Anisotropic Total Variation Based Image Restoration Using Graph Cuts

Abstract

In this thesis we consider a particular kind of edge-enhancing image restoration method based on total variation. We want to address the fact that the total variation method in some cases leads to contrast loss in thin structures. To reduce the contrast loss a directional dependence is introduced through an anisotropy tensor. The tensor controls the regularization applied based on the position in the image and the direction of the gradient. It is constructed using edge information extracted from the noisy image. We optimize the resulting functional using a graph cut framework; a discretization which is made possible by a coarea and a Cauchy Crofton formula. In the end we perform numerical studies, experiment with the parameters and discuss the results.