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Segmenting images of low quality or with missing data is a challengingproblem. Integrating statistical prior information about the shapes to besegmented can improve the segmentation results significantly. Most shape-basedsegmentation algorithms optimize an energy functional and find a point estimatefor the object to be segmented. This does not provide a measure of the degreeof confidence in that result, neither does it provide a picture of otherprobable solutions based on the data and the priors. With a statistical view,addressing these issues would involve the problem of characterizing theposterior densities of the shapes of the objects to be segmented. For suchcharacterization, we propose a Markov chain Monte Carlo (MCMC) sampling-basedimage segmentation algorithm that uses statistical shape priors. In addition tobetter characterization of the statistical structure of the problem, such anapproach would also have the potential to address issues with getting stuck atlocal optima, suffered by existing shape-based segmentation methods. Ourapproach is able to characterize the posterior probability density in the spaceof shapes through its samples, and to return multiple solutions, potentiallyfrom different modes of a multimodal probability density, which would beencountered, e.g., in segmenting objects from multiple shape classes. Wepresent promising results on a variety of data sets. We also provide anextension for segmenting shapes of objects with parts that can go throughindependent shape variations. This extension involves the use of local shapepriors on object parts and provides robustness to limitations in shape trainingdata size.

MCMC Shape Sampling for Image Segmentation with Nonparametric Shape Priors