Affine skeletons and monge-ampere equations

Abstract

An important question about a. ne skeletons is the existence of differential equations that are related to the 'affine distance' and the 'area distance' (hence to a. ne skeletons) in the same way the Eikonal equation is related to the 'Euclidean distance' (and the medial axis). We show a surprisingly simple nonlinear second order PDE of Monge-Ampere type that relates to the a. ne skeletons (and extends the Eikonal equation for the medial axis). We also discuss some consequences and ideas that this new PDE formulation suggests.