ABSTRACT
This chapter deals with higher-order graphical models and their applications. It discusses a number of recently proposed higher-order random field models and the associated algorithms that have been developed to perform MAP inference in them. The chapter introduces a class of higher-order functions which encode interactions between pixels belonging to image patches or regions. It relates the conventional latent variable CRF model for interactive image segmentation to a random field model with region-based higher-order functions. The chapter discusses models which encode image-wide (global) constraints. It discusses the problem of image segmentation under a connectivity constraint and solving labeling problems under constraints on label-statistics. The chapter discusses algorithms that have been used to perform Maximum a Posterior (MAP) inference in such models. It concentrates on two categories of techniques: the transformation approach, and the problem (dual) decomposition approach. The chapter gives pointer to many other inference techniques for higher-order random fields such as message passing.
