The Hough Transform's Implicit Bayesian Foundation

This paper shows that the basic Hough transform is implicitly a Bayesian process-that it computes an unnormalized posterior distribution over the parameters of a single shape given feature points. The proof motivates a purely Bayesian approach to the problem of finding parameterized shapes in digital images. A proof-of-concept implementation that finds multiple shapes of four parameters is presented. Extensions to the basic model that are made more obvious by the presented reformulation are discussed.