The aim of the paper is to study problem of image segmentation and missingboundaries completion introduced in [3], [4], [5] and [6]. We generalize approachpresented in [1] and apply it in the eld of image segmentation. So called regularisedRiemannian mean curvature ow equation is presented and the construction of thenumerical scheme based on the nite volume method approach is explained. Theprinciple of the level set, for the first time given in [2], is used. Based on the ideasfrom [1] we prove the stability estimates on the numerical solution and the uniquenessof the numerical solution. In the last section there is a proof of the convergence ofthe numerical scheme to the weak solution of the regularised Riemannian meancurvature ow equation and the proof of the convergence of the approximation ofthe numerical gradient is mentioned as well.
@article{614,
title = {Convergence of the numerical scheme for regularized Riemannian mean curvature flow equation},
journal = {Tatra Mountains Mathematical Publications},
volume = {72},
year = {2019},
doi = {10.2478/tmmp-2018-0025},
language = {EN},
url = {http://dml.mathdoc.fr/item/614}
}
Tibenský, Matúš; Handlovičová, Angela. Convergence of the numerical scheme for regularized Riemannian mean curvature flow equation. Tatra Mountains Mathematical Publications, Tome 72 (2019) . doi : 10.2478/tmmp-2018-0025. http://gdmltest.u-ga.fr/item/614/