A Synopsis onSTUDY OF SEGMENTATION TECHNIQUES USING VERTEBRAL CT IMAGES

NAME OF CANDIDATEMr. Gundavade Vikas Bhausaheb

NAME OF SUPERVISORDr. Patil S.A.

ABSTRACTWith the growing research on image segmentation of spinal vertebrae, it has become important to categorise the research outcomes and provide an overview of the existing segmentation techniques in it. In this project, different image segmentation techniques applied on 3D segmentation of spinal vertebrae are reviewed. The selection includes sources from image processing journals, conferences, books, IEEE transactions. The detail survey includes different approach on segmentation. The state of art research on each category is provided with emphasis on developed technologies and image properties used by them. The categories defined are not always mutually independent. Hence, their interrelationships are also stated. Finally, conclusions are drawn summarizing commonly used techniques and their complexities in application.

1. INTRODUCTIONAccurate vertebra segmentation in computed tomography (CT) images is important for numerous medical applications, e.g., diagnosis of osteolytic or osteoblastic cancer metastases within the spinal column [41], diagnosis of spine trauma, and detection of osteoporosis [32]. Accurate knowledge of the shape of the individual vertebrae is also important for spinal biopsies, implants, or the insertion of pedicle screws in spinal surgery [50]. However, manually delineating and annotating vertebrae is a subjective, tedious, and error prone task. Preparing an automatic vertebra segmentation system would greatly improve the process, thereby easing the workload on radiologists while also removing operator variability.

Fig.1 Fractures of vertebrae are indicated by arrows

Fig.2 Incomplete, missing information of vertebrae in CT images.Vertebra segmentation in CT images is a challenging task due to the presence of image artifacts, contrast variations, presence of neighboring structures, and shape variation [50]. Recently, a considerable amount of work has been done toward preparing automatic systems for detection and segmentation of vertebrae. In this work, we mainly focus on comparison of the level set segmentation with willmore flow and statistical shape modeling to compare the segmentation results. In the following, we start by preparing a brief review on state-of-the-art regarding the segmentation step. In Sec. 2, we explain in detail review of segmentation methods. In Sec. 3, we prepare qualitative and quantitative results of these methods and compare the results achieved by them.2. LITERATURE SURVEYVarious attempts have been made at spine segmentation in recent years, but majority of them use 2-D images and/or require user intervention in the process. For example, Naegel [2] combined the watershed method and morphological approaches to segment vertebrae. Although the proposed method is promising in segmenting healthy bones from high-resolution images, manual refinement is necessary to obtain accurate segmentations, and the level of refinement is patient and resolution dependent. Ghebreab and Smeulders [3] constructed a deformable integral spine model to segment vertebrae. The method learns the appearance of vertebrae boundaries a priori from a set of training images. This model is then used to generate landmark points, in order to reduce the complexity of the segmentation process through point-based shape representation. However, it remains unclear if the landmark points correspond to the actual anatomical locations and whether they capture the biologically meaningful variations across different subjects. The method is also not fully automated and needs step-by-step inputs from the user, which makes the whole process tedious and time consuming. Ma et al. [4] presented an automatic vertebra segmentation and identification method on thoracic vertebra CT images. A learning-based bone structure edge detection algorithm was used and a hierarchical, coarse-to-fine deformable surface-based segmentation method was proposed based on the response maps from the learned edge detector. Though satisfactory results were obtained, the segmented vertebrae were only in 2-D and reproducibility of results in 3-D was not known. Another limitation is the complexity and/or inaccuracy of current segmentation methods. For example, Lorenze and Krahnstoever [5] proposed a statistical shape model whereby the mean shape was constructed from a set of training samples. The initialization of the shape model for segmentation was done manually and is highly sensitive to dislocation. If the model is not located in the proximity of vertebrae, segmentation may fail. More recently Klinder et al. [6] used a mesh-based method to extract spine curves, and then generalized Hough transform and curved planar reformation to detect the vertebrae. The proposed approach has a further identification step to the detected vertebrae via rigid registration of appearance model. Although they achieved very competitive identification rates for vertebrae, their algorithm depends heavily on spatial registration of the model, which is computationally very expensive. In a paper by Mastmeyer et al. [7], a hierarchical 3-D technique was developed to segment the vertebral bodies in order to measure bone mineral density. The proposed framework needs excessive user intervention to precisely locate seed points to facilitate region growing segmentation. This process is time consuming and impractical for unhealthy bone segmentation. A similar approach integrating region growing segmentation with local shape and intensity refinement for delineating vertebrae was proposed by Kang et al. [8]. First, locally adaptive thresholds were used to facilitate region growing segmentations globally, followed by 3-D morphological operations to refine the segmented surfaces. This method still required a site specific separation of individual bones, which remains a challenge for vertebrae segmentation. Due to the aforementioned drawbacks of the existing spinal vertebrae segmentation methods, we have developed a new method capable of segmenting spinal accurately from noisy images with missing information. The method is developed by introducing an edge-mounted Willmore flow, as well as a prior shape kernel density estimator, to the level set segmentation framework. While the prior shape model provides much needed prior knowledge when information is missing from the image, the edge-mounted Willmore flow helps to capture the local geometry and smoothes the evolving level set surface.

2.1 Level SetThe level set method [10] has been widely used for image segmentation [11]. The level set segmentation obtained good results for highly challenging segmentation tasks, such as medical images, level set methods have achieved good results when coupled with prior knowledge or prior shape models [12][15]. The level set method embeds an interface in a higher dimensional function (the signed distance function) as a level set = 0. The equation that governs the evolution of the level set function (t) is /t + F|| = 0, where F represents the speed function. In more recent development, the variational framework is often considered. Under the variational framework, an energy E() is defined in relation to the speed function, and minimization of the energy generates the EulerLagrange equation and, hence, providing the evolution equation through the calculus of variation

To improve the results of level set segmentation we consider the fusion of energy, i.e., using a shape prior distribution estimator Es with an edge-mounted Willmore energy Ew0

where (0 < 1) is the weight parameter. Details on Es and Ew0 will be described in the following sections. In order to incorporate a prior dataset {1, 2, . . . , N }into the level set segmentation framework, we adopt a shape dissimilarity measure based on the Kernel density estimation (KDE) discussed by Cremers et al. [13]. This nonparametric distribution estimator overcomes the two shortcomings of existing algorithms: 1) the assumption that the shapes are Gaussian distributed, which is generally inappropriate when the number of training set is small, and not practical for modeling shapes with high complexity and structure; 2) the shapes are represented by signed distance functions, which constitute a nonlinear space that does not include the mean.2.1.1 Kernel Density EstimationKDE is a nonparametric approach in statistics for estimating the probability density function of a random variable. The underlying theory of KDE states that data with unknown statistical distribution converge to its actual distribution as the number of samples approaches infinity. In practice, KDE provides a fundamental smoothing estimator even with a small number of data samples. In application with N samples of shape models, the density estimation is formulated as a sum of Gaussian of shape dissimilarity measures d2 (H(),H(i)), i = 1, 2, . . .,N

where H() is the Heaviside function, the shape dissimilarity measure [16][18] is

dx

and 2 is the mean squared nearest neighbor distance

Note that the L2-norm is invariant under translation and scaling with respect to the principal axis of the shape. Hence, the shape dissimilarity measure d2 is also invariant under these transformations when the prior shapes are normalized with respect to translation and scaling accordingly [13]. The segmentation is obtained by maximizing the conditional probability of given image I

Since the negative logarithmic scale of the probability distribution P(|I) nicely defines an energy that associates the evolution of with the minimization problem, the shape energy is formulated asEs () = log P(|I). Hence, the variational with respect to becomes

2.1.2 Willmore FlowWillmore energy is a function of mean curvature, which isa quantitative measure of how much a given surface deviates from a round sphere. It has been applied to image inpainting, restoration of implicit surfaces [19], [20], and to studies of the bending energy of biological cell membranes as these cell membranes tend to position themselves to minimize Willmore energy [21]. Willmore flow is the gradient flow of Willmore energy.Willmore flow of a surface is the evolution of the surface in time to follow variations of the Willmore energy. Willmore energy was defined after the British Geometer T.Willmore [22] and is formulated as

where M is a d-dimensional surface embedded in Rd+1 and h the mean curvature on M.here we integrate Willmore flow into the level set segmentation framework as a geometric functional. Willmore energy is defined on the collection of level sets, and Willmore flow is enabled by defining a suitable metric, the Frobenius norm, on the space of the level sets. The Frobenius norm of an arbitrary matrix A = (aij )mn , coincides with the calculation for the gradient decent. It is equivalent to the l2-norm (the Euclidean norm) of a matrix, More importantly, it is computationally attainable comparing to l2-norm. As Frobenius norm is an inner-product norm, the optimization in the variational method comes naturally. Based on the formulation by Droske and Rumpf [23], Willmore flow or the variational form for the Willmore energy with respect to .In order to ensure that the smoothing effect of Willmore energy acts around the constructed surface and does not affect adversely the edge of vertebrae, we propose to multiply the edge indicator function

to the level set evolution

2.2.MODEL BASED SEGMENTATIONWe classify the existing vertebra segmentation approaches to two main groups: i) the ones, which do not consider shape prior information, and ii) the ones, which do. Regarding the first group, we can point to the following works: Ghosh et al. [36] extract the vertebra border as high gradient edges. Peng et al. [45] apply the Canny edge detector on 2D slices for vertebra segmentation. Aslan et al. [33] utilize a level set algorithm for vertebra segmentation. However, these methods [36,45,33] do not make use of shape prior knowledge. Therefore, they are vulnerable to leakage and thus lead to less accurate segmentation results. Considering the second group, there exist several vertebra segmentation methods which make use of shape prior information. Aslan et al. [32] consider shape prior information in a graph cut-based framework. Ma et al. [33] propose a template-based segmentation method. However, these methods only rely on mean shape information and do not benefit from the principal modes of variation. Herring et al. [39] compute a coarse segmentation by simple thresholding and then register it to a pre-computed vertebra shape model. However, their method requires a manual initialization; similar to the works in [44,49]. Klinder et al. [42] propose a modelbased segmentation approach using a region-based appearance model, which includes variance information.

2.2.1 METHOD

The general pipeline of our method is shown in Fig. 1. The input to our system is a 3D CT image of the spinal cord accompanied with vertebra-bounding box information. These bounding boxes, which are represented by their center, orientation, and scale, can be estimated by applying a vertebra body detection as proposed by Kelm et al. [41]. Combining our method with this method would lead to a fully automatic vertebra detection and segmentation system which does not require any user interaction. Our method combines statistical shape modeling (SSM) to capture global vertebra shape information and machine learning (ML) to capture local appearance-related prior information. We break down our method into two main steps: the training step and the testing step. In the training step, we compute the SSM and the boundary detector model. In the testing step, we make use of the trained models resulting from the previous step to segment vertebrae in an unseen image accompanied with its vertebra bounding box information.

2.2.2 Training StepThe training step of our framework consists of four main steps: i) finding the mesh point correspondences, ii) normalizing the meshes and volumes, iii) extracting the SSM, and iv) learning the boundary detector. Note that we do the learning step on cervical (V1 to V5), thoracic (V6 to V17), and lumbar (V18 to V22) parts separately, where Vi represents the vertebra number. In Fig. 2(b) the vertebrae inside the cervical, thoracic, and lumbar parts are represented by pink, green, and orange, respectively.

2.2.3 Finding Mesh Point CorrespondencesSince extracting a SSM requires a set of training shapes with well-defined correspondences [38], we apply a spectral-based algorithm to compute the point correspondences between the vertebra meshes [40]. In the respective block in Fig. 1, corresponding points between a pair of meshes are represented with the same color. Note that in our implementation of finding mesh-point correspondences, we use vertebrae V3, V12, and V20 of one patient in the training set as the reference meshes for cervical, thoracic, and lumbar parts and register all other meshes of each group to them.3.1.2. Normalizing Meshes and Volumes The next step as depicted in Fig. 1 is performing spatial normalization on the vertebra volumes and meshes. Regions within the bounding boxes are spatially normalized to image volumes with equal size, resolution, and orientation. The spatial normalization step is important in our machine learning-based approach. Extracting 3D steerable features from these normalized volumes simplifies learning due to more stable appearance patterns of the vertebra edges. A similar normalization step has beed proposed by Wels et al.[47] to extract local features from vertebral bodies for spinal bone lesion detection. We apply the same normalization step (normalizing w.r.t the box information) to the meshes. The normalized meshes are used for extracting the SSM, as explained in the following.

2.2.4. Extracting the SSMAfter finding correspondences and normalizing the meshes, we apply Generalized Procrustes Analysis (GPA) [37] to align the meshes rigidly. Let us represent aligned meshes by x1; x2; :::; xN, N N+, where xi consists of the spatial coordinates of the surface points of the meshes. Then, the mean shape and the corresponding covariance matrix S is given by:

By applying eigen decomposition on S, we can extract principal modes of variation _m (eigenvectors) and their respective variance _m (eigenvalue). Based on the main concept of SSM theory, each shape in the training dataset can be approximated by a linear combination of the first mth modes, i.e. given by: , where P =is thematrix of the m selected eigenvectors, and b = (b1; :::bm)Tare the shape parameters [4].2.2.5. Learning the Boundary DetectorTo learn the boundary detector, given the normalized meshes and volumes, the image voxels on the mesh surface are interpreted as positive training samples. Then, a set of 3D steerable features is extracted from the points on the surface [50]. The same set of features is extracted from several neighboring sampling points along the normal line of the mesh surface points providing negative training samples [50,48]. These feature vectors are used to train the boundary detector using a Probabilistic Boosting-Tree Classifier [50,48].2.2.6 Testing Step

Given an unseen image with its vertebra bounding box information, we first spatially normalize the volumes inside the box. On the normalized volumes, an initial estimation of the shape of the vertebra x is estimated using the computed mean shape,i.e.,. Then, a set of steerable features is extracted from the mesh points x and several neighbouring sampling points along the normal line of the mesh-surface points. After applying the boundary detector to the extracted feature vectors, x is updated by a displacement vector . To apply shape constraints on the updated mesh, it is registered to the SSM model space and projected such that it can be approximated by the mean shape and a linear combination of eigenvectors [4] (see Sec. 2.1.3).As shown in Fig. 1, the final estimation of all the vertebrae in the original image space is made by projecting back the detected meshes in the normalized space to the original image space.3. OBJECTIVEProposed research objectives are as follows,a) Implementation of willmore flow level set segmentation and statistical shape modeling on vertebral CT images.b) Selecting the most suitable one for further analysis using following parameters,1. Prior shape energy.2. Average measurement3. Sensitivity, Specificity and Dice Similarity Coefficient.c) Testing of the better algorithm on vertebral MRI images.

4. METHODOLOGY

CT IMAGES OF VERTEBRAE

SEGMENTATION USING STSTISTICAL SHAPE MODELINGSEGMENTATION OF VERTEBRAE USING WILLMORE FLOW LEVEL SET SEGMENTATION

COMPARE BOTH RESULTS

IMPLEMENTATION OF BETTER ONE ON MRI IMAGES OF VERTERBRAE

Image segmentation, is widely used in content based image retrieval, Machine vision, Medical Imaging ,Object detection, Pedestrian detection, Face detection, Brake light detection, Locate objects in satellite images, Recognition Tasks, Iris recognition, Traffic control systems. The main applications of medical imaging are Locate tumors and other pathologies, Measure tissue volumes, Diagnosis & study of anatomical structure. Medical imaging which consists mainly combination of sensors recording the anatomical body structure like magnetic resonance image (MRI), ultrasound or CT with sensors monitoring functional and metabolic body activities like positron emission tomography (PET), single photon emission computed tomography (SPECT) or magnetic resonance spectroscopy (MRS). Results can be applied, for instance, in radiotherapy and nuclear medicine. This project mainly deals with the application on CT image on spinal vertebrae.Segmentation is often the key step in interpreting the image. Image segmentation is a process in which regions or features sharing similar characteristics are identified and grouped together. Image segmentation may use statistical classification, thresholding, edge detection, region detection, or any combination of these techniques. The output of the segmentation step is usually a set of classified elements. Most segmentation techniques are either region-based or edge based- Region-based techniques rely on common patterns in intensity values within a cluster of neighboring pixels. The cluster is referred to as the region, and the goal of the segmentation algorithm is to group regions according to their anatomical or functional roles. Edge-based techniques rely on discontinuities in image values between distinct regions, and the goal of the segmentation algorithm is to accurately demarcate the boundary separating these regions. Segmentation is a process of extracting and representing information from an image is to group pixels together In order to compare willmore flow level set segmentation with statistical shape model we create a dataset of 20 ct images of normal spinal vertebrae images of patients. These images are carefully selected by radiologists to form a representative group. The ground truths are obtained by using TURTLESEG, 3D image segmentation software and verified by radiologists.The willmore flow level set segmentation and statistical shape model are applied on these set of images differently. a qualitative comparison between the segmented results are done between these two models and analyze the better suited model.For a quantitative evaluation we measure the errors of the segmented meshes from the model which is better than other and try to implement the same on similar MRI images.

5.POSSIBLE OUTCOMES Comparative results of willmore flow level set segmentation and statistical shape model Better segmentation results for diagnosis A method of segmentation for MRI images.

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