Survey on liver CT image segmentation methods <s> Statistical shape model based automatic methods <s> Abstract This paper describes a technique for building compact models of the shape and appearance of flexible objects (such as organs) seen in 2D images. The models are derived from the statistics of labelled images containing examples of the objects. Each model consists of a flexible shape template, describing how the relevant locations of important points on the objects can vary, and a statistical model of the expected grey levels in a region around each model point. We describe how the models can be used in local image search, and give examples of their application to medical images. <s> BIB001 </s> Survey on liver CT image segmentation methods <s> Statistical shape model based automatic methods <s> In this paper we address the problem of extracting geometric models from low contrast volumetric images, given a template or reference shape of that model. We proceed by deforming a reference model in a volumetric image. This reference deformable model is represented as a simplex mesh submitted to regularizing shape constraint. Furthermore, we introduce an original approach that combines the deformable model framework with the elastic registration (based on iterative closest point algorithm) method. This new method increases the robustness of segmentation while allowing very complex deformation of the original template. Examples of segmentation of the liver and brain ventricles are provided. <s> BIB002 </s> Survey on liver CT image segmentation methods <s> Statistical shape model based automatic methods <s> Nonlinear diffusion filtering in image processing is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a discrete nonlinear diffusion scale-space framework we present semi-implicit schemes which are stable for all time steps. These novel schemes use an additive operator splitting (AOS), which guarantees equal treatment of all coordinate axes. They can be implemented easily in arbitrary dimensions, have good rotational invariance and reveal a computational complexity and memory requirement which is linear in the number of pixels. Examples demonstrate that, under typical accuracy requirements, AOS schemes are at least ten times more efficient than the widely used explicit schemes. <s> BIB003 </s> Survey on liver CT image segmentation methods <s> Statistical shape model based automatic methods <s> We propose a shape-based approach to curve evolution for the segmentation of medical images containing known object types. In particular, motivated by the work of Leventon, Grimson, and Faugeras, we derive a parametric model for an implicit representation of the segmenting curve by applying principal component analysis to a collection of signed distance representations of the training data. The parameters of this representation are then manipulated to minimize an objective function for segmentation. The resulting algorithm is able to handle multidimensional data, can deal with topological changes of the curve, is robust to noise and initial contour placements, and is computationally efficient. At the same time, it avoids the need for point correspondences during the training phase of the algorithm. We demonstrate this technique by applying it to two medical applications; two-dimensional segmentation of cardiac magnetic resonance imaging (MRI) and three-dimensional segmentation of prostate MRI. <s> BIB004 </s> Survey on liver CT image segmentation methods <s> Statistical shape model based automatic methods <s> This paper presents an automatic approach for segmentation of the liver from computer tomography (CT) images based on a 3D statistical shape model. Segmentation of the liver is an important prerequisite in liver surgery planning. One of the major challenges in building a 3D shape model from a training set of segmented instances of an object is the determination of the correspondence between different surfaces. We propose to use a geometric approach that is based on minimizing the distortion of the correspondence mapping between two different surfaces. For the adaption of the shape model to the image data a profile model based on the grey value appearance of the liver and its surrounding tissues in contrast enhanced CT data was developed. The robustness of this method results from a previous nonlinear diffusion filtering of the image data. Special focus is turned to the quantitative evaluation of the segmentation process. Several different error measures are discussed and implemented in a study involving more than 30 livers. <s> BIB005 </s> Survey on liver CT image segmentation methods <s> Statistical shape model based automatic methods <s> We propose a nonlinear statistical shape model for level set segmentation which can be efficiently implemented. Given a set of training shapes, we perform a kernel density estimation in the low dimensional subspace spanned by the training shapes. In this way, we are able to combine an accurate model of the statistical shape distribution with efficient optimization in a finite-dimensional subspace. In a Bayesian inference framework, we integrate the nonlinear shape model with a nonparametric intensity model and a set of pose parameters which are estimated in a more direct data-driven manner than in previously proposed level set methods. Quantitative results show superior performance (regarding runtime and segmentation accuracy) of the proposed nonparametric shape prior over existing approaches. <s> BIB006 </s> Survey on liver CT image segmentation methods <s> Statistical shape model based automatic methods <s> We propose a two-stage algorithm to segment the liver in CT images. First, we estimate the pose and global shape properties using a statistical shape model defined in the low dimensional space spanned by a training set of shapes. Then, we apply a template matching procedure to recover local deformations that were not present in the learning set. In both steps, we optimize the same image term: the likelihood of the intensity inside the region of interest and its background. The method requires a single seed point inside the liver for the initialization. We show that this global-to-local strategy is able to recover livers with peculiar shapes in arbitrary poses. <s> BIB007
A statistical shape model (SSM) is built by given a set of examples of a shape. Each shape in the training set is represented by a set of n labeled landmark points. The labeled training examples are aligned into a common co-ordinate frame using procreates analysis. This translates, rotates and scales each training shape to minimize the sum of squared distances to the mean of the set. BIB005 proposed a liver segmentation method based on a SSM to achieve a high robustness to noise and outliers. A semiautomatic mapping procedure is used to build the model. In this method, the user intervention is required to mark corresponding points on all liver training data. The principle component analysis (PCA) is used with the training data to capture the liver shape variations. The model is allowed then to deform within the captured space of variations, by means of the best-matching profile technique described by BIB001 . The method presented by Kainm et al. (2007) matches a SSM to the image data and refines the solution using a deformable mesh. The SSM consists of around 7.000 landmarks and is built from an extensive training set of 112 liver shapes. The required correspondences are determined using a semi-automatic method where the principal ridges of each liver are specified manually. The employed appearance model is based on profiles running perpendicular to the surface at all landmarks. A heuristic method estimates the position of liver boundary within each profile. This classification process employs specific intensity models for liver and tumor, each represented by an intensity interval. The interval bounds are estimated by means of a histogram of the voxel intensities inside the current liver-segmentation. A sum of Gaussians is fitted to this histogram via the expectation-maximization (EM) algorithm proposed by BIB002 , and the interval bounds are derived from the obtained means and standard deviations. Before starting the segmentation, images are smoothed using nonlinear isotropic diffusion proposed by BIB003 . To initialize the pose of the SSM, the right lung lobe is identified using thresholding and morphological operations proposed by  . The detected lobe is then projected downwards to the first slice that does not contain any lung voxels, and the center and orientation of the projection entail the initial transformation of the SSM. Subsequently, four iterations of intensity model estimation and SSM search are conducted with increasing number of modes for the SSM and varying parameters. After that, the resulting surface is re-meshed to initialize the freely deformable mesh. BIB007 embed their algorithm in a variational framework proposed by BIB004 , where an SSM segmentation step is followed by free deformation. The statistical model is built from 50 training samples which are represented by signed distance functions. As no landmarks are involved, determination of correspondences is not necessary. The authors used a non-parametrical shape distribution based on kernel density estimation proposed by BIB006 . To initialize the SSM, an intensity histogram of the image is analyzed using a Gaussian mixture model. The intensity of liver tissue deduced from this analysis is employed to threshold the image. The pixel yielding the highest response in a subsequent smoothing of the mask is assumed to lie inside the liver and is used as starting point for the level set evolution. A gradient descent algorithm is then employed to find the boundary which minimizes the segmentation energy. Subsequently, non-rigid registration is used to refine the segmentation.