Difference between revisions of "Publications/darbon.06.jmiv"

From LRDE

(Created page with "{{Publication | date = 2006-03-24 | authors = Jérôme Darbon, Marc Sigelle | title = Image restoration with discrete constrained Total Variation---Part~I: Fast and exact opti...")
 
 
(11 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
{{Publication
 
{{Publication
  +
| published = true
 
| date = 2006-03-24
 
| date = 2006-03-24
 
| authors = Jérôme Darbon, Marc Sigelle
 
| authors = Jérôme Darbon, Marc Sigelle
| title = Image restoration with discrete constrained Total Variation---Part~I: Fast and exact optimization
+
| title = Image restoration with discrete constrained Total Variation—Part I: Fast and exact optimization
 
| journal = Journal of Mathematical Imaging and Vision
 
| journal = Journal of Mathematical Imaging and Vision
 
| volume = 26
 
| volume = 26
 
| number = 3
 
| number = 3
 
| pages = 261 to 276
 
| pages = 261 to 276
| project = Image
+
| lrdeprojects = Olena
 
| abstract = This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under <math>L^1</math> data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.
| urllrde = 2006XXX-JMIVa
 
| abstract = This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under $L^1$ data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.
 
 
| lrdekeywords = Image
 
| lrdekeywords = Image
 
| lrdenewsdate = 2006-03-24
 
| lrdenewsdate = 2006-03-24
Line 25: Line 25:
 
month = dec,
 
month = dec,
 
pages = <nowiki>{</nowiki>261--276<nowiki>}</nowiki>,
 
pages = <nowiki>{</nowiki>261--276<nowiki>}</nowiki>,
project = <nowiki>{</nowiki>Image<nowiki>}</nowiki>,
 
 
abstract = <nowiki>{</nowiki>This paper deals with the total variation minimization
 
abstract = <nowiki>{</nowiki>This paper deals with the total variation minimization
 
problem in image restoration for convex data fidelity
 
problem in image restoration for convex data fidelity
Line 41: Line 40:
 
self-dual contrast invariant filter. Finally we present
 
self-dual contrast invariant filter. Finally we present
 
some results.<nowiki>}</nowiki>
 
some results.<nowiki>}</nowiki>
<nowiki>}</nowiki>
 
 
@Article<nowiki>{</nowiki> darbon.06.jmivb,
 
author = <nowiki>{</nowiki>J\'er\^ome Darbon and Marc Sigelle<nowiki>}</nowiki>,
 
title = <nowiki>{</nowiki>Image restoration with discrete constrained <nowiki>{</nowiki>T<nowiki>}</nowiki>otal
 
<nowiki>{</nowiki>Variation<nowiki>}</nowiki>---Part~<nowiki>{</nowiki>II<nowiki>}</nowiki>: Levelable functions, convex priors
 
and non-convex case<nowiki>}</nowiki>,
 
journal = <nowiki>{</nowiki>Journal of Mathematical Imaging and Vision<nowiki>}</nowiki>,
 
year = 2006,
 
volume = 26,
 
number = 3,
 
month = dec,
 
pages = <nowiki>{</nowiki>277--291<nowiki>}</nowiki>,
 
project = <nowiki>{</nowiki>Image<nowiki>}</nowiki>,
 
abstract = <nowiki>{</nowiki>In Part II of this paper we extend the results obtained in
 
Part I for total variation minimization in image
 
restoration towards the following directions: first we
 
investigate the decomposability property of energies on
 
levels, which leads us to introduce the concept of
 
levelable regularization functions (which TV is the
 
paradigm of). We show that convex levelable posterior
 
energies can be minimized exactly using the
 
level-independant cut optimization scheme seen in part I.
 
Next we extend this graph cut scheme optimization scheme to
 
the case of non-convex levelable energies. We present
 
convincing restoration results for images corrupted with
 
impulsive noise. We also provide a minimum-cost based
 
algorithm which computes a global minimizer for Markov
 
Random Field with convex priors. Last we show that
 
non-levelable models with convex local conditional
 
posterior energies such as the class of generalized
 
gaussian models can be exactly minimized with a generalized
 
coupled Simulated Annealing.<nowiki>}</nowiki>
 
 
<nowiki>}</nowiki>
 
<nowiki>}</nowiki>
   

Latest revision as of 11:06, 15 May 2020

Abstract

This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.


Bibtex (lrde.bib)

@Article{	  darbon.06.jmiv,
  author	= {J\'er\^ome Darbon and Marc Sigelle},
  title		= {Image restoration with discrete constrained {T}otal
		  {Variation}---Part~{I}: Fast and exact optimization},
  journal	= {Journal of Mathematical Imaging and Vision},
  year		= 2006,
  volume	= 26,
  number	= 3,
  month		= dec,
  pages		= {261--276},
  abstract	= {This paper deals with the total variation minimization
		  problem in image restoration for convex data fidelity
		  functionals. We propose a new and fast algorithm which
		  computes an exact solution in the discrete framework. Our
		  method relies on the decomposition of an image into its
		  level sets. It maps the original problems into independent
		  binary Markov Random Field optimization problems at each
		  level. Exact solutions of these binary problems are found
		  thanks to minimum cost cut techniques in graphs. These
		  binary solutions are proved to be monotone increasing with
		  levels and yield thus an exact solution of the discrete
		  original problem. Furthermore we show that minimization of
		  total variation under $L^1$ data fidelity term yields a
		  self-dual contrast invariant filter. Finally we present
		  some results.}
}