized as follows: A briefer view of some well-known active contour models for image segmentation is given in Section 2. Then, Section 3 devotes to the Applications of modeling methods, in this paper. In Section 4, an extensive literature survey for level set methods, ASM and AAM for synthetic or medical image segmentation is done In section V experiment result analysis of these three methods in different scenario is done using as it is existing form and tested on images. In last VI section we will recapitulate the main points and predict future possible development.

2. BACKGROUND WORK IMAGE SEGMENTATION USING ACTIVE

CONTOURS (REVIEW PAPER-4)

Before reviewing statistical shape models for medical image segmentation, first define background work that will not be discussed further in this article. There are two major approaches in image segmentation: edge- and region- based. Edge based segmentation partitions an image based on discontinuities with sub-regions, while region-based



segmentation does the similar function based on the uniformity of a desired property within a sub-region

2.1. Edge-Based Segmentation

In edge-based segmentation approach, the discontinuities in the intensity of an images are located. Thus this approach may also called as edge detection or boundary detection technique rather than the exact meaning of image segmentation. An edge can be defined as the border between two regions with relatively separate properties. The assumption of edgebased segmentation is that every sub-region in an image is sufficiently uniform so that the transition between two sub-regions can be determined on the basis of discontinuities alone. When this statement is not valid, region-based segmentation, discussed in the next section, regularly provides more reasonable segmentation outcome. Basically, the idea underlying most edge-detection techniques is the computation of a local derivative operator. Edge detection by gradient operations usually works well only in the images with sharp intensity transitions and relatively low noise. Due to its sensitivity to noise, various smoothing operation is usually essential as preprocessing, and the smoothing effect consequently blurs the edge information. However, the computational cost is comparatively lower than other segmentation methods because the computation can be complete by a local filtering operation, i.e. convolution of an image with a kernel.

2.2. Region-Based Segmentation

Region-based segmentation looks for equality inside a sub-region, based on a desired property, e.g. intensity, color, and texture. Clustering techniques encountered in pattern classification literature have related objectives and can be applied for image segmentation [47,20].Region rising [47,21] is a technique that merges pixels or small sub-regions into a bigger sub region. The simplest implementation of this approach is pixel aggregation [47,22], which starts with a set of seed points and grows regions from these seeds by appending nearby pixels if they satisfy the given criteria.

Additional criteria that use properties to raise the regions lead area growing into more sophisticated methods, e.g. region competition. Region competition [47, 23, 24] merges neighboring sub-regions under criteria involving the equality of regions or sharpness of boundaries. Strong criteria tend to generate over-segmented results, while weak criteria lean to produce poor segmentation outcome by over-merging the sub-regions with blurry boundaries. An alternative of region rising is split-and-merge [25], which partitions an image firstly into a set of arbitrary, disjointed sub-regions, and then combine and/or split the sub-regions in an attempt to satisfy the segmentation criteria.

Despite the simple character of the algorithm, there are basic problems in region rising: the selection of initial seeds and suitable properties to grow the regions. Selecting initial seeds can be frequently based on the character of applications or images. For example, the ROI is generally brighter than the background in IR images. In this case, choosing bright pixels as initial seeds would be a suitable choice.

2.3. Active Contours

The method of active contours has become quite popular for a range of applications, mainly image segmentation and motion tracking, through the last decade. This methodology is based upon the use of deformable contours which match to various object shapes and motions. This section provides a theoretical setting of active contours and an indication of existing active contour methods. There are two main approaches in active contours based on the mathematic implementation: snakes and level sets. Snakes explicitly shift predefined snake points based



on an energy minimization method, while level set approaches move contours completely as a particular level of a function.

As image segmentation methods, there are two kinds of active contour models according to the force evolving the contours: edge- and region-based. Edge- based active contours apply an edge detector, typically based on the image gradient, to locate the boundaries of sub-regions and to draw the contours to the detected boundaries. Edge-based approaches are closely connected to the edge-based segmentation. Region based active contours apply the statistical information of image intensity inside each subset instead of searching geometrical boundaries. Region-based approaches are also closely connected to the region-based segmentation.

2.4. Snakes

The initial model of active contour was proposed by Kass et al. [6,47] and named snakes suitable to the appearance of contour evolution. Solving the problem of snakes is to locate the contour C that minimizes the total energy term E with the certain set of weights α , β , and λ . In numerical experiments, a set of snake points residing on the image plane are defined in the first stage, and then the next location of those snake points are determined by the local minimum E. The associated form of those snake points is considered as the contour. Figure 2.1 shows an example of classic snakes [26,47]. There are about 70 snakes points in the image, and the snake points form a contour around the moth. The snakes points are firstly placed at more distance from the boundary of the object, i.e. the moth. Then, every point moves towards the optimum coordinates, where the energy utility converges to the minimum. The snakes points ultimately stop on the boundary of the object.

The classic snakes give an perfect location of the edges only if the first contour is given sufficiently near the edges because they make use of only the local information along the contour. Estimating a correct position of first contours without prior knowledge is a complex problem. Also, classic snakes cannot detect more than one boundary concurrently because the snakes maintain the equal topology throughout the evolution stage. That is, snakes cannot divide to several boundaries or combine from multiple first contours. Level set theory [27,47] has given a result for this problem.

Figure 2.1 An example of classic snakes

2.5. Level Set Methods

Level set theory, a formulation to apply active contours, was proposed by Osher and Sethian [27,47].They represented a contour implicitly via a two dimensional Lipschitz - continuous – function φ (x, y) :Ω→ℜ defined on the image plane. The function φ (x, y) is called level set function, and a particular level, generally the zero level, of φ (x, y) is defined as the contour.



2.6. Edge-Based Active Contours

Edge-based active contours are strongly connected to the edge-based segmentation. Most edge based active contour models consist of two parts: the regularity part, which determines the form of contours, and the edge recognition part, which attracts the contour towards the boundaries. Edge-based active contour models have a little disadvantages compared to the region-based active contour models, discussed in the next section. Because of the constant term, edge-based active contour models evolve the contour towards only one way, each inside or outside. Therefore, an primary contour must be placed completely inside or outside of ROI, and some level of a previous knowledge is still necessary .Also, edge-based active contours inherit a few disadvantages of the edge-based segmentation methods due to the parallel method used.

Since both edge-based segmentation and edge-based active contours rely on the image gradient process, edge-based active contours may omit the blurry boundaries, and they are sensitive to local minima or noise as edge-based segmentation does. Gradient vector flow quick geodesic dynamic contours [28,29,47] proposed by Paragios replaced the border detection (boundary attraction) word with gradient vector field [30,31,32,33,34,47], that refers to a spatial diffusion of the boundary information and guides the propagation to the object boundaries from equally sides, to give extra freedom from the restriction of first contour position.

2.7. Region-based Active Contours

Most region-based active contour models consist of two parts: the regularity part, which determines the smooth form of contours, and the energy minimization part, which searches for equality of a preferred feature within a subset. A good characteristic of region-based active contours is that the first contours can be situated anyplace in the image as region-based segmentation relies on the global energy minimization rather than local energy minimization. Therefore, less previous knowledge is required than edge-based active contours.

Although usual region-based active contours partition an image into several sub regions, those several regions belong to only two subsets: both the inside or the outside of contours. Chan and Vese proposed multi-phase active contour model [35, 36, 37, 38, 39,47], which increases the amount of subsets that active contours can locate simultaneously. Multiple active contours evolve independently based on the piecewise-constant model or the piecewise-smooth model, and multiple subsets are defined by a set of disjoint combination of the level set functions.

Due to the global energy minimization; region based active contours usually do not have any restriction on the placement of first contours. That is, region-based active contour can detect interior boundaries regardless of the position of initial contour. That is, region-based active contour can detect inner boundaries regardless of the position of initial contours. The use of pre-defined initial contours provides a method of independent segmentation. Also, they are less responsive to local minima or noise than edge-based active contours. However, due to the supposition of uniform image intensity, most methods are relevant only to images where each subset is stand for able by a simple expression, e.g. single Gaussian distribution or a constant. If a subset, i.e. class, consists of multiple distinguishing sub-classes, these methods would produce over-segmented or under-segmented results. We propose novel region-based active contour models which produce better results using multivariate mixture density functions.



2.8. Active Contours integrating Edge- and Region based Segmentation

In order to develop the segmentation performance, the integration of edge- and region based information sources using active contours has been proposed by a few authors. Geodesic active region is a supervised active contour model, proposed by Paragios [40, 41, 42,47], integrating edge- and region-based segmentation module in an energy function. A statistical analysis based on the Minimum Description Length (MDL) measure and the Maximum Likelihood (ML) principle for the observed density function, i.e. an image histogram, indicates the number of sub-regions and the statistical PDF within those sub-regions using a mixture of Gaussian elements. Regional probability is estimated from the statistical PDF based on previous knowledge, i.e. training samples. Then, the margin information is resolute by a probabilistic edge detector, expected from the regional probabilities of neighborhood [36, 37,47]. For example, an image pixel is more likely an edge pixel if the neighborhood pixels, located on the opposed sides, have high regional probabilities for a different class. The geodesic active region model is later useful to a medical imaging problem [43, 44, 47] with a gradient vector flow-based boundary factor. The approach was based on a joined propagation of two active contours, and integrates visual information with anatomical constraints.

Jehan-Besson et al. also proposed an active contour model [45, 46, 47] minimizing an energy criterion concerning both region and boundary functional. These functional are consequent through a shape derivative approach as an alternative of classical calculus of variation. They focus on statistical property, i.e. the PDF of the color histogram of a sub-region. Active contours are propagated minimizing the distance between two histograms for corresponding or tracking purposes.

3. LITERATURE REVIEW

3.1. Level Set Methods (IJARECE)

The level set method amounts to representing a closed curve using auxiliary function called as zero level set. The formulation of level set implies that the level set value of a point on the contour with motion must always be zero. The level set method is boundary driven and region driven model free segmentation

Chunming Li et.al. (2011) have discussed about how the intensity in homogeneity foreput the technical challenges during the segmentation process with an application to MRI. In this paper they proposed an innovative idea to tackle the intensity in homoginity issue during region-based segmentation. In this they developed a model by keeping in sight Inhomogeneous intensities with a local intensity clustering property of the image intensities, and defines a local clustering criterion function for the image intensities in a neighborhood of each point. This local clustering criterion function is then integrated with respect to the neighborhood center to give a global criterion of image segmentation. In a level set formulation, this criterion defines an energy in terms of the level set functions that represent a partition of the image domain and a bias field that accounts for the intensity In homogeneity of the image. Therefore, by minimizing, this energy this model able to simultaneously segment the image and estimate the bias field, and the estimated bias field can be used for intensity In homogeneity correction (or bias correction). This model has been validated on synthetic images and real images of various modalities like MRI and experiments show that the method is more robust to initialization.



Figure 3.1 Applications to an MRI image of lungs (a) Initial contour (b) Final contour (c)Estimated bias (d) Bias corrected field image [Source Gaikwad A.,2016]

Kaihua Zhang et al. (2015) suggested a process model for inhomogeneous objects as a Gaussian distributions of different means and variances in which original image is transformed into another domain by using sliding window where the intensity distribution of each object is still Gaussian but better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying a bias field with the original signal within the window. A maximum likelihood energy functional is then defined on the whole image region, which combines the bias field, the level set function, and the piecewise constant function approximating the true image signal. The proposed method can be directly applied to simultaneous segmentation and bias correction for 3 and 7T MRI. Extensive evaluation on synthetic and real-images demonstrate the superiority of the proposed method over other representative algorithms. It is difficult to use local region statistics to well segment images with severe intensity In homogeneity because the regions must have sharp discontinuities in the statistics. The proposed method can yield the closed-form solutions for the estimated parameters in the distribution, which significantly reduces computation effort.

Figure 3.2 Segmentation results with intensity inhomogeneity

Suvadip M. et al. (March 2015) have developed a a robust region based segmentation method which has an ability to segmentize the image in the presence of significant varying intensity constraints using traditional concept active contour without edges. Comparing with other conventional techniques, this paper use illumination of the regions of interest in a lower dimensional subspace using a set of pre-specified basis functions, which enables representation of variety of biological/biomedical images objects, even in presence of noise This paper proposes an edge independent segmentation approach i.e. Legendre Level Set (L2S) which is robust to variation in intensity levels. Initially proposed model focused on bi-level segmentation and later extension is given to multi-level framework. The result of this method is as shown below



Figure 3.3 Segmentation output (a) Initial (b)Chan-Vese (c) Lankton (d)C. Li et.al. (e) Final Contour Model Model Model Contour

Mengjuan C.et al (2014) proposed a PS model is based on the assumption that the intensity in each region can be approximated by a piecewise smooth function, therefore, it can handle some images with intensity In homogeneity. However, the PS model has a very expensive computational cost which limits its application in practice. So to overcome this paper proposed a new local region-based level set model in a variational level set formulation for image segmentation. Difficulties in practical applications arise due to the presence of noise, complex background, low intensity contrast with weak edges and intensity In homogeneity. This model, a data term with a local region-based function is introduced to stop the contours at edges. Then, the data term is incorporated into a variational level set framework with a length term to smooth the contour and a distance regularization term to maintain the evolution of contour stable. The initial contour with this model can be served as a constant function which is convenient and efficient. Results obtained on synthetic and medical images show good performance in handling with images with intensity In homogeneity and noise. The result of this method is as shown below.

Figure 3.4 Segmentation of vessel image. (a) Vessel image (b) Initial contour (b) Intermediate contour (c) Final contour

Rajitha B. et al (2015) The existing image segmentation approaches suffer from the problem of over segmentation. There is a scope to increase accuracy of segmentation. To address the drawbacks of conventional image segmentation approaches homogeneity based approaches can be used which deal with image texture. Image segmentation is based on two properties- similarities and dissimilarities in intensity inside image. Latest image segmentation techniques using homogeneity is presented in this paper. Homogeneity is one of the most widely used approaches for image segmentation because of its robust characteristics for texture segmentation. This paper focuses on local homogeneity based approaches for image segmentation and image defect detection. For this the approaches like image local homogeneity analysis with region merging, local homogeneity analysis with discrete cosine transform, local homogeneity analysis with wavelet transform, homogeneity with FFD method, homogeneity with color features, local homogeneity with Gabor filtering and homogeneity with watershed algorithm are used. The result of this method is as shown below.



Figure 3.5 Segmentation of color image (a) Original image (b) Final segmentation.

Anju Soosan Baby (2015) In recent years a number of algorithms have been proposed and different approaches have been adopted in image segmentation due to its important. Two basic approaches are often seen in image segmentation - edge-based and region-based. Edge detection techniques consist of coming at a decision as to whether pixels are an edge or not where edges are local modifications in the image intensity. Edges typically occur along the bounds between two areas. The main features can be drawn out from the boundaries of an image. Region-based partitioning is a technique for setting the regions directly, on which divide an image into areas. This partitioning is performed frequently by using gray values of image pixels and it is based on similarity. This paper proposed image segmentation using a region growing algorithm. The primary goal behind this theme is to enhance performance or speed up the image segmentation on large volume image data sets, i.e. Very high resolution images (VHR). Since sequential processing of Very High Resolution (VHR) images takes a bunch of time, fronting for a parallel computer architecture which make usage of multiple cores. This paper targets for the origin of a Region-growing algorithm suited for GPU processing, developers with NVIDIA’s CUDA (Compute Unified Device Architecture) platform. An experimental analysis upon different orbital sensor images has made out in order to assess the quality of results. The result of this method is as shown below.

Figure 3.6 Segmentation of satellite image of Golden Gate Bridge, San Francisco.

Chunming Li et.al.(2010) Level set methods have been mostly used in image Processing and computer vision applications. In conventional level set function generally generates the irregularities during its evolution, which may increases numerical errors and looses the stability of the evolution. Hence degraded Level set function periodically replace by numerical remedy called reinitialization with a signed distance function. However, the reinitialization raises serious problems as when and how it should be performed, but also affects numerical accuracy. To avoid this, in proposed method level set evolution is designed as the gradient flow that minimizes energy function with a distance regularization term and an external energy that drives the motion of the zero level set toward desired locations. The distance regularization term is defined with a potential function such as Single Well, Double Well, Triple Well, Quad Well & Huber such that the derived level set evolution has forward-and-backward (FAB) diffusion effect, which is able to maintain a desired shape of the level



set function, particularly a signed distance profile near the zero level set. This proposes a new type of level set evolution called distance regularized level set evolution (DRLSE). The distance regularization of level set function eliminates the need for reinitialization and reduced the induced numerical errors. DRLSE uses the more general and efficient initialization of the level set function which able to use relatively large time steps in the finite difference scheme to reduce the number of iterations, while ensuring sufficient numerical accuracy. To demonstrate the effectiveness of the DRLSE formulation, we apply it to an edge-based active contour model for image segmentation. The proposed DRLSE with various Potential Functions has capability to maintain the regularity of Level set function, particularly the desirable signed distance property in a vicinity of the zero level set, which ensures accurate computation and stable level set evolution. DRLSE is implemented by a simpler and more computational efficient numerical scheme than conventional level set methods. DRLSE is more flexible and provides efficient initialization for generating a signed distance function as the initial LSF. By varying the time step, proposed method able to reduce the iteration numbers and computation time, while maintaining sufficient numerical accuracy, due to the intrinsic distance regularization embedded in the level set evolution. The distance regularization of level set function eliminates the need for reinitialization and reduced the induced numerical errors. To demonstrate the effectiveness of the the results of proposed method shown below.

Figure 3.7 Curve evolution in the narrowband implementation of the DRLSE model for an MR image of bladder. The initial contour, and the contours at iterations 50, 140, and 220 are shown from left to right.

3.2. Active Shape and Appearance Models

Because of the challenging nature of the medical image segmentation problem, statistical model based segmentation approaches such as Active Shape Models (ASM) and Active Appearance Models (AAM)[56-58] are widely adopted. An ASM is a statistical shape model learned a priori from examples to capture variations in the shape of an object of interest in certain kinds of medical images. When applied to segmentation, the models deform toward object boundary but with constraints to deform only in ways characteristic of the object they represent. These statistical models encode high-level knowledge in a more specific manner and are often more robust for image interpretation. The boundary finding process in ASMs is deterministic, however, which requires a model to be initialized sufficiently close to the object to converge and is sometimes prone to local minima.

Active Appearance Models (AAM) have been successfully used in many applications such as tracking, medical image segmentation, recognition and synthesis. AAM is a exible and powerful learning-based deformable model proposedby Cootes et al. [18]. A primary advantage of AAM is that both the shape and texture of the deformable object is modeled through a set of training examples and a range of valid instances of the object can be synthesized. There has been a vigor in the research community involving AAMs owing to the model's exibility and the simple framework.

The idea of active shape models (ASMs) is first suggested by put forward by Cootes and Taylor [61,62]. We have implemented the method based on the description of the ASM



segmentation method detailed in [61,63]. The shape model in ASMs is given by the principal components of vectors of landmark points. The gray-level appearance model is limited to the border of the object and consists of the normalized first derivative of profiles centered at each landmark that run perpendicular to the object contour. The cost (or energy) function to be minimized is the Mahalanobis distance of these first derivative profiles. The fitting procedure is an alternation of landmark displacements and model fitting in a multiresolution framework.

Several comparable approaches are found in the literature. Shapes and objects have been modeled by landmarks, finite-element methods, Fourier descriptors and by expansion in spherical harmonics (especially for surfaces in three dimensions [61,64,65]). Jain et al. [66] have presented a Bayesian framework in which templates are deformed and more probable deformations are more likely to occur. They use a coarse-to-fine search algorithm. Ronfard [67] has used statistics of object and background appearance in the energy function of a snake.

Brejl and Sonka [61,68] have described a scheme similar to ASMs but with a nonlinear shape and appearance model that is optimized with an energy function after an exhaustive search to find a suitable initialization. Pizer et al. [61,69] describe an object model that consists of linked primitives which can be fitted to images using methods similar to ASMs. Cootes and Taylor have explored active appearance models (AAMs) [61,70,71] as an alternative to ASMs. In AAMs, a combined principal component analysis of the landmarks and pixel values inside the object is made which allows one to generate plausible instances of both geometry and texture. The iterative steps in the optimization of the segmentation are steered by the difference between the true pixel values and the modeled pixel values within the object. Sclaroff and co-workers [61,71], [61,72] have proposed a comparable method in which the object is modeled as a finite-element model.

4. ANALYSIS AND DISCUSSIONS ABOUT CURRENT METHODS

4.1. Level Set Method

Let I be an image, and g be the edge indicator function defined by,

21

1

IGg

∗∇+=

σ (4.1)

Then find coefficient of the internal (penalizing) energy term that help contour to outside the object boundary. It defines an external energy for a function Ø(x, y) as below:

)()()(,, φφλφε λ ggvg vAl += (4.2)

where λ > 0 and ν are constants, and the terms )(φgl and )(φgA are defined by,

dxdygl gg ∫Ω

∇= φφδφ )()(

(4.3)

And

∫Ω

−= dxdygHAg )()( φφ (4.4)

This function is known as the level set function. A contour (or level set) C(t) is a curve described by a set of points where the function has the same particular value. The zero level set can be written as

0),,(:),()( =Ω∈= tyxyxtC φ (4.5)



where t is a variable that indicates the time step in the evolution of the contour. The zero level contour of the level set function segtnents the image. The contour C is initially approximated.

The level set function is then initialized as the signed Euclidean distance to the contour C. Fig.4.1 shows the level set function. On the left is the initialization of the level set function and on the right is the level set function that leads to the final segmentation of the image. The initialization has a lot of disconnected pixels on the zero level set, but the level set obtained after applying the segmentation algorithm has only those points that segment the ventricles on its zero level. Here we follow the convention that this level set graph has negative values inside C (pixels belonging to the heart) and positive values outside C.

0),,(:),()( 1 <Ω∈=Ω= tyxyxCinside φ

Figure 4.1 Level set function before segmentation (left) and after segmentation (right).

0),,(:),()( 1 >Ω∈=Ω= tyxyxCinside φ Using an initialization of the level set function based on the initial contour, it is iteratively

approximated by minimizing an energy functional. The energy functional is a measure of the deviation of the existing contour from the ideal contour according to image characteristics.

Table 1

Image Mean Standard

Deviation

RMS Variance Smoothness Energy

1Section 0.0031107 0.0897608 0.0898027 0.00804787 0.920457 0.7621

2Section 0.0032427 0.0897562 0.0898027 0.00801859 0.923447 0.740911

3Section 0.0020681 0.0897909 0.0898027 0.00803049 0.884969 0.769087

4Section 0.0019318 0.0897939 0.0898027 0.00805185 0.877845 0.749118

5Section 0.00193931 0.0897938 0.0898027 0.00798716 0.87826 0.755387

6Section 0.00253273 0.089779 0.0898027 0.00805623 0.904047 0.755693

4.2. Active Shape and Appearance Model

4.2.1. Active Shape Models

Active shape model (ASM) [Cootes 1995], is one of the most popular model-based approaches for medical image segmentation. It can be considered as an extension of deformable models when incorporating prior shape information. The shape prior is constructed by Point Distribution Model (PDM) which models the shape variations from a training set. In the PDM, the shape is represented by a set of points distributed on the

Input Image initial contour

50 100 150 200

50

100

150

200

400 Iterations Segmented Image



boundary. Mathematically, it can be defined by a DN × dimensional vector concatenating

each point’s coordinates, where n is the number of the points and d is the dimension of the

point coordinates. For example, a 2D shape of n points is defined as: T

NXXXXX ),.......,,( 321= (4.6)

Given a training set, each shape is represented by n points referring to the same

coordinate system (order) throughout the entire training set. Then, these shapes have to be aligned into the same coordinates system to filter out the shape variations caused by translation, rotation and scaling. This procedure is commonly accomplished using the Generalized Procrustes Analysis [Gower 1975], which minimizes the least squared error between the points. Once correspondences have been established, a Principal Component Analysis (PCA) is used to build the statistical shape model. The mean shape of the training

set of N samples is calculated using:

∑=

=N

i

iXN

X1

1

(4.7)

A covariance matrix S is computed by:

∑=

−−−

=N

i

T

ii XXXXN

S1

))((1

1

(4.8)

An eigen decomposition of S yields the eigenvectors Pmnd m=1 (representing the principle modes of variation) and the corresponding eigen values λmnd m=1 ((indicating their importance in the construction of model). Sorting all modes from largest to smallest variance, the first k modes are employed to model the observed variability of the training set. Then, shape instances of this population can be expressed by a linear combination of the k significant modes of variation.

VWXX += (4.9)

Figure 4.2 First three modes of shape model of 3D liver [Heimann 2009].

where ).......,( 21 kvvvV = is the matrix of the first k eigenvectors, and T

kwwwW ).......,( 21= is a vector of weights, referred to as the shape parameters. We note that

the number k is significantly smaller than the number of the dimension ND. Varying the

parameters w can generate new examples of the shape. The interval values of w are imposed to constrain the resulting new shape to be valid. We show an example of point distribution model of 3D liver in Fig. 4.2., where the columns from left to right represent the first, the second and the third largest eigen modes, and the rows from top to bottom represent the

resulting shapes taking the variation parameter as kD3 and kD3− respectively.



Now given an image, the instance y of the model in the image is defined by a similarity transform T and the shape parameter vector b.

)( vwxTy += (4.10)

In order to find both the transform T (also called as pose parameters) and the shape parameters w , an iterative method is used given an initial model state. At each iteration, a current model state y is known in the image space. First, an optimal displacement of each

model point is calculated according to image observations. This leads to a vector of a

suggested movement of the model dy in the image space. Second, the pose T is adjusted by a

Pro-crustes match of the model to dyy + , leading to a new transformation T and a new

residual displacements dys . Next, dys is transformed into model space and then projected

into the parameter space to give the optimal parameter updates:

)(1 dysTVvw T −=)

whereT)

is equal to T but without the translation part. After updating w, a new model example is generated and used to update the state of the model in the image. In this way, only deformations that are similar to the shapes in the training set are allowed. This procedure is repeated until the changes of pose and shape parameters become insignificant. In order to improve the image appearance, variants of the ASM use different features going beyond simple reasoning on intensity. [Jiao 2003] uses Gabor wavelets and models the feature distribution by Gaussian mixture models. [Langs 2006] employs the steerable features to represent the object appearance. Beside Gaussian mixture models, other nonlinear models are

also used for modeling the appearance distribution. [De Bruijne 2003] proposes a non-

parametric appearance model which is trained on both true and false examples of boundary profiles and the probability of a given image profile being part of the boundary is obtained

using k nearest neighbor (kNN) probability density estimation.

Similarly, [Van Ginneken 2002] uses the non-linear kNN classifier to estimate if the point is inside or outside of the object. [Li 2004, Li 2005] use Adaboost algorithm to build appearance models. Parallel to the feature space, efforts have been made on the ASM search schemes.

[De Bruijne 2004] combines the PDM with a maximum likelihood shape inference, where the optimal solution can be found using particle filtering in an iterated likelihood weighing scheme. The use of a large number of hypotheses makes segmentation by shape particle filtering robust to local maxima and independent of initialization at the expense of increasing computational cost. [De Bruijne 2005] is the extension work of segmenting multi-objects using particle filters. Another direction of improving the search scheme is to incorporate MRF regularization. [Behiels 1999] incorporates a regularization constraint penalizing outlier configurations that is minimized using a dynamic programming algorithm. [Tresadern 2009] proposes a method that combines an MRF-based local shape model for guided candidate selection with a PCA-based global shape model for regularization.

Given a new image, the shape estimation involves an alternating scheme: first an MRF inference technique selects the best candidates for each point, then they are used to update the parameters of the global pose and shape model.

4.2.2. Active Appearance Models

Active appearance model (AAM) [Cootes 1998, Cootes 2001] is an extension to ASM, where the prior model is constructed using shape and appearance information. Similar to PDM that captures the mean shape and the shape variations, AAM encodes an appearance model



consisting the mean appearance of the object and its variations, thus it can generate realistic images of the modeled data. To build a statistical appearance model, each image in the training set is at first warped

...2var1 sdsbyiesC ±

...2var2 sdsbyiesC ±

Figure 2.5 First two modes of appearance model of full brain cross-section from an MR image [Cootes 1999a].

So that its control points match the mean shape obtained through the PDM procedure of the ASM. After intensity normalization on the shape-normalized images, a PCA is applied to analyze the gray-level variations with a linear model:

gg wVgg +=)

where g)

is the mean normalized gray-level vector, Pg is a matrix consisting of significant

modes and bg is a vector of gray-level parameters. We show an appearance model of brain images in Figure 2.5, where each row represents a variation mode. As described previously in the ASM, an instance shape is given as

gg wVxx +=)

where Ps denotes the principal shape variations and bs denotes the shape parameters.

Then, the shape parameters and the gray-level parameters are combined into a single vector T

bss vvDw )(= b where Ds is a diagonal matrix of weights taking account of the units

differences between shape and gray-level parameters. Because the shape and gray-level

parameters may have correlations, a further PCA is applied on the vector V obtained from the training set, yielding a further linear model QCv = where Q is a set of eigenvectors and c is a

vector of appearance parameters that control both shape and gray-level pattern of the model. As a result, the shape model and gray-level model can be represented by a common parameter vector c:



The key idea of AAMsearch is to adjust the parameters in p so that the difference between the given image and a synthetic example generated by the appearance model is as small as possible.

5. APPLICATIONS

As our survey demonstrates, there is already a considerable amount of statistical shape models (SSMs) exits in medical image analysis. Segmentation is the driving application for now, with noticeable focus on synthetic images like lung, brain and cardiac structures. The striking aspect here is that the majority of applications do not make full use of the techniques available: A considerable amount of applications, e.g. still uses generic appearance models, although the possibility to train appearance is a key aspect of SSMs.

Statistical shape models achieve their best performance for objects with systematic variations that can be captured by a reasonable number of modes – in our experience, a good model should be able to capture 90% of the total variance in the training set with less than a dozen modes. Medical objects of interest with a relatively stable shape over the population like the above-mentioned deep brain and cardiac structures – but also most bones – belong to this category and are ideal for shape modeling. Highly varying soft-tissue structures like the liver or vessel-systems are much harder to model and will most likely need some kind of additional flexibility in the search algorithm.

6. CONCLUSION AND DIRECTION TO THE FUTURE WORK

In this article with an extensive survey and analysis of the medical image segmentations its is observed that the in medical image segmentation using level set based active contour is effective for surface and edge segmentation but when applied on synthetic images the performance is not much effective. As an alternate method for synthetic medical images like CT,MRI and PET segmentation statistical approach such as ASM (Active Shape Model) and AAM (Active appearance Model) can be used. During the analysis of the active contour based method it is also observed that the medical modalities acquired through CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography) etc. generate a huge amount of image information useful to rule out the medical related issues. Further it is also observed that there are some models suggested based like AAM and ASM on PCA in which first the input image is preprocessed for noise removal and then represented normalized image. These normalized image is the segemntized using level set methods improving the accuracy level. But PCA is projection based method and generates the eigen features. These features are unstable i.e. retains the noise during the reconstruction of the original image. Hence there is need of statistical method like SVD to generate the stable features and represented using AAM and further can be segmentized by uisng level set method into different regions.

In our next paper a detailed analysis of the medical image segmentation using active contour with statistical (SVD) approach would be explored.

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