Embedding Gestalt laws in Markov random fields

The goal of this paper is to study a mathematical framework of 2D object shape modeling and learning for middle level vision problems, such as image segmentation and perceptual organization. For this purpose, we pursue generic shape models which characterize the most common features of 2D object shapes. In this paper, shape models are learned from observed natural shapes based on a minimax entropy learning theory. The learned shape models are Gibbs distributions defined on Markov random fields (MRFs). The neighborhood structures of these MRFs correspond to Gestalt laws-colinearity, cocircularity, proximity, parallelism, and symmetry. Thus, both contour-based and region-based features are accounted for. Stochastic Markov chain Monte Carlo (MCMC) algorithms are proposed for learning and model verification. Furthermore, this paper provides a quantitative measure for the so-called nonaccidental statistics and, thus, justifies some empirical observations of Gestalt psychology by information theory. Our experiments also demonstrate that global shape properties can arise from interactions of local features.