PIMS/CSC Research Seminar: Nathan King

Maps from a manifold M to a manifold N appear in mathematical physics, image processing, computer vision, medical imaging, and many other areas. This talk introduces a numerical framework for variational problems and partial differential equations (PDEs) that map between manifolds. The problem of solving a constrained PDE between M and N is reduced into two simpler problems: solving a PDE on M and projecting onto N. The proposed algorithm uses closest point representations of M and N. This leads to a simple algorithm built on standard Cartesian grid methods that treats rather general manifold geometry. Numerical examples of denoising texture maps, diffusing random maps, and enhancing colour images are presented.