Cues for a Grammar of Potentials in Markov Field Models of Computer Vision

Several well-known models in present-day computer vision take the form of Markov random fields. Any model of this kind amounts to a network of soft constraints, which are called potentials. These are the subject of this study. First, three kinds of information that are involved in any computer vision inference task are identified, namely, evidence, target, and principled information, and the concept of a variable as applied in this context is discussed. The general meaning of a potential is then described, which is a local soft constraint that aims to promote a corresponding desired condition. Following this, the formal structure of a potential is highlighted, which includes a set of parameters and an analytic frame, with this being a hierarchy of operations by which the value of the potential can be computed. The possible presence of a core in the analytic frame is considered, and two salient kinds of cores are distinguished and illustrated using examples from the literature: one involving a distance function and the other given by a probabilistic conditional. In summary, this contribution highlights substantial aspects of the semantics and syntax of potentials in Markov field models of computer vision, and constructs a framework within which these aspects may be consistently arranged and explained.