We show how models for transportation networks can be reduced to Mumford-Shah-type image inpainting problems. Classical functional lifting allows to relax the inpainting problem into a convex optimization in a higher-dimensional space. We present a corresponding adaptive finite element discretization with heuristic refinement strategies based on the duality gap and an active-set type approach to deal with the large number of involved nonlocal convex constraints and their update after grid refinement.

This presentation is part of Minisymposium “MS64 - Images and Finite Elements”
organized by: Roland Herzog (Technische Universität Chemnitz) , Stephan Schmidt (University of Würzburg) .

Authors:

Benedikt Wirth (Universität Münster)

Rossmanith Carolin (Westfälische Wilhelms-Universität Münster)

Keywords:

image reconstruction, image segmentation, nonlinear optimization, transportation networks