Abstract

Segmenting images of low quality or with missing datais a challenging problem. Integrating statistical prior in-formation about the shapes to be segmented can improvethe segmentation results significantly. Most shape-basedsegmentation algorithms optimize an energy functional andfind a point estimate for the object to be segmented. Thisdoes not provide a measure of the degree of confidence inthat result, neither does it provide a picture of other proba-ble solutions based on the data and the priors. With a statistical view, addressing these issues would involve the problem of characterizing the posterior densities of the shapes of the objects to be segmented. For such characterization, wepropose a Markov chain Monte Carlo (MCMC) sampling-based image segmentation algorithm that uses statistical shape priors. In addition to better characterization of the statistical structure of the problem, such an approach would also have the potential to address issues with getting stuck at local optima, suffered by existing shape-based segmentation methods. Our approach is able to characterize the posterior probability density in the space of shapes through its samples, and to return multiple solutions, potentially from different modes of a multimodal probability density, which would be encountered, e.g., in segmenting objects from multiple shape classes. We present promising results on a variety of data sets. We also provide an extension for segmenting shapes of objects with parts that can go through independent shape variations. This extension involves the use of local shape priors on object parts and provides robustness to limitations in shape training data size.