A Robust Skeletonization Method for Topological Complex Shapes

Abstract

In this paper, we describe a skeletonization method effective and robust when applied to complex shapes, even if affected by boundary perturbations. This approach has been applied to binary segmented images containing bi-dimensional bounded shapes, generally not simply connected. It has been considered an external force field derived by an anisotropic flow. Through the divergence, we have examined the field flow at different times, discovering that the field divergence satisfies an anisotropic diffusion equation as well. Curves of positive divergence may be thought as propagating fronts converging to a steady state formed by shocks points. It has been proved that the sets of points, inside the shape, where divergence assumes positive values, converge to the skeleton. The curves with negative values of divergence remain static, so they may be directly used for edge extraction. This methodology has also been tested respect to boundary perturbations and disconnections.