Issue No. 06 - June (1995 vol. 17)
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.387504
<p><it>Abstract</it>—A variety of analytic and probabilistic models in connection to Markov random fields (MRFs) have been proposed in the last decade for solving low level vision problems involving <it>discontinuities</it>. This paper presents a systematic study of these models and defines a general discontinuity adaptive (DA) MRF model. By analyzing the <it>Euler equation</it> associated with the energy minimization, it shows that the fundamental difference between different models lies in the behavior of <it>interaction</it> between neighboring points, which is determined by the <it>a priori</it> smoothness constraint encoded into the energy function. An important necessary condition is derived for the interaction to be adaptive to discontinuities to avoid oversmoothing. This forms the basis on which a class of <it>adaptive interaction functions</it> (AIFs) is defined. The DA model is defined in terms of the Euler equation constrained by this class of AIFs. Its solution is <it>C</it><super>1</super> continuous and allows arbitrarily large but bounded slopes in dealing with discontinuities. Because of the continuous nature, it is stable to changes in parameters and data, a good property for regularizing ill-posed problems. Experimental results are shown.</p>
Discontinuities, energy functions, Euler equation, computer vision, Markov random fields, minimization, regularization.
S. Li, "On Discontinuity-Adaptive Smoothness Priors in Computer Vision," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 17, no. , pp. 576-586, 1995.