Graphical gaussian shape models and their application to image segmentation

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Abstract
This paper presents a novel approach to shape modeling and a model-based image segmentation procedure tailor-made for the proposed shape model. A common way to represent shape is based on so-called key points and leads to shape variables, which are invariant with respect to similarity transformations. We propose a graphical shape model, which relies on a certain conditional independence structure among the shape variables. Most often, it is sufficient to use a sparse underlying graph reflecting both nearby and long-distance key point interactions. Graphical shape models allow for specific shape modeling, since, e.g., for the subclass of decomposable graphical Gaussian models both model selection procedures and explicit parameter estimates are available. A further prerequisite to a successful application of graphical shape models in image analysis is provided by the "toolbox" of Markov chain Monte Carlo methods offering highly flexible and effective methods for the exploration of a specified distribution. For Bayesian image segmentation based on a graphical Gaussian shape model, we suggest applying a hybrid approach composed of the well-known Gibbs sampler and the more recent slice sampler. Shape modeling as well as image analysis are demonstrated for the segmentation of vertebrae from two-dimensional slices of computer tomography images.

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