A variational model in image processing with focal points

Andrea Braides; Giuseppe Riey

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • Volume: 42, Issue: 5, page 729-748
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Braides, Andrea, and Riey, Giuseppe. "A variational model in image processing with focal points." ESAIM: Mathematical Modelling and Numerical Analysis 42.5 (2008): 729-748. <http://eudml.org/doc/250363>.

@article{Braides2008,
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. },
author = {Braides, Andrea, Riey, Giuseppe},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Γ-convergence; curvature functionals; segmentation problems; image processing.; -convergence; segmentation problems; image processing},
language = {eng},
month = {7},
number = {5},
pages = {729-748},
publisher = {EDP Sciences},
title = {A variational model in image processing with focal points},
url = {http://eudml.org/doc/250363},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Braides, Andrea
AU - Riey, Giuseppe
TI - A variational model in image processing with focal points
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2008/7//
PB - EDP Sciences
VL - 42
IS - 5
SP - 729
EP - 748
AB - 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.
LA - eng
KW - Γ-convergence; curvature functionals; segmentation problems; image processing.; -convergence; segmentation problems; image processing
UR - http://eudml.org/doc/250363
ER -

References

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