Discrete, nonlinear curvature-dependent contour evolution

There has been much recent interest in curvature-dependent contour evolution, particularly when the resultant family of contours satisfies the heat (diffusion) equation. Modeling the evolution of a shape's boundary as a real-valued solution to the reaction-diffusion equation has been shown to be useful for shape decomposition [3]. This approach to contour evolution involves solving a partial differential equation (PDE), is computationally demanding, and must deal with the problem of singularities. In this paper, we describe a low-precision discrete method of contour evolution, based on the 8-connected chain code of the contour, that performs analogously to PDE-based methods and avoids the singularity problem. (Preliminary work along these lines was described in [12].) Our discrete method is not limited to linear functions of curvature; we give several examples of contour evolution processes that depend nonlinearly on curvature, including examples studied in [6], and illustrate their possible uses.