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Optimizing Parametric Total Variation Models

Strandmark, Petter LU ; Kahl, Fredrik LU and Overgaard, Niels Christian LU (2009) IEEE International Conference on Computer Vision (ICCV), 2009 In [Host publication title missing] p.2240-2247
Abstract
One of the key factors for the success of recent energy

minimization methods is that they seek to compute global

solutions. Even for non-convex energy functionals, optimization

methods such as graph cuts have proven to produce

high-quality solutions by iterative minimization based on

large neighborhoods, making them less vulnerable to local

minima. Our approach takes this a step further by enlarging

the search neighborhood with one dimension.

In this paper we consider binary total variation problems

that depend on an additional set of parameters. Examples

include:

(i) the Chan-Vese model that we solve globally

(ii) ratio and... (More)
One of the key factors for the success of recent energy

minimization methods is that they seek to compute global

solutions. Even for non-convex energy functionals, optimization

methods such as graph cuts have proven to produce

high-quality solutions by iterative minimization based on

large neighborhoods, making them less vulnerable to local

minima. Our approach takes this a step further by enlarging

the search neighborhood with one dimension.

In this paper we consider binary total variation problems

that depend on an additional set of parameters. Examples

include:

(i) the Chan-Vese model that we solve globally

(ii) ratio and constrained minimization which can be formulated

as parametric problems, and

(iii) variants of the Mumford-Shah functional.

Our approach is based on a recent theorem of Chambolle

which states that solving a one-parameter family of binary

problems amounts to solving a single convex variational

problem. We prove a generalization of this result and show

how it can be applied to parametric optimization. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
segmentation, total variation, image analysis, optimization
in
[Host publication title missing]
pages
2240 - 2247
conference name
IEEE International Conference on Computer Vision (ICCV), 2009
external identifiers
  • wos:000294955300289
  • scopus:77953227527
DOI
10.1109/ICCV.2009.5459464
language
English
LU publication?
yes
id
559df996-3daa-4815-b12e-8d6c10cdb379 (old id 1444558)
alternative location
http://www.maths.lth.se/vision/publdb/reports/pdf/strandmark-kahl-etal-iccv-09.pdf
date added to LUP
2009-07-17 09:28:36
date last changed
2017-06-11 05:00:37
@inproceedings{559df996-3daa-4815-b12e-8d6c10cdb379,
  abstract     = {One of the key factors for the success of recent energy<br/><br>
minimization methods is that they seek to compute global<br/><br>
solutions. Even for non-convex energy functionals, optimization<br/><br>
methods such as graph cuts have proven to produce<br/><br>
high-quality solutions by iterative minimization based on<br/><br>
large neighborhoods, making them less vulnerable to local<br/><br>
minima. Our approach takes this a step further by enlarging<br/><br>
the search neighborhood with one dimension.<br/><br>
In this paper we consider binary total variation problems<br/><br>
that depend on an additional set of parameters. Examples<br/><br>
include:<br/><br>
(i) the Chan-Vese model that we solve globally<br/><br>
(ii) ratio and constrained minimization which can be formulated<br/><br>
as parametric problems, and<br/><br>
(iii) variants of the Mumford-Shah functional.<br/><br>
Our approach is based on a recent theorem of Chambolle<br/><br>
which states that solving a one-parameter family of binary<br/><br>
problems amounts to solving a single convex variational<br/><br>
problem. We prove a generalization of this result and show<br/><br>
how it can be applied to parametric optimization.},
  author       = {Strandmark, Petter and Kahl, Fredrik and Overgaard, Niels Christian},
  booktitle    = {[Host publication title missing]},
  keyword      = {segmentation,total variation,image analysis,optimization},
  language     = {eng},
  pages        = {2240--2247},
  title        = {Optimizing Parametric Total Variation Models},
  url          = {http://dx.doi.org/10.1109/ICCV.2009.5459464},
  year         = {2009},
}