A Generative Gaussian Mixture Statistical Shape Model

Abstract

Statistical shape models are a valuable tool in medical image analysis and are efficiently used in classification, recognition, reconstruction and segmentation methods. The models incorporate statistical knowledge mainly about the expected shape and shape variability. The collection of that knowledge is done by statistically evaluating the shape information of a number of observations of the respective structure. To do so, the fundamental problem of determining proper correspondence between the observations has to be solved. The solution of the correspondence problem as well as the method of model computation depends on the representation of the shapes. In this chapter, a generative method for the computation of a parametric 3D statistical shape model for point-based shape representations is developed. A probabilistic modeling is chosen instead of a deterministic one and the shapes are represented by mixtures of Gaussians. The computation of the Gaussian Mixture SSM is formulated in a generative framework.