Pseudo-Marginal MCMC Sampling for Image Segmentation Using Nonparametric Shape Priors

Segmenting images of low quality or with missing data is a challenging problem. In such scenarios, exploiting statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Incorporating prior density of shapes into a Bayesian framework leads to the posterior density of segmenting shapes given the observed data. Most segmentation algorithms that exploit shape priors optimize a cost function based on the posterior density and find a point estimate (e.g., using maximum a posteriori estimation). However, especially when the prior shape density is multimodal leading to a multimodal posterior density, a point estimate does not provide a measure of the degree of confidence in that result, neither does it provide a picture of other probable solutions based on the observed data and the shape priors. With a statistical view, addressing these issues would involve the problem of characterizing the posterior distributions of the shapes of the objects to be segmented. An analytic computation of such posterior distributions is intractable; however, characterization is still possible through their samples. In this paper, we propose an efficient pseudo-marginal Markov chain Monte Carlo (MCMC) sampling approach to draw samples from posterior shape distributions for image segmentation. The computation time of the proposed approach is independent from the training set size. Therefore, it scales well for very large data sets. In addition to better characterization of the statistical structure of the problem, such an approach has 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 synthetic and real data sets.