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 -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.
Mots clés : $\Gamma $-convergence, curvature functionals, segmentation problems, image processing
@article{M2AN_2008__42_5_729_0,
author = {Braides, Andrea and Riey, Giuseppe},
title = {A variational model in image processing with focal points},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {729--748},
publisher = {EDP-Sciences},
volume = {42},
number = {5},
year = {2008},
doi = {10.1051/m2an:2008024},
mrnumber = {2454621},
zbl = {1213.94012},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2008024/}
}
TY - JOUR AU - Braides, Andrea AU - Riey, Giuseppe TI - A variational model in image processing with focal points JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2008 SP - 729 EP - 748 VL - 42 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2008024/ DO - 10.1051/m2an:2008024 LA - en ID - M2AN_2008__42_5_729_0 ER -
%0 Journal Article %A Braides, Andrea %A Riey, Giuseppe %T A variational model in image processing with focal points %J ESAIM: Modélisation mathématique et analyse numérique %D 2008 %P 729-748 %V 42 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2008024/ %R 10.1051/m2an:2008024 %G en %F M2AN_2008__42_5_729_0
Braides, Andrea; Riey, Giuseppe. A variational model in image processing with focal points. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 5, pp. 729-748. doi : 10.1051/m2an:2008024. http://www.numdam.org/articles/10.1051/m2an:2008024/
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