3D mouse brain volume and its unfolded 2D slices. 

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... Cerebellum (S1), Neocortex (S2), Corpus Callosum & External Capsule (S3), Caudate Putamen (left: S4; right: S5), Hippocampus (left: S6; right: S7), Lat- eral Ventricles (left front: S8; right front: S9; left rear: S10; right rear: S11), Third Ventricle (S12) and Fourth Ventricle (S13). All regions of interest were selected by experts and were based on a stereotaxic rodent brain atlas [10]. Among these component brain structures, class 1 (C1) contains S1, S2, S3, S8, S9 and S13. Class 2 (C2) contains S1, S2, S3, S8, S9, S12 and S13. Class 3 (C3) contains all structures except S10 and S11. Class 4 (C4) contains all structures. Class 5 (C5) contains all structures except S1 and S3. Given a slice, if we know which class it belongs to, we can get proper prior shape information for further ASM segmentation. In this paper, we use Support Vector Machines (SVM) [11] to deal with this task of classi fi cation. SVM has been known for its successes in many pattern recognition applications [12]. Its idea is fi rst to project the input data into an implicit feature space F , i.e., x ∈ R N → Φ( x ) ∈ F with the kernel trick, and then fi nd the optimum decision hyper-plane in F to maximize the margins between two classes. In im- plementation, the kernel trick does not need to compute the implicit feature Φ( x ) explicitly and the dot product of two implicit features Φ( x 1 ) and Φ( x 2 ) can be written as a kernel function k ( x 1 , x 2 ) . Given a sample x , its label predicted by SVM is given by the following: where x i , i = 1 , 2 , ..., n are the training samples, y i = { 1 , − 1 } represents the label of the training samples, the coef- fi cients a i and b are the solutions of a quadratic programming problem. The training samples with non-zero a i are called the support vectors [13]. There are several popular kernels. In our experiments, we use the Gaussian Radial Basis Function as the kernel: k ( x , x ) = exp( − γ x − x 2 ) . The classical SVM is a typical binary classi fi er. In this paper, we adopt one-to-all strategy to handle the multi-class problem. An active shape model represents the features of a shape as the point distribution model (PDM) [14]. Given a set of training images, the feature of interest in each image is manually labeled with n landmark points and repre- sented as a vector in 2 n -dimensional space, i.e., x = < x 0 , y 0 , x 1 , y 1 , ..., x n − 1 , y n − 1 > . After aligning these vectors into a common coordinate system, a set of orthogonal bases P is computed with the principal component analysis. Then, each aligned shape can be reconstructed as x = x + P b , where x and b are the mean shape and the shape parameter vector, respectively. This equation also allows us to search for a new example of the shape in an unlabeled image by varying b appropriately, often based on low-level image features such as the gradients along normal directions to the boundary of an initial shape toward the strongest edge in the image. Al- though it has been used successfully in many applications, ASM has two important limitations for the segmentation of brain structures in MRI. In the next two sections, we will address these limitations and propose methods to overcome these drawbacks. The major drawback of ASM for searching for a new example of the shape in an unlabeled image is the initialization of the model. If the model is initialized too far from the feature of interest, the process may fail. To automate the accurate initialization of the model, we fi rst rapidly extract the ventricles areas from unlabeled images by applying a series of thresh- olding and morphological operators. The coarse segmentation process is illustrated in Fig. 3. The given images in top row are fi rst normalized and thresh- olded, using the 90% quantile intensity value of the normalized image as the threshold value, to generate a binary images shown in middle row. Then we applied a series of morphological operators to obtain the coarse segmentation of brain structures as shown in bottom row. Note that our interest at this step is not the accurate segmentation of the brain structures. The coarse brain structures obtained here are used only to automate the accurate initialization of the shape model on unlabeled images. We achieve the automatic and accurate initialization by aligning the centers of the shape models to the centers of the segmented coarse brain structures. Another limitation of ASM in fi nding an object in unlabeled images is that it heavily relies on the low-level image features to guide the search for the optimal positions of the feature points. For example, the gradient descent search on the image intensity pro fi le has been widely used to move the model points toward the strongest edge in the image [14]. However, this approach is not suitable for the accurate delineation of Cerebellum of the brain in MRI since Cerebellum is intensity non-uniformity with stripes occlude structures and ap- pear as the strongest edge (Fig. 1). We overcome this dif fi culty by introducing a robust error function based on the M- estimator [15]. Given an orthogonal basis P obtained in Sec. 2.2, the projection C of a new example shape X is given by C = P T dX , where X = X ̄ + dX and X ̄ is the mean shape of the aligned shapes from the training images. Using the projection C , we can also fi nd a corresponding shape as X ˆ = X ̄ + P C , in which X ˆ and P C approximates X and dX , respectively. Therefore, instead of obtaining X by optimizing dX using low-level image features only, our goal is to fi nd the optimal C by minimizing the following robust energy function: where, ρ ( x, σ ) = x 2 / ( x 2 + σ 2 ) is the Geman-McClure error function and σ is a scale parameter that controls the convex- ity of the robust function. With an iterative gradient descent search on E , we ...

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... paper reports a novel method for fully automated segmentation of rodent brain volume by extending the robust active shape models to incorporate an automatic prior shape selection process. This automatic prior shape selection process using support vector machines provides an automatic shape initialization method for further segmentation of rodent brain structures such as Cerebellum, Neocortex, Corpus Callosum, External Capsule, Caudate Putamen, Hippocampus and Ventricles with the robust active shape model framework in mag- netic resonance images (MRI). The mean successful rate of this classi fi cation method shows 92.2% accuracy compared to the expert-de fi ned ground truth. We also demonstrate the very promising segmentation results of the robust active shape model framework in rodent brain volume. Index Terms — Biomedical image processing, Image segmentation, Learning systems, Robust active shape model Segmentation of 3D brain images is very important to ad- vance knowledge about relationships between anatomy and mental diseases in brains [1]. Volumetric analysis of rodent brain structures, such as, cerebellum, caudate putamen, hippocampus, fi bria, external capsule and neocortex are important in studying the structural changes occuring in speci fi c brain regions as a function of development, trauma or neu- rodegeneration [2]. Volumetric analysis of gray matter (GM), white matter (WM) and cerebrospinal fl uid (CSF) is used to characterize morphological differences between subjects in psychiatric disease including schizophrenia, epilepsy or Alzheimer’s disease [3, 4]. Currently, many semi-automatic and automatic segmentation methods in clinical studies have been developed [5, 6, 7, 8, 9], since manual segmentation of brain images are time- consuming and lack the reproducibility because of a large intra-observer and inter-observer variability. Pitiot et al. developed an expert-knowledge guided segmentation system for anatomical structures in MRI which uses medical expertise in the form of implicit or explicit knowledge [5]. Leventon et al. presented a method of incorporating shape information into the image segmentation process [6]. Barra and Boire com- bined medical expertise with fuzzy maps using information fusion to segment anatomical structures in brain MRIs [7]. Niessen et al. presented an MRI brain segmentation method which combines an edge dependent multiscale representation with an intensity based linking scheme [8]. Shen el al. presented an adaptive deformable model for automatically seg- menting brain structures from volumetric MR images [9]. Miscellaneous approaches have been applied to segment volume from all above papers. We will apply learning methods which can utilize autonomous acquisition and integration of knowledge to develop an automatic prior shape selection process. The goal of this paper is to develop an automatic brain structure segmentation method from 3D rodent brain MRIs by extending the robust active shape models to incorporate an automatic prior shape selection process. The proposed method fi rst builds a set of priori shapes for each brain structure. Then, by classifying the brain structures present in a given image using a machine learning method (in section 2.1), it quickly selects a set of prior shapes and con- structs a composite model by combining the selected priori shape models (in section 2.2). The composite model is automatically initialized (in section 2.3) and then deformed to fi t to the corresponding brain structures using the active shape model (ASM) framework with signi fi cant improvements (in section 2.4). The method presented in this paper was specif- ically developed for segmentation of mouse brain structures in 3D brain images. However, it is generally applicable to any task involving deformable shape analysis of objects that change their topological structures in a given dataset. As shown in Fig. 1, if we unfold the 3D mouse brain volume into 2D slices, we can see that the topology of the brain structures vary with the slice positions. According to experts [2], these variations of brain structures can be classi fi ed as fi ve classes (see Fig. 2) and each class contains different combi- nations of different brain structures. To classify brain images into 5 classes, we speci fi cally consider the following structures of the mouse brain: Cerebellum (S1), Neocortex (S2), Corpus Callosum & External Capsule (S3), Caudate Putamen (left: S4; right: S5), Hippocampus (left: S6; right: S7), Lat- eral Ventricles (left front: S8; right front: S9; left rear: S10; right rear: S11), Third Ventricle (S12) and Fourth Ventricle (S13). All regions of interest were selected by experts and were based on a stereotaxic rodent brain atlas [10]. Among these component brain structures, class 1 (C1) contains S1, S2, S3, S8, S9 and S13. Class 2 (C2) contains S1, S2, S3, S8, S9, S12 and S13. Class 3 (C3) contains all structures except S10 and S11. Class 4 (C4) contains all structures. Class 5 (C5) contains all structures except S1 and S3. Given a slice, if we know which class it belongs to, we can get proper prior shape information for further ASM segmentation. In this paper, we use Support Vector Machines (SVM) [11] to deal with this task of classi fi cation. SVM has been known for its successes in many pattern recognition applications [12]. Its idea is fi rst to project the input data into an implicit feature space F , i.e., x ∈ R N → Φ( x ) ∈ F with the kernel trick, and then fi nd the optimum decision hyper-plane in F to maximize the margins between two classes. In im- plementation, the kernel trick does not need to compute the implicit feature Φ( x ) explicitly and the dot product of two implicit features Φ( x 1 ) and Φ( x 2 ) can be written as a kernel function k ( x 1 , x 2 ) . Given a sample x , its label predicted by SVM is given by the following: where x i , i = 1 , 2 , ..., n are the training samples, y i = { 1 , − 1 } represents the label of the training samples, the coef- fi cients a i and b are the solutions of a quadratic programming problem. The training samples with non-zero a i are called the support vectors [13]. There are several popular kernels. In our experiments, we use the Gaussian Radial Basis Function as the kernel: k ( x , x ) = exp( − γ x − x 2 ) . The classical SVM is a typical binary classi fi er. In this paper, we adopt one-to-all strategy to handle the multi-class problem. An active shape model represents the features of a shape as the point distribution model (PDM) [14]. Given a set of training images, the feature of interest in each image is manually labeled with n landmark points and repre- sented as a vector in 2 n -dimensional space, i.e., x = < x 0 , y 0 , x 1 , y 1 , ..., x n − 1 , y n − 1 > . After aligning these vectors into a common coordinate system, a set of orthogonal bases P is computed with the principal component analysis. Then, each aligned shape can be reconstructed as x = x + P b , where x and b are the mean shape and the shape parameter vector, respectively. This equation also allows us to search for a new example of the shape in an unlabeled image by varying b appropriately, often based on low-level image features such as the gradients along normal directions to the boundary of an initial shape toward the strongest edge in the image. Al- though it has been used successfully in many applications, ASM has two important limitations for the segmentation of brain structures in MRI. In the next two sections, we will address these limitations and propose methods to overcome these drawbacks. The major drawback of ASM for searching for a new example of the shape in an unlabeled image is the initialization of the model. If the model is initialized too far from the feature of interest, the process may fail. To automate the accurate initialization of the model, we fi rst rapidly extract the ventricles areas from unlabeled images by applying a series of thresh- olding and morphological operators. The coarse segmentation process is illustrated in Fig. 3. The given images in top row are fi rst normalized and thresh- olded, using the 90% quantile intensity value of the normalized image as the threshold value, to generate a binary images shown in middle row. Then we applied a series of morphological operators to obtain the coarse segmentation of brain structures as shown in bottom row. Note that our interest at this step is not the accurate segmentation of the brain structures. The coarse brain structures obtained here are used only to automate the accurate initialization of the shape model on unlabeled images. We achieve the automatic and accurate initialization by aligning the centers of the shape models to the centers of the segmented coarse brain structures. Another limitation of ASM in fi nding an object in unlabeled images is that it heavily relies on the low-level image ...