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.