Exemplar-based Likelihoods Using the PDF Projection Theorem
Consider a vision task where we want to classify shapes by matching them to exemplars. To make the system modular and capable of handling prior knowledge, we want this process to be probabilistic. That is, we want a likelihood p(x|c) which is high when the observation x matches the exemplar c, and low otherwise. We also want the likelihood to be normalized so that comparisons between p(x|c = 1) and p(x|c = 2) make sense. Suppose our matching score is f(x, c), e.g. the chamfer distance between x’s edge map and the exemplar edge map. One common approach is to define