Level set regularization using geometric flows

Abstract

In this paper we study a geometric partial differential equation including a forcing term. This equation defines a hypersurface evolution that we use for level set regularization. We study the shape of the radial solutions of the equation and some qualitative properties about the level set propagations. We show that under a suitable choice of the forcing term, the geometric equation has nontrivial asymptotic states and it represents a model for level set regularization. We show that by using a forcing term which is merely a bounded Hölder continuous function, we can obtain finite time stabilization of the solutions. We introduce an explicit finite difference scheme to compute numerically the solution of the equation and we present some applications of the model to nonlinear two-dimensional image filtering and three-dimensional segmentation in the context of medical imaging.