Affine Skeletons and Monge-Ampère Equations
Moacyr Alvim Silva | Teixeira, Ralph | Velho, Luiz
affine distance | medial axis | skeleton | affine geometry | monge-ampère equation | differential propagation
An important question about affine skeletons is the existence of differential equations that is related to the 'affine distance' and 'area distance' (hence to the affine skeletons) as the Eikonal equation is related to the 'euclidean distance' (and medial axis). We show that some nonlinear second order PDE of Monge-Ampère type are, in fact, related to the affine skeletons. We also discuss some consequences and ideas that the PDE formulation suggests.