ALGORITHMS FOR AREA PRESERVING FLOWS.

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner.

Inpainting of binary images using the Cahn-Hilliard equation.

Image inpainting is the filling in of missing or damaged regions of images using information from surrounding areas. We outline here the use of a model for binary inpainting based on the Cahn-Hilliard equation, which allows for fast, efficient inpainting of degraded text, as well as super-resolution of high contrast images.