A Markov process using curvature for filtering curve images

Abstract

A Markov process model for contour curvature is introduced via a stochastic differential equation. We analyze the distribution of such curves, and show that its mode is the Euler spiral, a curve minimizing changes in curvature. To probabilistically enhance noisy and low contrast curve images (e.g., edge and line operator responses), we combine this curvature process with the curve indicator random field, which is a prior for ideal curve images. In particular, we provide an expression for a nonlinear, minimum mean square error filter that requires the solution of two elliptic partial differential equations. Initial computations are reported, highlighting how the filter is curvature-selective, even when curvature is absent in the input.