Constrained anisotropic diffusion and some applications

Minimal surface regularization has been used in several applications ranging from stereo to image segmentation, sometimes hidden as a graph-cut discrete formulation, or as a strictly convex approximation to TV minimization. In this paper we consider a modified version of minimal surface regularization coupled with a robust data fitting term for interpolation purposes, where the corresponding evolution equation is constrained to diffuse only along the isophotes of a given image u and we design a convergent numerical scheme to accomplish this. To illustrate the usefulness of our approach, we apply this framework to the digital elevation model interpolation and to constrained vector probability diffusion.