Calculus of Variations and Geometric Measure Theory

G. Bellettini - R. March

An image segmentation variational model with free discontinuities and contour curvature

created on 28 Jul 2002
modified on 13 Jul 2004


Published Paper

Inserted: 28 jul 2002
Last Updated: 13 jul 2004

Journal: Math. Mod. Meth. Appl. Sci.
Volume: 14
Pages: 1-45
Year: 2004


We introduce a functional for image segmentation which takes into account the trasparencies (or shadowing) and the occlusions between objects located at different dephts in space. By minimizing the functional, we try to reconstruct a piecewise smooth approximation of the input image, the contours due to trasparencies, and the contours of the objects together with their hidden portions. The functional includes a Mumford-Shah type energy and a term involving the curvature of the contours. The variational properties of the functional are studied, as well as its approximation by Gamma-convergence. The comparison with the Nitzberg-Mumford variational model for segmentation with depth is also discussed.

Keywords: $\Gamma$-convergence, Computer Vision, Variational problems, relaxation of functionals