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Publications about Optimization
Result of the query in the list of publications :
3 Technical and Research Reports |
1 - Optimization Techniques for Energy Minimization Problem in a Marked Point Process Application to Forestry.
G. Perrin and X. Descombes and J. Zerubia. Research Report 5704, INRIA, France, September 2005.
Keywords : Simulated Annealing, Marked point process, Stochastic geometry, Optimization.
@TECHREPORT{rr_perrin_optim_05,
|
| author |
= |
{Perrin, G. and Descombes, X. and Zerubia, J.}, |
| title |
= |
{Optimization Techniques for Energy Minimization Problem in a Marked Point Process Application to Forestry}, |
| year |
= |
{2005}, |
| month |
= |
{September}, |
| institution |
= |
{INRIA}, |
| type |
= |
{Research Report}, |
| number |
= |
{5704}, |
| address |
= |
{France}, |
| url |
= |
{https://hal.inria.fr/inria-00070312}, |
| pdf |
= |
{https://hal.inria.fr/file/index/docid/70312/filename/RR-5704.pdf}, |
| ps |
= |
{https://hal.inria.fr/docs/00/07/03/12/PS/RR-5704.ps}, |
| keyword |
= |
{Simulated Annealing, Marked point process, Stochastic geometry, Optimization} |
| } |
Résumé :
Dans ce rapport de recherche, nous utilisons les processus ponctuels marqués afin d'extraire un nombre inconnu d'objets dans des images aériennes. Ces processus sont définis par une énergie, qui contient un terme a priori formalisant les interactions entre objets ainsi qu'un terme d'attache aux données. Nous cherchons à minimiser cette énergie, afin d'obtenir la meilleure configuration d'objets, à l'aide d'un recuit simulé qui s'inscrit dans l'algorithme d'échantillonnage MCMC à sauts réversibles.
Nous comparons ici différents schémas de décroissance de température, et présentons certaines méthodes qui permettent d'améliorer la convergence de l'algorithme en un temps fini. |
Abstract :
We use marked point processes to detect an unknown number of trees from high resolution aerial images. This approach turns to be an energy minimization problem, where the energy contains a prior term which takes into account the geometrical properties of the objects, and a data term to match these objects onto the image. This stochastic process is simulated via a Reversible Jump Markov Chain Monte Carlo procedure, which embeds a Simulated Annealing scheme to extract the best configuration of objects.
We compare in this paper different cooling schedules of the Simulated Annealing algorithm which could provide some good minimization in a short time. We also study some adaptive proposition kernels. |
|
2 - A Multiresolution Approach for Shape from Shading Coupling Deterministic and Stochastic Optimization.
A. Crouzil and X. Descombes and J.D. Durou. Research Report 5006, INRIA, France, December 2003.
Keywords : Shape from shading, Simulated Annealing, Optimization, Multiresolution.
@TECHREPORT{Crouzil03,
|
| author |
= |
{Crouzil, A. and Descombes, X. and Durou, J.D.}, |
| title |
= |
{A Multiresolution Approach for Shape from Shading Coupling Deterministic and Stochastic Optimization}, |
| year |
= |
{2003}, |
| month |
= |
{December}, |
| institution |
= |
{INRIA}, |
| type |
= |
{Research Report}, |
| number |
= |
{5006}, |
| address |
= |
{France}, |
| url |
= |
{https://hal.inria.fr/inria-00071578}, |
| pdf |
= |
{https://hal.inria.fr/file/index/docid/71578/filename/RR-5006.pdf}, |
| ps |
= |
{https://hal.inria.fr/docs/00/07/15/78/PS/RR-5006.ps}, |
| keyword |
= |
{Shape from shading, Simulated Annealing, Optimization, Multiresolution} |
| } |
Résumé :
Le Shape from shading est un problème inverse mal posé pour lequel aucune méthode de résolution complètement satisfaisante n'a encore été proposée. Dans ce rapport technique, nous ramenons le à un problème d'optimisation. Nous montrons d'abord que l'approche déterministe fournit des algorithmes efficaces en termes de temps de calcul, mais est d'un intérêt limité lorsque l'énergie comporte des minima locaux très profonds. Nous proposons comme alternative une approche stochastique utilisant le recuit simulé. Les résultats obtenus dépassent largement ceux de l'approche déterministe. La contrepartie est l'extrême lenteur du processus d'optimisation. Pour cette raison, nous proposons une approche hybride qui combine les approches déterministe et stochastique dans un cadre de multi-résolution. |
Abstract :
Shape from shading is an ill-posed inverse problem for which there is no completely satisfactory solution in the existing literature. In this technical report, we address shape from shading as an energy minimization problem. We first show that the deterministic approach provides efficient algorithms in terms of CPU time, but reaches its limits since the energy associated to shape from shading can contain multiple deep local minima. We derive an alternative stochastic approach using simulated annealing. The obtained results strongly outperform the results of the deterministic approach. The shortcoming is an extreme slowness of the optimization. Therefore, we propose an hybrid approach which combines the deterministic and stochastic approaches in a multiresolution framework. |
|
3 - Modeling very Oscillating Signals : Application to Image Processing.
G. Aubert and J.F. Aujol. Research Report 4878, INRIA, France, July 2003.
Keywords : Bounded Variation Space, Sobolev space, Image decomposition, Optimization, Partial differential equation.
@TECHREPORT{4878,
|
| author |
= |
{Aubert, G. and Aujol, J.F.}, |
| title |
= |
{Modeling very Oscillating Signals : Application to Image Processing}, |
| year |
= |
{2003}, |
| month |
= |
{July}, |
| institution |
= |
{INRIA}, |
| type |
= |
{Research Report}, |
| number |
= |
{4878}, |
| address |
= |
{France}, |
| url |
= |
{https://hal.inria.fr/inria-00071705}, |
| pdf |
= |
{https://hal.inria.fr/file/index/docid/71705/filename/RR-4878.pdf}, |
| ps |
= |
{https://hal.inria.fr/docs/00/07/17/05/PS/RR-4878.ps}, |
| keyword |
= |
{Bounded Variation Space, Sobolev space, Image decomposition, Optimization, Partial differential equation} |
| } |
Résumé :
Cet article complète le travail présenté dans cite{Aujol[3]} dans lequel nous avions développé l'analyse numérique d'un modéle variationnel, initialement introduit par L. Rudin, S. Osher and E. Fatemi cite{Rudin[1]}, et revisité depuis par Y. Meyer cite{Meyer[1]}, pour supprimer le bruit et isoler les textures dans une image. Dans un tel modèle, on décompose l'image f en deux composantes (u+v), u et v minimisant une énergie. La première composante u appartient à BV et contient l'information géométrique de l'image, alors que la seconde v appartient à un espace G qui contient les signaux à fortes oscillations, i.e. le bruit et les textures. Dans cite{Meyer[1]}, Y. Meyer effectue son étude dans ^2 entier, et son approche repose principalement sur des outils d'analyse harmonique. Nous nous pla ons dans le cas d'un ouvert borné de ^2, ce qui constitue le cadre adapté au traitement d'images, et notre approche repose sur des arguments d'analyse fonctionnelle. Nous définissons l'espace G dans ce cadre puis donnons quelques unes de ses propriétés. Nous étudions ensuite la fonctionnelle permettant de calculer les composantes u et v. |
Abstract :
This article is a companion paper of a previous work cite{Aujol[3]} where we have developed the numerical analysis of a variational model first introduced by L. Rudin, S. Osher and E. Fatemi cite{Rudin[1]} and revisited by Y. Meyer cite{Meyer[1]} for removing the noise and capturing textures in an image. The basic idea in this model is to decompose f into two components (u+v) and then to search for (u,v) as a minimizer of an energy functional. The first component u belongs to BV and contains geometrical informations while the second one v is sought in a space G which contains signals with large oscillations, i.e. noise and textures. In Y. Meyer carried out his study in the whole ^2 and his approach is rather built on harmonic analysis tools. We place ourselves in the case of a bounded set of ^2 which is the proper setting for image processing and our approach is based upon functional analysis arguments. We define in this context the space G, give some of its properties and then study in this continuous setting the energy functional which allows us to recover the components u and v. model signals with strong oscillations. For instance, in an image, this space models noises and textures. case of a bounded open set of ^2 which is the proper setting for image processing. We give a definition of G adapted to our case, and we show that it still has good properties to model signals with strong oscillations. In cite{Meyer[1]}, the author had also paved the way to a new model to decompose an image into two components: one in BV (the space of bounded variations) which contains the geometrical information, and one in G which consists in the noises ad the textures. An algorithm to perform this decomposition has been proposed in cite{Meyer[1]}. We show here its relevance in a continuous setting. |
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