Discontinuity-adaptive Mrf Prior and Robust Statistics: a Comparative Study

Discontinuity adaptive MRF priors have been used for modeling vision problems involving discontinuities and robust statistics models for solving regression problems involving outliers. This paper presents a comparative study of the two kinds of models. We analyze the mechanisms of adaptation (to discontinuities) and robustness (to outliers) and give a necessary condition for the adaptation and the robustness. We then give a common deenition of both models. The deenition captures the essence of the adaptation ability and gives in theory innnitely many choices of functions suitable for the adaptation in MRF and robust models. The likeness between the two models suggests that results in the two areas are interchangeable to beneet each other.