Calculus of Variations and Geometric Measure Theory

A. Braides - G. Riey

A variational model in Image Processing with focal points

created by braidesa on 18 Jun 2007
modified on 27 Sep 2008


Published Paper

Inserted: 18 jun 2007
Last Updated: 27 sep 2008

Journal: ESAIM: M2AN
Volume: 42
Pages: 729-748
Year: 2008


We propose a model for segmentation problems involving an energy concentrated on the vertices of an unknown polyhedral set, where the contours of the images to be recovered have preferred directions and focal points. Such an energy is obtained as a $\Gamma$-limit of functionals defined on sets with smooth boundary that involve curvature terms of the boundary. The minimizers of the limit functional are polygons with edges either parallel to some prescribed directions or pointing to some fixed points, that can also be taken as unknown of the problem.

Keywords: Gamma-convergence, free discontinuity problems, curvature functionals, Image reconstruction