Convergence of the numerical scheme for regularized Riemannian mean curvature flow equation

Abstract

The aim of the paper is to study problem of image segmentation and missing
boundaries completion introduced in [3], [4], [5] and [6]. We generalize approach
presented in [1] and apply it in the eld of image segmentation. So called regularised
Riemannian mean curvature ow equation is presented and the construction of the
numerical scheme based on the nite volume method approach is explained. The
principle of the level set, for the first time given in [2], is used. Based on the ideas
from [1] we prove the stability estimates on the numerical solution and the uniqueness
of the numerical solution. In the last section there is a proof of the convergence of
the numerical scheme to the weak solution of the regularised Riemannian mean
curvature ow equation and the proof of the convergence of the approximation of
the numerical gradient is mentioned as well.