Publications about Stochastic geometry

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• 3 Articles
• 5 PhD Thesis and Habilitations
• 8 Conference articles
• 9 Technical and Research Reports

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8 Conference articles

3 - Evaluation des Ressources Forestières à l'aide de Processus Ponctuels Marqués. G. Perrin and X. Descombes and J. Zerubia. In Proc. Reconnaissance des Formes et Intelligence Artificielle (RFIA), Tours, France, January 2006. Keywords : Tree Crown Extraction, Stochastic geometry, Marked point process, Object extraction. @INPROCEEDINGS{perrin_06_a, author = {Perrin, G. and Descombes, X. and Zerubia, J.}, title = {Evaluation des Ressources Forestières à l'aide de Processus Ponctuels Marqués}, year = {2006}, month = {January}, booktitle = {Proc. Reconnaissance des Formes et Intelligence Artificielle (RFIA)}, address = {Tours, France}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/perrin_rfia06.pdf}, keyword = {Tree Crown Extraction, Stochastic geometry, Marked point process, Object extraction} } Résumé : Les images aériennes et satellitaires jouent un role de plus en plus important dans le domaine de la gestion des ressources naturelles, et en particulier des forêts. Les organismes chargés d'en faire l'inventaire, comme l'Inventaire Forestier National (IFN) en France, s'appuient en effet sur ces images pour observer les différentes espèces d'arbres d'une zone boisée, avant de se rendre sur le terrain pour une étude plus poussée. La résolution submétrique des données permet, en outre, d'entrevoir une étude plus fine, à savoir un comptage à l'arbre près et une classification automatique des houppiers (ensemble des branches et du feuillage d'un arbre). Cette évaluation précise des ressources forestières n'est actuellement pas disponible. Aussi, le développement d'outils automatiques, chargés d'aider les gestionnaires du paysage dans leur travail en leur apportant une connaissance des ressources à l'échelle de l'arbre, se révèle-t-il être d'un intérêt grandissant.L'objectif de notre travail est donc d'extraire des houppiers à partir d'images aériennes de forêts à très haute résolution. Notre approche consiste à modéliser les peuplements forestiers par un processus ponctuel marqué d'ellipses, dont les points représentent les positions des arbres et les marques leurs caractéristiques géométriques. La densité de ce processus comporte une composante de régularisation, dite a priori, qui introduit des interactions entre les objets du processus, ainsi qu'une composante d'attache aux données, afin que les objets du processus se positionnent sur les houppiers que l'on souhaite extraire. Il s'agit de trouver la configuration d'objets, en nombre inconnu a priori, qui maximise cette densité. La simulation de tels processus fait appel aux algorithmes de type Monte Carlo par Chaîne de Markov (MCMC) à sauts réversibles, l'optimisation étant réalisée à l'aide d'un recuit simulé.Nous présentons ici un nouveau modèle d'attache aux données. Contrairement à nos précédents modèles testés sur des plantations, ce modèle n'est plus bayésien puisque le terme d'attache aux données est désormais calculé au niveau des objets et non de l'image. Ceci nous permet de travailler sur des images plus générales, avec des densités d'arbres plus variables. Des résultats obtenus sur des images fournies par l'IFN valident ce modèle. Abstract : Aerial and satellite imagery has a key role to play in natural resources management, especially in forestry application. Indeed, forest inventories, such as the French National Inventory (IFN), refer to these images to analyse the different tree species in a stand, before sending a team on the ground to obtain some more advanced knowledge. Moreover, the submetric resolution of the data enables to study forests at the scale of trees, and also to get a more accurate evaluation of the resources such as the number of stems. It would be also of important economical and environmental concerns to develop automatic tools to analyze and monitor forests.We aim at extracting tree crowns from high resolution aerial images of forests. Our approach consists in modelling the forestry images as realizations of a marked point process of ellipses, whose points are the positions of the trees and marks their geometric features. The density of this process embeds a regularization term (prior density), which introduces some interactions between the objects, and a data term, which links the objects to the features to be extracted. Our goal is to find the best configuration of an unknown number of objects, i.e. the configuration that maximizes this density. To sample the marked point process, we use Monte Carlo dynamics (Reversible Jump Markov Chain Monte Carlo), while the optimization is performed via a simulated annealing algorithm.We present here a new model for the data term. Contrary to our previous models tested on plantations images, this model is not Bayesian anymore : the data term is calculated for each object and not for the whole image. This enables us to work on more general images, with variable tree crown densities. Example results are shown on aerial images provided by the French Forest Inventory (IFN).

4 - Point process of segments and rectangles for building extraction from DEM. M. Ortner and X. Descombes and J. Zerubia. In Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2006. Keywords : Stochastic geometry, Buildings. @INPROCEEDINGS{ortner06, author = {Ortner, M. and Descombes, X. and Zerubia, J.}, title = {Point process of segments and rectangles for building extraction from DEM}, year = {2006}, booktitle = {Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_ortner06.pdf}, keyword = {Stochastic geometry, Buildings} }

5 - Adaptive Simulated Annealing for Energy Minimization Problem in a Marked Point Process Application. G. Perrin and X. Descombes and J. Zerubia. In Proc. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), St Augustine, Florida, USA, November 2005. Keywords : Simulated Annealing, Marked point process, Stochastic geometry, MAP estimation, RJMCMC. Copyright : Springer Verlag @INPROCEEDINGS{perrin_emmcvpr05, author = {Perrin, G. and Descombes, X. and Zerubia, J.}, title = {Adaptive Simulated Annealing for Energy Minimization Problem in a Marked Point Process Application}, year = {2005}, month = {November}, booktitle = {Proc. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR)}, address = {St Augustine, Florida, USA}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/perrin_emmcvpr.pdf}, ps = {ftp://ftp-sop.inria.fr/ariana/Articles/perrin_emmcvpr.ps.gz}, keyword = {Simulated Annealing, Marked point process, Stochastic geometry, MAP estimation, RJMCMC} } Abstract : We use marked point processes to detect an unknown number of trees from high resolution aerial images. This is in fact 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 to 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 here 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.

6 - A Marked Point Process Model for Tree Crown Extraction in Plantations. G. Perrin and X. Descombes and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Genoa, Italy, September 2005. Keywords : Stochastic geometry, RJMCMC, Tree Crown Extraction, Object extraction, Marked point process. @INPROCEEDINGS{perrin_icip05, author = {Perrin, G. and Descombes, X. and Zerubia, J.}, title = {A Marked Point Process Model for Tree Crown Extraction in Plantations}, year = {2005}, month = {September}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Genoa, Italy}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/perrin_icip05.pdf}, ps = {ftp://ftp-sop.inria.fr/ariana/Articles/perrin_icip05.ps.gz}, keyword = {Stochastic geometry, RJMCMC, Tree Crown Extraction, Object extraction, Marked point process} } Abstract : This work presents a framework to extract tree crowns from remotely sensed data, especially in plantation images, using stochastic geometry. We aim at finding the tree top positions, and the tree crown diameter distribution. Our approach consists in considering that these images are some realizations of a marked point process. First we model the tree plantation as a configuration of an unknown number of ellipses. Then, a Bayesian energy is defined, containing both a prior energy which incorporates the prior knowledge of the plantation geometric properties, and a likelihood which fits the objects to the data. Eventually, we estimate the global minimum of this energy using Reversible Jump Markov Chain Monte Carlo dynamics and a simulated annealing scheme. We present results on optical aerial images of poplars provided by IFN.

7 - Tree Crown Extraction using Marked Point Processes. G. Perrin and X. Descombes and J. Zerubia. In Proc. European Signal Processing Conference (EUSIPCO), University of Technology, Vienna, Austria, September 2004. Keywords : RJMCMC, Marked point process, Simulated Annealing, Tree Crown Extraction, Object extraction, Stochastic geometry. @INPROCEEDINGS{perrin04a, author = {Perrin, G. and Descombes, X. and Zerubia, J.}, title = {Tree Crown Extraction using Marked Point Processes}, year = {2004}, month = {September}, booktitle = {Proc. European Signal Processing Conference (EUSIPCO)}, address = {University of Technology, Vienna, Austria}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/perrin_eusipco2004.pdf}, ps = {ftp://ftp-sop.inria.fr/ariana/Articles/perrin_eusipco2004.ps.gz}, keyword = {RJMCMC, Marked point process, Simulated Annealing, Tree Crown Extraction, Object extraction, Stochastic geometry} } Abstract : In this paper we aim at extracting tree crowns from remotely sensed images. Our approach is to consider that these images are some realizations of a marked point process. The first step is to define the geometrical objects that design the trees, and the density of the process. Then, we use a Reversible Jump Markov Chain Monte Carlo dynamics and a simulated annealing to get the maximum a posteriori estimator of the tree crown distribution on the image. Transitions of the Markov chain are managed by some specific proposition kernels. Results are shown on aerial images of poplars provided by IFN.

8 - Marked Point Process in Image Analysis : from Context to Geometry. X. Descombes and F. Kruggel and C. Lacoste and M. Ortner and G. Perrin and J. Zerubia. In International Conference on Spatial Point Process Modelling and its Application (SPPA), Castellon, Spain, 2004. Keywords : RJMCMC, Object extraction, Marked point process, Stochastic geometry. @INPROCEEDINGS{geostoch04a, author = {Descombes, X. and Kruggel, F. and Lacoste, C. and Ortner, M. and Perrin, G. and Zerubia, J.}, title = {Marked Point Process in Image Analysis : from Context to Geometry}, year = {2004}, booktitle = {International Conference on Spatial Point Process Modelling and its Application (SPPA)}, address = {Castellon, Spain}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/SPPA_2004.pdf}, ps = {ftp://ftp-sop.inria.fr/ariana/Articles/SPPA_2004.ps.gz}, keyword = {RJMCMC, Object extraction, Marked point process, Stochastic geometry} } Abstract : We consider the marked point process framework as a natural extension of the Markov random field approach in image analysis. We consider a general model defined by its density allowing us to consider some geometrical constraints on objects and between objects in feature extraction problems. Some examples are derived for small brain lesions detection from MR Images, road network, tree crown and building extraction from remotely sensed images. The results obtained on real data show the relevance of the proposal approach.

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9 Technical and Research Reports

1 - A Non-Bayesian Model for Tree Crown Extraction using Marked Point Processes. G. Perrin and X. Descombes and J. Zerubia. Research Report 5846, INRIA, France, February 2006. Keywords : Data energy, Object extraction, Tree Crown Extraction, Marked point process, Stochastic geometry, 3D reconstruction. @TECHREPORT{rr_perrin_nonbay_05, author = {Perrin, G. and Descombes, X. and Zerubia, J.}, title = {A Non-Bayesian Model for Tree Crown Extraction using Marked Point Processes}, year = {2006}, month = {February}, institution = {INRIA}, type = {Research Report}, number = {5846}, address = {France}, url = {http://hal.inria.fr/inria-00070180/fr/}, pdf = {http://hal.inria.fr/inria-00070180/fr/}, keyword = {Data energy, Object extraction, Tree Crown Extraction, Marked point process, Stochastic geometry, 3D reconstruction} } Résumé : Dans ce rapport de recherche, notre but est d'extraire les houppiers à partir d'images aériennes de forêts à l'aide de processus ponctuels marqués d'ellipses ou d'ellipsoïdes. Notre approche consiste, en effet, à modéliser les données comme des réalisations de tels processus. Une fois l'objet géométrique de référence choisi, nous échantillonnons le processus objet défini par une densité grâce à un algorithme MCMC à sauts réversibles, optimisé par un recuit simulé afin d'extraire la meilleure configuration d'objets, qui nous donne l'extraction recherchée. Nous obtenons ainsi le nombre des arbres, leur localisation et leur taille. Nous présentons, dans ce rapport, un modèle 2D et un modèle 3D pour extraire des statistiques forestières. Ceux-ci sont testés sur des images aériennes infrarouge couleur très haute résolution fournies par l'Inventaire Forestier National (IFN). Abstract : High resolution aerial and satellite images of forests have a key role to play in natural resource management. As they enable forestry managers to study forests at the scale of trees, it is now possible to get a more accurate evaluation of the resources. Automatic algorithms are needed in that prospect to assist human operators in the exploitation of these data. In this paper, we present a stochastic geometry approach to extract 2D and 3D parameters of the trees, by modelling the stands as some realizations of a marked point process of ellipses or ellipsoids, whose points are the locations of the trees and marks their geometric features. As a result we obtain the number of stems, their position, and their size. This approach yields an energy minimization problem, where the energy embeds a regularization term (prior density), which introduces some interactions between the objects, and a data term, which links the objects to the features to be extracted, in 2D and 3D. Results are shown on Colour Infrared aerial images provided by the French National Forest Inventory (IFN)

2 - 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.

3 - Point Processes in Forestry : an Application to Tree Crown Detection. G. Perrin and X. Descombes and J. Zerubia. Research Report 5544, INRIA, France, April 2005. Keywords : Marked point process, Object extraction, RJMCMC, Tree Crown Extraction, Stochastic geometry. @TECHREPORT{5544, author = {Perrin, G. and Descombes, X. and Zerubia, J.}, title = {Point Processes in Forestry : an Application to Tree Crown Detection}, year = {2005}, month = {April}, institution = {INRIA}, type = {Research Report}, number = {5544}, address = {France}, url = {https://hal.inria.fr/inria-00070463}, pdf = {https://hal.inria.fr/file/index/docid/70463/filename/RR-5544.pdf}, ps = {https://hal.inria.fr/docs/00/07/04/63/PS/RR-5544.ps}, keyword = {Marked point process, Object extraction, RJMCMC, Tree Crown Extraction, Stochastic geometry} } Résumé : Dans ce rapport de recherche, notre but est d'extraire des houppiers à partir d'images aériennes de forêts à l'aide de processus ponctuels marqués de disques et d'ellipses. Notre approche consiste, en effet, à modéliser les données comme des réalisations de tels processus. Une fois l'objet géométrique de référence choisi, nous échantillonnons le processus objet défini par une densité grâce à un algorithme MCMC à sauts réversibles, optimisé par un recuit simulé afin d'extraire le maximum a posteriori de cette densité. Cette configuration optimale nous donnera l'extraction recherchée. Dans une première partie, nous proposons de revenir quelque peu sur les processus ponctuels marqués et leur application dans la foresterie. Puis, nous présentons deux nouveaux modèles d'extraction de houppiers à base de disques et d'ellipses, et discutons de quelques améliorations au niveau de la simulation et de l'optimisation de notre algorithme. Nous présentons des résultats obtenus sur des images aériennes très haute résolution fournies par l'Inventaire Forestier National (IFN), ainsi que sur des images synthétiques simulées avec le logiciel AMAP (Bionatics, projet Digiplante). Abstract : In this research report, we aim at extracting tree crowns from remotely sensed images using marked point processes of discs and ellipses. Our approach is indeed to consider that the data are some realizations of a marked point process. Once a geometrical object is defined, we sample a marked point process defined by a density with a Reversible Jump Markov Chain Monte Carlo dynamics and simulated annealing to get the maximum a posteriori estimator of the tree crown distribution on the image. In a first part, we propose to review the basis of marked point processes and some of their examples used in forestry statistic inference. Then, we present two new models, with discs and ellipses, and discuss some improvements made in the optimization or in the simulation. Results are shown on high resolution aerial images of poplars provided by the French Forest Inventory (IFN), and synthetic images simulated with AMAP software (Bionatics, Digiplante project).

4 - Extraction de Houppiers par Processus Objet. G. Perrin and X. Descombes and J. Zerubia. Research Report 5037, INRIA, France, December 2003. Keywords : Object extraction, Tree Crown Extraction, Stochastic geometry, Marked point process, RJMCMC. @TECHREPORT{Perrin03, author = {Perrin, G. and Descombes, X. and Zerubia, J.}, title = {Extraction de Houppiers par Processus Objet}, year = {2003}, month = {December}, institution = {INRIA}, type = {Research Report}, number = {5037}, address = {France}, url = {https://hal.inria.fr/inria-00071547}, pdf = {https://hal.inria.fr/file/index/docid/71547/filename/RR-5037.pdf}, ps = {https://hal.inria.fr/docs/00/07/15/47/PS/RR-5037.ps}, keyword = {Object extraction, Tree Crown Extraction, Stochastic geometry, Marked point process, RJMCMC} } Résumé : Nous cherchons à extraire des houppiers à partir d'images de télédétection. Pour ce faire, nous construisons un processus objet et assimilons nos images d'arbres à des réalisations de ce processus. La première étape consiste à définir d'une part les objets géométriques modélisant les arbres, et d'autre part la densité du processus à simuler.La seconde étape consiste à construire un algorithme MCMC à sauts réversibles, et une estimée de la configuration d'objets. Les transitions aléatoires de la chaîne sont régies par des noyaux de propositions, chacun étant associé à une perturbation.Nous testons notre modèle sur des images aériennes de peupleraies fournies par l'IFN. Abstract : In this paper we aim at extracting tree crowns from remotely sensed images. Our approach is to consider that these images are some realizations of a marked point process. The first step is to define the geometrical objects that design the trees, and the density of the process.Then, we use a reversible jump MCMC dynamics and a simulated annealing to get the maximum a posteriori estimator of the tree crowns distribution on the image. Transitions of the Markov chain are managed by some specific proposition kernels.Results are shown on aerial images of poplars given by IFN.

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