Embedding Gestalt laws in Markov random fields

The goal of this paper is to study a mathematical framework of 2D object sh ape modeling and learning for middle level vision problems, such as image s egmentation and perceptual organization. For this purpose, we pursue generi c shape models which characterize the most common features of 2D object sha pes. In this paper, shape models are learned from observed natural shapes b ased on a minimax entropy learning theory [31], [32]. The learned shape mod els are Gibbs distributions defined on Markov random fields (MRFs). The nei ghborhood structures of these MRFs correspond to Gestalt laws-colinearity, cocircularity, proximity, parallelism, and symmetry. Thus, both contour-bas ed and region-based features are accounted for. Stochastic Markov chain Mon te 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 demonstra te that global shape properties can arise from interactions of local featur es.