Publications about Tree Crown Extraction

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• 1 Article
• 1 PhD Thesis and Habilitation
• 12 Conference articles
• 5 Technical and Research Reports

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Article

1 - A higher-order active contour model of a ‘gas of circles' and its application to tree crown extraction. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. Pattern Recognition, 42(5): pages 699-709, May 2009. Keywords : Shape, Higher-order, Active contour, Gas of circles, Tree Crown Extraction, Bayesian. @ARTICLE{Horvath09, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {A higher-order active contour model of a ‘gas of circles' and its application to tree crown extraction}, year = {2009}, month = {May}, journal = {Pattern Recognition}, volume = {42}, number = {5}, pages = {699-709}, url = {http://dx.doi.org/10.1016/j.patcog.2008.09.008}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Horvathetal09.pdf}, keyword = {Shape, Higher-order, Active contour, Gas of circles, Tree Crown Extraction, Bayesian} } Abstract : We present a model of a ‘gas of circles’: regions in the image domain composed of a unknown number of circles of approximately the same radius. The model has applications to medical, biological, nanotechnological, and remote sensing imaging. The model is constructed using higher-order active contours (HOACs) in order to include non-trivial prior knowledge about region shape without constraining topology. The main theoretical contribution is an analysis of the local minima of the HOAC energy that allows us to guarantee stable circles, fix one of the model parameters, and constrain the rest. We apply the model to tree crown extraction from aerial images of plantations. Numerical experiments both confirm the theoretical analysis and show the empirical importance of the prior shape information.

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PhD Thesis and Habilitation

1 - Etude du couvert forestier par processus ponctuels marqués. G. Perrin. PhD Thesis, Ecole Centrale Paris, October 2006. Keywords : Tree Crown Extraction, Marked point process, Stochastic geometry, Object extraction, RJMCMC. @PHDTHESIS{perrin_phd06, author = {Perrin, G.}, title = {Etude du couvert forestier par processus ponctuels marqués}, year = {2006}, month = {October}, school = {Ecole Centrale Paris}, url = {http://www-sop.inria.fr/ariana/personnel/Guillaume.Perrin/resume.php}, pdf = {http://www-sop.inria.fr/ariana/personnel/Guillaume.Perrin/DOWNLOADS/these_perrin_2006.pdf}, keyword = {Tree Crown Extraction, Marked point process, Stochastic geometry, Object extraction, RJMCMC} } Résumé : Cette thèse aborde le problème de l'extraction d'arbres à partir d'images aériennes InfraRouge Couleur (IRC) de forêts. Nos modèles reposent sur l'utilisation de processus objets ou processus ponctuels marqués. Il s'agit de variables aléatoires dont les réalisations sont des configurations d'objets géométriques. Une fois l'objet géométrique de référence choisi, nous définissons l'énergie du processus par le biais d'un terme a priori, modélisant les contraintes sur les objets et leurs interactions, ainsi qu'un terme image. Nous échantillonnons le processus objet grâce à un algorithme de type Monte Carlo par Chaînes de Markov à sauts réversibles (RJMCMC), optimisé par un recuit simulé afin d'extraire la meilleure configuration d'objets, qui nous donne l'extraction recherchée. Dans ce manuscrit, nous proposons différents modèles d'extraction de houppiers, qui extraient des informations à l'échelle de l'arbre selon la densité du peuplement. Dans les peuplements denses, nous présentons un processus d'ellipses, et dans les zones de plus faible densité, un processus d'ellipsoïdes. Nous obtenons ainsi le nombre d'arbres, leur localisation, le diamètre de la couronne et leur hauteur pour les zones non denses. Les algorithmes automatiques résultant de cette modélisation sont testés sur des images IRC très haute résolution fournies par l'Inventaire Forestier National (IFN). Abstract : This thesis addresses the problem of tree crown extraction from Colour InfraRed (CIR) aerial images of forests. Our models are based on object processes, otherwise known as marked point processes. These mathematical objects are random variables whose realizations are configurations of geometrical shapes. This approach yields an energy minimization problem, where the energy is composed of a regularization term (prior density), which introduces some constraints on the objects and their interactions, and a data term, which links the objects to the features to be extracted. Once the reference object has been chosen, we sample the process and extract the best configuration of objects with respect to the energy, using a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm embedded in a Simulated Annealing scheme. We propose different models for tree crown extraction depending on the density of the stand. In dense areas, we use an ellipse process, while in sparse vegetation an ellipsoïd process is used. As a result we obtain the number of stems, their position, the diameters of the crowns and the heights of the trees for sparse areas. The resulting algorithms are tested on high resolution CIR aerial images provided by the French National Forest Inventory (IFN).

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12 Conference articles

1 - A `Gas of Circles' Phase Field Model and its Application to Tree Crown Extraction. P. Horvath and I. H. Jermyn. In Proc. European Signal Processing Conference (EUSIPCO), Poznan, Poland, September 2007. Keywords : Phase Field, Tree Crown Extraction. @INPROCEEDINGS{Horvath07d, author = {Horvath, P. and Jermyn, I. H.}, title = {A `Gas of Circles' Phase Field Model and its Application to Tree Crown Extraction}, year = {2007}, month = {September}, booktitle = {Proc. European Signal Processing Conference (EUSIPCO)}, address = {Poznan, Poland}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Horvath07d.pdf}, keyword = {Phase Field, Tree Crown Extraction} } Abstract : The problem of extracting the region in the image domain corresponding to an a priori unknown number of circular objects occurs in several domains. We propose a new model of a `gas of circles', the ensemble of regions in the image domain composed of circles of a given radius. The model uses the phase field reformulation of higher-order active contours (HOACs). Phase fields possess several advantages over contour and level set approaches to region modelling, in particular for HOAC models. The reformulation allows us to benefit from these advantages without losing the strengths of the HOAC framework. Combined with a suitable likelihood energy, and applied to the tree crown extraction problem, the new model shows markedly improved performance, both in quality of results and in computation time, which is two orders of magnitude less than the HOAC level set implementation.

2 - A Multispectral Data Model for Higher-Order Active Contours and its Application to Tree Crown Extraction. P. Horvath. In Proc. Advanced Concepts for Intelligent Vision Systems, Delft, Netherlands, August 2007. Keywords : Higher-order, Tree Crown Extraction, Colour. @INPROCEEDINGS{Horvath07c, author = {Horvath, P.}, title = {A Multispectral Data Model for Higher-Order Active Contours and its Application to Tree Crown Extraction}, year = {2007}, month = {August}, booktitle = {Proc. Advanced Concepts for Intelligent Vision Systems}, address = {Delft, Netherlands}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Horvath07c.pdf}, keyword = {Higher-order, Tree Crown Extraction, Colour} } Abstract : Forestry management makes great use of statistics concerning the individual trees making up a forest, but the acquisition of this information is expensive. Image processing can potentially both reduce this cost and improve the statistics. The key problem is the delineation of tree crowns in aerial images. The automatic solution of this problem requires considerable prior information to be built into the image and region models. Our previous work has focused on including shape information in the region model; in this paper we examine the image model. The aerial images involved have three bands. We study the statistics of these bands, and construct both multispectral and single band image models. We combine these with a higher-order active contour model of a `gas of circles' in order to include prior shape information about the region occupied by the tree crowns in the image domain. We compare the results produced by these models on real aerial images and conclude that multiple bands improves the quality of the segmentation. The model has many other potential applications, e.g. to nano-technology, microbiology, physics, and medical imaging.

3 - A New Phase Field Model of a `Gas of Circles' for Tree Crown Extraction from Aerial Images. P. Horvath and I. H. Jermyn. In Proc. International Conference on Computer Analysis of Images and Patterns (CAIP), Vienna, Austria, August 2007. Keywords : Phase Field, Tree Crown Extraction. @INPROCEEDINGS{Horvath07b, author = {Horvath, P. and Jermyn, I. H.}, title = {A New Phase Field Model of a `Gas of Circles' for Tree Crown Extraction from Aerial Images}, year = {2007}, month = {August}, booktitle = {Proc. International Conference on Computer Analysis of Images and Patterns (CAIP)}, address = {Vienna, Austria}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Horvath07b.pdf}, keyword = {Phase Field, Tree Crown Extraction} } Abstract : We describe a model for tree crown extraction from aerial images, a problem of great practical importance for the forestry industry. The novelty lies in the prior model of the region occupied by tree crowns in the image, which is a phase field version of the higher-order active contour inflection point `gas of circles' model. The model combines the strengths of the inflection point model with those of the phase field framework: it removes the `phantom circles' produced by the original `gas of circles' model, while executing two orders of magnitude faster than the contour-based inflection point model. The model has many other areas of application e.g., to imagery in nanotechnology, biology, and physics.

4 - Circular object segmentation using higher-order active contours. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. In In Proc. Conference of the Hungarian Association for Image Analysis and Pattern Recognition (KEPAF'07), Debrecen, Hungary, January 2007. Note : In Hungarian Keywords : Higher-order, Tree Crown Extraction, Shape. @INPROCEEDINGS{Horvath07a, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {Circular object segmentation using higher-order active contours}, year = {2007}, month = {January}, booktitle = {In Proc. Conference of the Hungarian Association for Image Analysis and Pattern Recognition (KEPAF'07)}, address = {Debrecen, Hungary}, note = {In Hungarian}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Horvath07a.pdf}, keyword = {Higher-order, Tree Crown Extraction, Shape} }

5 - An improved 'gas of circles' higher-order active contour model and its application to tree crown extraction. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. In Proc. Indian Conference on Computer Vision, Graphics, and Image Processing (ICVGIP), Madurai, India, December 2006. Keywords : Tree Crown Extraction, Aerial images, Higher-order, Active contour, Gas of circles, Shape. @INPROCEEDINGS{Horvath06_icvgip, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {An improved 'gas of circles' higher-order active contour model and its application to tree crown extraction}, year = {2006}, month = {December}, booktitle = {Proc. Indian Conference on Computer Vision, Graphics, and Image Processing (ICVGIP)}, address = {Madurai, India}, url = {http://dx.doi.org/10.1007/11949619_14}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_Horvath06_icvgip.pdf}, keyword = {Tree Crown Extraction, Aerial images, Higher-order, Active contour, Gas of circles, Shape} } Abstract : A central task in image processing is to find the region in the image corresponding to an entity. In a number of problems, the region takes the form of a collection of circles, eg tree crowns in remote sensing imagery; cells in biological and medical imagery. In~citeHorvath06b, a model of such regions, the `gas of circles' model, was developed based on higher-order active contours, a recently developed framework for the inclusion of prior knowledge in active contour energies. However, the model suffers from a defect. In~citeHorvath06b, the model parameters were adjusted so that the circles were local energy minima. Gradient descent can become stuck in these minima, producing phantom circles even with no supporting data. We solve this problem by calculating, via a Taylor expansion of the energy, parameter values that make circles into energy inflection points rather than minima. As a bonus, the constraint halves the number of model parameters, and severely constrains one of the two that remain, a major advantage for an energy-based model. We use the model for tree crown extraction from aerial images. Experiments show that despite the lack of parametric freedom, the new model performs better than the old, and much better than a classical active contour.

6 - 2D and 3D Vegetation Resource Parameters Assessment using Marked Point Processes. G. Perrin and X. Descombes and J. Zerubia. In Proc. International Conference on Pattern Recognition (ICPR), Hong-Kong, August 2006. Keywords : Data energy, Object extraction, Tree Crown Extraction, Stochastic geometry, Marked point process. @INPROCEEDINGS{perrin_06_c, author = {Perrin, G. and Descombes, X. and Zerubia, J.}, title = {2D and 3D Vegetation Resource Parameters Assessment using Marked Point Processes}, year = {2006}, month = {August}, booktitle = {Proc. International Conference on Pattern Recognition (ICPR)}, address = {Hong-Kong}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_perrin_06_c.pdf}, keyword = {Data energy, Object extraction, Tree Crown Extraction, Stochastic geometry, Marked point process} } Abstract : High resolution aerial and satellite images of forests have a key role to play in natural resource management. As they enable to study forests at the scale of trees, it is now possible to get a more accurate evaluation of the forest resources, from which can be deduced information of biodiversity and ecological sustainability. In that prospect, automatic algorithms are needed to give a further exploitation of the data and to assist human operators. 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 positions of the trees and marks their geometric features. This approach gives also the number of stems, their position, and their size. It is 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. Results are shown on aerial images provided by the French National Forest Inventory (IFN).

7 - A Higher-Order Active Contour Model for Tree Detection. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. In Proc. International Conference on Pattern Recognition (ICPR), Hong Kong, August 2006. Keywords : Active contour, Gas of circles, Higher-order, Shape, Prior, Tree Crown Extraction. @INPROCEEDINGS{horvath_icpr06, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {A Higher-Order Active Contour Model for Tree Detection}, year = {2006}, month = {August}, booktitle = {Proc. International Conference on Pattern Recognition (ICPR)}, address = {Hong Kong}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_horvath_icpr06.pdf}, keyword = {Active contour, Gas of circles, Higher-order, Shape, Prior, Tree Crown Extraction} } Abstract : We present a model of a ‘gas of circles’, the ensemble of regions in the image domain consisting of an unknown number of circles with approximately fixed radius and short range repulsive interactions, and apply it to the extraction of tree crowns from aerial images. The method uses the re- cently introduced ‘higher order active contours’ (HOACs), which incorporate long-range interactions between contour points, and thereby include prior geometric information without using a template shape. This makes them ideal when looking for multiple instances of an entity in an image. We study an existing HOAC model for networks, and show via a stability calculation that circles stable to perturbations are possible for constrained parameter sets. Combining this prior energy with a data term, we show results on aerial imagery that demonstrate the effectiveness of the method and the need for prior geometric knowledge. The model has many other potential applications.

8 - A comparative study of three methods for identifying individual tree crowns in aerial images covering different types of forests. M. Eriksson and G. Perrin and X. Descombes and J. Zerubia. In Proc. International Society for Photogrammetry and Remote Sensing (ISPRS), Marne La Vallee, France, July 2006. Keywords : Region Growing, Marked point process, Markov Fields, Object extraction, Tree Crown Extraction. @INPROCEEDINGS{eriksson06a, author = {Eriksson, M. and Perrin, G. and Descombes, X. and Zerubia, J.}, title = {A comparative study of three methods for identifying individual tree crowns in aerial images covering different types of forests}, year = {2006}, month = {July}, booktitle = {Proc. International Society for Photogrammetry and Remote Sensing (ISPRS)}, address = {Marne La Vallee, France}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_eriksson06a.pdf}, keyword = {Region Growing, Marked point process, Markov Fields, Object extraction, Tree Crown Extraction} } Abstract : Most of today's silviculture methods has the goal to optimise the outcome of the forest in stem volume when it is cut.‭ ‬It might also be relevant to save parts of the forest,‭ ‬for instance,‭ ‬to protect a habitat.‭ ‬In order to get a good survey of the forest,‭ ‬remote sensed images are often used.‭ ‬These images are most often manually interpreted in combination with field measurements in order to estimate the forest parameters that are of importance in the decision how to optimally maintain the forest.‭ ‬Among these parameters the most common are stem number,‭ ‬stem volume,‭ ‬and tree species.‭ ‬Interpretation of images are often labour and time consuming.‭ ‬Thus,‭ ‬automatically developed methods for interpretation can lower the work load and speed up the interpretation time.‭ The interpretation is often done using images captured from a far distance from the ground in order to capture as large area as possible.‭ ‬However,‭ ‬this lower the accuracy of the estimates since it must be done stand wise.‭ ‬Knowledge of where each individual trees in the forest is located together with its size will increase accuracy.‭ ‬It makes it also possible to plan the cutting in detail.‭ ‬With this knowledge in mind,‭ ‬research about finding automatically methods for finding individual tree crowns in aerial images has been a subject for researchers the last decades.‭ Today's methods are not capable to alone handle all kind of forests.‭ ‬Therefore,‭ ‬comparative studies of different segmentation methods with different types of forests are of importance in order to clarify how much a method is reliable at a certain type of forest.‭ ‬This knowledge can,‭ ‬for instance,‭ ‬be used to build up an expert system which are supposed to be able to find individual tree crowns in any kind of forests.‭ ‬The comparison is done using images covering different types of forests.‭ ‬The types of forests that are included in the study ranges from isolated tree crown where the ground is clearly visible between the crowns to dense forest which is naturally regenerated via planted forest. In this study we compare three existing segmentation methods for extracting individual tree crowns from aerial images.‭ ‬The first two methods are probabilistic methods which minimises some energy function while the third is a region growing algorithm.‭ ‬The first probabilistic method is based on a Markov Random Field modelling.‭ ‬We define a prior Markov model to segment the image into three classes‭ (‬background,‭ ‬vegetation and tree centres‭)‬.‭ ‬The prior model embed a circular shape model of the tree crown with a‭ ‬random radius.‭ ‬The data term allows to well position the tree centres onto the image and to describe the tree shape as fluctuations around the circular template.‭ ‬Besides,‭ ‬some long range interactions models the relations between the trees locations,‭ ‬such as some periodicity in case of plantations.‭ The second probabilistic method consists in modeling the trees in the forestry images as random configurations of ellipses or ellipsoids,‭ ‬whose points are the positions of the stems 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.‭ ‬We estimate the best configuration of an unknown number of objects,‭ ‬from which‭ ‬2D and‭ ‬3D vegetation resource parameters can be extracted.‭ ‬To sample this marked point process,‭ ‬we use Monte Carlo dynamics,‭ ‬while the optimization is performed via a Simulated Annealing algorithm,‭ ‬which results in a fully automatic approach.‭ ‬This approach works well on plantations,‭ ‬where there are high spatial relations between the trees,‭ ‬and on isolated trees where‭ ‬3D parameters can be extracted,‭ ‬but some difficulties remain in dense areas.‭ The third method,‭ ‬the region growing algorithm,‭ ‬relies as all region growing methods on good seed points,‭ ‬i.e.‭ ‬in this case approximate locations of the tree crowns.‭ ‬From the seed points the segments are grown according to a grey level value of the neighbouring pixels.‭ ‬The larger the value is the sooner it is connected to the neighbouring segment.‭ ‬The segments stops to grow when all pixels belongs to a segment.‭ ‬This method,‭ ‬contrary the others,‭ ‬will have as a result,‭ ‬segments that have captured the actual shape of the tree crown if the forest is not too sparse.‭ ‬If the forest is too sparse such that the ground is visible,‭ ‬there are problems of finding the seed points.‭ ‬In the cases when the forest is sparse,‭ ‬there are difficulties to separate the tree crowns from the ground.‭ ‬Even if the seed points would be located only at the tree crowns the result will contain a lot of errors since all pixels most belong to a segment,‭ ‬i.e.‭ ‬even the ground pixels must be connected to a segment in this case.‭

9 - Forest Resource Assessment using Stochastic Geometry. G. Perrin and X. Descombes and J. Zerubia and J.G. Boureau. In Proc. International Precision Forestry Symposium, March 2006. Keywords : Tree Crown Extraction, Object extraction, Stochastic geometry, RJMCMC, Data energy. @INPROCEEDINGS{perrin_06_b, author = {Perrin, G. and Descombes, X. and Zerubia, J. and Boureau, J.G.}, title = {Forest Resource Assessment using Stochastic Geometry}, year = {2006}, month = {March}, booktitle = {Proc. International Precision Forestry Symposium}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/perrin_ipfs06.pdf}, keyword = {Tree Crown Extraction, Object extraction, Stochastic geometry, RJMCMC, Data energy} } Abstract : Aerial and satellite imagery has a key role to play in natural resource management, especially in forestry application. The submetric resolution of the data enables to study forests at the scale of trees, and to get a more accurate assessment of the resources such as the number of stems or the forest cover. To develop automatic tools in order to help the inventories in their work and to bring more knowledge about the stands is also nowadays of important economical and environmental concerns. In this paper, we aim at extracting tree crowns from high resolution aerial Color Infrared images (CIR) of forests using marked point processes. Our approach consists in modelling the trees in the forestry images as random configurations of ellipses, whose points are the positions of the stems 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 this marked point process, we use Monte Carlo dynamics while the optimization is performed via a Simulated Annealing algorithm, which results in a fully automatic approach. We present different models for the data term in order to cope with different kinds of stands : plantations, isolated trees and mixed stands. Results are shown on aerial CIR images provided by the French Forest Inventory (IFN)

10 - 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).

11 - 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.

12 - 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.

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5 Technical and Research Reports

1 - A higher-order active contour model of a `gas of circles' and its application to tree crown extraction. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. Research Report 6026, INRIA, France, November 2006. Keywords : Tree Crown Extraction, Aerial images, Higher-order, Active contour, Gas of circles, Shape. @TECHREPORT{Horvath05, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {A higher-order active contour model of a `gas of circles' and its application to tree crown extraction}, year = {2006}, month = {November}, institution = {INRIA}, type = {Research Report}, number = {6026}, address = {France}, url = {http://hal.inria.fr/inria-00115631}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_Horvath05.pdf}, keyword = {Tree Crown Extraction, Aerial images, Higher-order, Active contour, Gas of circles, Shape} } Abstract : Many image processing problems involve identifying the region in the image domain occupied by a given entity in the scene. Automatic solution of these problems requires models that incorporate significant prior knowledge about the shape of the region. Many methods for including such knowledge run into difficulties when the topology of the region is unknown a priori, for example when the entity is composed of an unknown number of similar objects. Higher-order active contours (HOACs) represent one method for the modelling of non-trivial prior knowledge about shape without necessarily constraining region topology, via the inclusion of non-local interactions between region boundary points in the energy defining the model. The case of an unknown number of circular objects arises in a number of domains, \eg medical, biological, nanotechnological, and remote sensing imagery. Regions composed of an a priori unknown number of circles may be referred to as a `gas of circles'. In this report, we present a HOAC model of a `gas of circles'. In order to guarantee stable circles, we conduct a stability analysis via a functional Taylor expansion of the HOAC energy around a circular shape. This analysis fixes one of the model parameters in terms of the others and constrains the rest. In conjunction with a suitable likelihood energy, we apply the model to the extraction of tree crowns from aerial imagery, and show that the new model outperforms other techniques.

2 - Tree Crown Extraction using a Three States Markov Random Field. X. Descombes and E. Pechersky. Research Report 5982, INRIA, September 2006. Keywords : Markov Fields, Tree Crown Extraction. @TECHREPORT{Descombes-Pechersky, author = {Descombes, X. and Pechersky, E.}, title = {Tree Crown Extraction using a Three States Markov Random Field}, year = {2006}, month = {September}, institution = {INRIA}, type = {Research Report}, number = {5982}, url = {https://hal.inria.fr/inria-00097555}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_Descombes-Pechersky.pdf}, keyword = {Markov Fields, Tree Crown Extraction} }

3 - 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)

4 - 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).

5 - 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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