Markov random fields (MRFs) are used to perform spatial (or spatiotemporal) regularization by imposing prior knowledge on the types of admissible images, depth maps, flow fields, and so on. While such models have proven useful for regularizing problems in computer vision, MRFs have mostly been limited in three respects: (1) They have used very simple neighborhood structures. Most models in low-level vision are based on pairwise graphs, where the potential functions are formulated in terms of pixel differences (image derivatives) between neighboring sites (see chapter 1). (2) In many cases, potentials have remained hand-defined and hand-tuned. Consequently, many MRFs do not necessarily reflect the statistical properties of the data. (3) MRF models have typically not been spatially adaptive, that is, their potentials do not depend on the spatial location within the image. The first two shortcomings have been addressed by a number of recent approaches [306, 397, 549] (also chapter 19). This chapter describes a spatially adaptive random field model that addresses the third limitation as well.
