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A variational model in image processing with focal points

Published online by Cambridge University Press:  04 July 2008

Andrea Braides  and
Giuseppe Riey
Andrea Braides
Affiliation:
Dipartimento di Matematica, Università di Roma `Tor Vergata', Via della Ricerca scientifica 1, 00133 Roma, Italy. riey@mat.unical.it
Giuseppe Riey
Affiliation:
Dipartimento di Matematica, Università della Calabria, Via P. Bucci, 87036 Arcavacata di Rende (CS), Italy.
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Abstract

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. We prove that such an energy is obtained as a Γ-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

Γ-convergencecurvature functionalssegmentation problemsimage processing.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 42 , Issue 5 , September 2008 , pp. 729 - 748
Copyright
© EDP Sciences, SMAI, 2008

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