Mesh adaptation-aided image segmentation

Abstract We focus on a variational approach to image segmentation based on the Ambrosio-Tortorelli functional. To make the procedure more effective with respect to standard algorithms, we combine the functional minimization with the employment of an optimal discretization. More precisely, we perform a finite element approximation of the Ambrosio-Tortorelli functional on a triangular adapted mesh able to follow exactly the contours present in the images, in the spirit of a mesh adaptation-aided image segmentation. This challenging goal is reached via a rigorous a posteriori error analysis enriched with anisotropic information. The benefits due to the proposed algorithm are evident both in terms of increased resolution in the edge detection and in a considerable reduction of the computational costs, as confirmed by an extensive numerical investigation.