Sparse Interaction Neighborhood Selection for Markov Random Fields via Reversible Jump and Pseudoposteriors

Markov Random Fields on two-dimensional lattices are popular probabilistic models for describing features of digital images in a wide range of applications. Classical problems like image segmentation rely on these models to describe unobserved variables used for pixel classification, see for example Held et al. (1997); Zhang et al. (2001). More general inference-oriented models, such as the ones used in texture modeling problems, describe pixel values directly as a Markov Random Field being first introduced by Hassner and Sklansky (1981); Cross and Jain (1983). For a review of Markov Random Fields in image processing and segmentation see, for example, Blake et al. (2011) and Kato et al. (2012). A Markov Random Field in a lattice is a collection of random variables whose dependence structure is implicitly defined by a graph. When the edge structure is completely known, one of the main inferential challenges is caused by cycles that prevent expressing the likelihood function as a product of simpler conditional probabilities as in classical Markov Chain models.