Two approaches for the approximation of the nonlinear smoothing term in the image segmentation

Abstract

Purpose of the paper is to study nonlinear smoothing term initiated in [3], [4],[6] and [7] for problems of image segmentation and missing boundaries completion.  The generalization of approach presented in [1] is proposed and applied in the field of image segmentation. So called regularised Riemannian mean curvature flow equation is studied and the construction of the numerical scheme based on the finite volume method approach is explained. The principle of the level set, for the first time given in [2], is used. We mention two different approaches for the approximation of the nonlinear smoothing term in the equation and known theoretical results for both of them. We provide the numerical tests for both schemes. It the last section we discuss obtained results and propose possibilities for the future research.