Study of a finite volume scheme for the regularized mean curvature flow level set equation

We propose a new finite volume numerical scheme for the approximation of regularized mean curvature flow level set equations, which ensures the maximum principle, and which is shown to converge to the solution of the problem. The convergence proof uses the monotonicity of the operator in order to get the strong convergence of the approximation of the gradient. Numerical examples provide indications about the accuracy of the method. Applications to noisy image filtering show less diffusive behaviour than the classical finite difference scheme.