# A variational model in image processing with focal points

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

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

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topBraides, 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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