Abstract

This talk deals with free discontinuity problems related to contour enhancement in image segmentation and inpainting. The segmentation we look for provides a cartoon of the given image satisfying some requirements: the decomposition of the image is performed by choosing a pattern of lines of steepest discontinuity for light intensity, and this pattern will be called segmentation of the image. In image restoration the term inpainting denotes the process of filling in the missing information over subdomains where a given image is damaged: these domains may correspond to scratches in a camera picture, occlusion by objects, blotches in an old movie film or aging of canvas and colors in a painting. We focus on the mathematical analysis of Blake & Zisserman functional, precisely: existence of strong solution under Dirichlet boundary condition is shown; several extremality conditions on optimal segmentation are stated; well-posedness of the problem is discussed; non trivial local minimizers are analyzed; a variational approximation is introduced and implemented.