Encoding of a priori Information in Active Contour Models

The theory of active contours models the problem of contour recovery as an energy minimization process. The computational solutions based on dynamic programming require that the energy associated with a contour candidate can be decomposed into an integral of local energy contributions. In this paper we propose a grammatical framework that can model different local energy models and a set of allowable transitions between these models. The grammatical encodings are utilized to represent a priori knowledge about the shape of the object and the associated signatures in the underlying images. The variability encountered in numerical experiments is addressed with the energy minimization procedure which is embedded in the grammatical framework. We propose an algorithmic solution that combines a nondeterministic version of the Knuth-Morris-Pratt algorithm for string matching with a time-delayed discrete dynamic programming algorithm for energy minimization. The numerical experiments address practical problems encountered in contour recovery such as noise robustness and occlusion.