A generative model for image contours: a completely characterized non-Gaussian joint distribution

Jonas August and Stephen Zucker

Yale University

What is an ideal edge map? Can one construct a probabilistic, generative model of images of contours that is tractable? Motivated by these questions, we define a prior model for ideal edge maps by assuming that they are generated by Markov processes via an indicator function. In this theoretical paper we analyze this curve indicator random field model both in the single curve and multiple curve cases. In particular, we derive exact, usable expressions for this generative model's moment generating functional as well as all of its joint cumulants. We show that this prior is non-Gaussian, and we outline how it can be combined with an observation model. The resulting filter requires the solution of two partial differential equations.

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