Curvature correction of the Hamilton-Jacobi skeleton

The Hamilton-Jacobi approach has proved to be a powerful and elegant method for extracting the skeleton of a shape. The approach is based on the fact that the inward evolving boundary flux is conservative everywhere except at skeletal points. Nonetheless this method appears to overlook the fact that the linear density of the evolving boundary front is not constant where the front is curved. In this paper we present an analysis, which takes into account variations of density due to boundary curvature. This yields a skeletonization algorithm that is both better localized and less susceptible to boundary noise than the Hamilton-Jacobi method.