|
Publications of 2002
Result of the query in the list of publications :
4 Articles |
1 - Marked Point Processes in Image Analysis. X. Descombes and J. Zerubia. IEEE Signal Processing Magazine, 19(5): pages 77-84, September 2002.
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2 - Extension of phase correlation to subpixel registration. H. Foroosh and J. Zerubia and M. Berthod. IEEE Trans. on Image Processing, 11(3): pages 188 - 200, March 2002.
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{March}, |
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{IEEE Trans. on Image Processing}, |
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3 - Local registration and deformation of a road cartographic database on a SPOT Satellite Image. G. Rellier and X. Descombes and J. Zerubia. Pattern Recognition, 35(10), 2002.
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{Local registration and deformation of a road cartographic database on a SPOT Satellite Image}, |
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{Pattern Recognition}, |
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4 - Hyperparameter estimation for satellite image restoration using a MCMC Maximum Likelihood method. A. Jalobeanu and L. Blanc-Féraud and J. Zerubia. Pattern Recognition, 35(2): pages 341--352, 2002.
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2 PhD Thesis and Habilitations |
1 - Segmentation d'images d'observation de la Terre par des techniques de géométrie probabiliste. S. Drot. PhD Thesis, Universite de Nice Sophia Antipolis, December 2002. Note : papier (tu-0758)
@PHDTHESIS{drot,
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{Drot, S.}, |
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{Segmentation d'images d'observation de la Terre par des techniques de géométrie probabiliste}, |
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{2002}, |
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{Universite de Nice Sophia Antipolis}, |
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2 - Analyse de texture dans l'espace hyperspectral par des méthodes probabilistes. G. Rellier. PhD Thesis, Universite de Nice Sophia Antipolis, November 2002. Keywords : Hyperspectral imaging, Texture, Classification, Markov Fields.
@PHDTHESIS{rellier,
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author |
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{Rellier, G.}, |
title |
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{Analyse de texture dans l'espace hyperspectral par des méthodes probabilistes}, |
year |
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{2002}, |
month |
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{November}, |
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{Universite de Nice Sophia Antipolis}, |
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{https://hal.inria.fr/tel-00505898}, |
keyword |
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{Hyperspectral imaging, Texture, Classification, Markov Fields} |
} |
Résumé :
Dans cette thèse, on aborde le problème de l'analyse de texture pour l'étude des zones urbaines. La texture est une notion spatiale désignant ce qui, en dehors de la couleur ou du niveau de gris, caractérise l'homogénéité visuelle d'une zone donnée d'une image. Le but de cette étude est d'établir un modèle qui permette une analyse de texture prenant en compte conjointement l'aspect spatial et l'aspect spectral, à partir d'images hyperspectrales. Ces images sont caractérisées par un nombre de canaux largement supérieur à celui des images multispectrales classiques. On désire tirer parti de l'information spectrale pour améliorer l'analyse spatiale. Les textures sont modélisées par un champ de Markov gaussien vectoriel, qui permet de prendre en compte les relations spatiales entre pixels, mais aussi les relations inter-bandes à l'intérieur d'un même pixel. Ce champ est adapté aux images hyperspectrales par une simplification évitant l'apparition de problèmes d'estimation statistique dans des espaces de grande dimension. Dans le but d'éviter ces problèmes, on effectue également une réduction de dimension des données grâce à un algorithme de poursuite de projection. Cet algorithme permet de déterminer un sous-espace de projection dans lequel une grandeur appelée indice de projection est optimisée. L'indice de projection est défini par rapport à la modélisation de texture proposée, de manière à ce que le sous-espace optimal maximise la distance entre les classes prédéfinies, dans le cadre de la classification. La méthode d'analyse de texture est testée dans le cadre d'une classification supervisée. Pour ce faire, on met au point deux algorithmes que l'on compare avec des algorithmes classiques utilisant ou non l'information de texture. Des tests sont réalisés sur des images hyperspectrales AVIRIS. |
Abstract :
In this work, we investigate the problem of texture analysis of urban areas. Texture is a spatial concept that refers to the visual homogeneity characteristics of an image, not taking into account color or grey level. The aim of this research is to define a model which allows a joint spectral and spatial analysis of texture, and then to apply this model to hyperspectral images. These images many more bands than classical multispectral images. We intend to make use of spectral information and improve simple spatial analysis. Textures are modeled by a vectorial Gauss-Markov random field, which allows us to take into account the spatial interactions between pixels as well as inter-band relationships for a single pixel. This field has been adapted to hyperspectral images by a simplification which avoids statistical estimation problems common to high dimensional spaces. In order to avoid these problems, we also reduce the dimensionality of the data, using a projection pursuit algorithm. This algorithm determines a projection subspace in which an index, called projection index, is optimized. This index is defined in relation to the proposed texture model so that, when a classification is being carried out, the optimal subspace maximizes the distance between predefined training samples. This texture analysis method is tested within a supervised classification framework. For this purpose, we propose two classification algorithms that we compare to two classical algorithms, one which uses texture information and one which does not. Tests are carried out on AVIRIS hyperspectral images. |
|
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12 Conference articles |
1 - Segmentation of Pathological Features in MRI Brain Datasets. F. Kruggel and C. Chalopin and X. Descombes and V. Kovalev and J.C. Rajapakse. In ICONIP, invited paper, Singapore, November 2002.
@INPROCEEDINGS{kruggelXd,
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{Kruggel, F. and Chalopin, C. and Descombes, X. and Kovalev, V. and Rajapakse, J.C.}, |
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{Segmentation of Pathological Features in MRI Brain Datasets}, |
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{2002}, |
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{November}, |
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{ICONIP, invited paper}, |
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{Singapore}, |
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2 - Fusion of Radiometry and Textural Information for SIRC Image Classification. O. Viveros-Cancino and X. Descombes and J. Zerubia and N. Baghdadi. In Proc. IEEE International Conference on Image Processing (ICIP), Rochester, USA, September 2002.
@INPROCEEDINGS{oscarbaghdadi,
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{Viveros-Cancino, O. and Descombes, X. and Zerubia, J. and Baghdadi, N.}, |
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{Fusion of Radiometry and Textural Information for SIRC Image Classification}, |
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{2002}, |
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{September}, |
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{Proc. IEEE International Conference on Image Processing (ICIP)}, |
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{Rochester, USA}, |
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3 - Unsupervised Image Segmentation via Markov Trees and Complex Wavelets. C. Shaffrey and N. Kingsbury and I. H. Jermyn. In Proc. IEEE International Conference on Image Processing (ICIP), Rochester, USA, September 2002. Keywords : Segmentation, Hidden Markov Model, Texture, Colour.
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{Shaffrey, C. and Kingsbury, N. and Jermyn, I. H.}, |
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{Unsupervised Image Segmentation via Markov Trees and Complex Wavelets}, |
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{2002}, |
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{Proc. IEEE International Conference on Image Processing (ICIP)}, |
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{Rochester, USA}, |
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{http://www-sop.inria.fr/members/Ian.Jermyn/publications/Shaffrey02icip.pdf}, |
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{Segmentation, Hidden Markov Model, Texture, Colour} |
} |
Abstract :
The goal in image segmentation is to label pixels in an image based
on the properties of each pixel and its surrounding region. Recently
Content-Based Image Retrieval (CBIR) has emerged as an
application area in which retrieval is attempted by trying to gain
unsupervised access to the image semantics directly rather than
via manual annotation. To this end, we present an unsupervised
segmentation technique in which colour and texture models are
learned from the image prior to segmentation, and whose output
(including the models) may subsequently be used as a content
descriptor in a CBIR system. These models are obtained in a
multiresolution setting in which Hidden Markov Trees (HMT) are
used to model the key statistical properties exhibited by complex
wavelet and scaling function coefficients. The unsupervised Mean
Shift Iteration (MSI) procedure is used to determine a number of
image regions which are then used to train the models for each
segmentation class. |
|
4 - Psychovisual Evaluation of Image Segmentation Algorithms. C. Shaffrey and I. H. Jermyn and N. Kingsbury. In Proc. Advanced Concepts for Intelligent Vision Systems, Ghent, Belgique, September 2002.
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{Psychovisual Evaluation of Image Segmentation Algorithms}, |
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{Proc. Advanced Concepts for Intelligent Vision Systems}, |
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5 - Evaluation Methodologies for Image Retrieval Systems. I. H. Jermyn and C. Shaffrey and N. Kingsbury. In Proc. Advanced Concepts for Intelligent Vision Systems, Ghent, Belgique, September 2002.
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{Proc. Advanced Concepts for Intelligent Vision Systems}, |
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{Ghent, Belgique}, |
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6 - Satellite and aerial image deconvolution using an EM method with complex wavelets. A. Jalobeanu and R. Nowak and J. Zerubia and M. Figueiredo. In Proc. IEEE International Conference on Image Processing (ICIP), Rochester, USA, September 2002.
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{Jalobeanu, A. and Nowak, R. and Zerubia, J. and Figueiredo, M.}, |
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{Satellite and aerial image deconvolution using an EM method with complex wavelets}, |
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{2002}, |
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{September}, |
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{Proc. IEEE International Conference on Image Processing (ICIP)}, |
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7 - Image processing for high resolution satellite and aerial data. J. Zerubia. In Proc. European Signal Processing Conference (EUSIPCO), Toulouse, France, September 2002.
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{Image processing for high resolution satellite and aerial data}, |
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{2002}, |
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{September}, |
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{Proc. European Signal Processing Conference (EUSIPCO)}, |
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{Toulouse, France}, |
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8 - Unsupervised segmentation of textured satellite and aerial images with Bayesian methods. S. Wilson and J. Zerubia. In Proc. European Signal Processing Conference (EUSIPCO), Toulouse, France, September 2002.
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{Unsupervised segmentation of textured satellite and aerial images with Bayesian methods}, |
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{Proc. European Signal Processing Conference (EUSIPCO)}, |
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{Toulouse, France}, |
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9 - A Gauss-Markov Model for Hyperspectral Texture Analysis of Urban Areas. G. Rellier and X. Descombes and J. Zerubia and F. Falzon. In Proc. International Conference on Pattern Recognition (ICPR), Québec, Canada, August 2002.
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{A Gauss-Markov Model for Hyperspectral Texture Analysis of Urban Areas}, |
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{Proc. International Conference on Pattern Recognition (ICPR)}, |
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{Québec, Canada}, |
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{http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1044850}, |
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10 - Object Point Processes for Image Segmentation. S. Drot and X. Descombes and H. Le Men and J. Zerubia. In Proc. International Conference on Pattern Recognition (ICPR), Québec, Canada, August 2002.
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{Proc. International Conference on Pattern Recognition (ICPR)}, |
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11 - A variational approach to one dimensional phase unwrapping. C. Lacombe and P. Kornprobst and G. Aubert and L. Blanc-Féraud. In Proc. International Conference on Pattern Recognition (ICPR), Québec, Canada, August 2002.
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12 - Estimation of blur and noise parameters in remote sensing. A. Jalobeanu and L. Blanc-Féraud and J. Zerubia. In Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Orlando, USA, May 2002.
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{Estimation of blur and noise parameters in remote sensing}, |
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{2002}, |
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{May}, |
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{Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, |
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{Orlando, USA}, |
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{http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5745429}, |
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|
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9 Technical and Research Reports |
1 - Supervised Classification for Textured Images. J.F. Aujol and G. Aubert and L. Blanc-Féraud. Research Report 4640, Inria, France, November 2002. Keywords : Texture, Classification, Wavelets, Partial differential equation, Level sets.
@TECHREPORT{4640,
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{Aujol, J.F. and Aubert, G. and Blanc-Féraud, L.}, |
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{Supervised Classification for Textured Images}, |
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{2002}, |
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{https://hal.inria.fr/docs/00/07/19/45/PS/RR-4640.ps}, |
keyword |
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{Texture, Classification, Wavelets, Partial differential equation, Level sets} |
} |
Résumé :
Dans ce rapport, nous présentons un modèle de classification supervisée basé sur une approche variationnelle. Ce modèle s'applique spécifiquement aux images texturées. Nous souhaitons obtenir une partition optimale de l'image constituée de textures séparées par des interfaces régulières. Pour cela, nous représentons les régions définies par les classes ainsi que leurs interfaces par des fonctions d'ensemble de niveaux. Nous définissons une fonctionnelle sur ces ensembles de niveaux dont le minimum est une partition optimale. Cette fonctionnelle comporte en particulier un terme d'attache aux données spécifique aux textures. Nous utilisons une transformée en paquets d'ondelettes pour analyser les textures, ces dernières étant caractérisées par la distribution de leur énergie dans chaque sous-bande de la décompositon. Les équations aux dérivées partielles (EDP) relatives à la minimisation de la fonctionnelle sont couplées et plongées dans un schéma dynamique. En fixant un ensemble de niveaux initial, les différents termes des EDP guident l'évolution des interfaces (ensemble de niveau zéro) vers les frontières de la partion optimale, par le biais de forces externes (régularité de l'interface) et internes (attache aux données et contraintes partition). Nous avons effectué des tests sur des images synthétiques et sur des images réelles. |
Abstract :
In this report, we present a supervised classification model based on a variational approach. This model is specifically devoted to textured images. We want to get an optimal partition of an image which is composed of textures separated by regular interfaces. To reach this goal, we represent the regions defined by the classes as well as their interfaces by level set functions. We define a functional on these level sets whose minimizers define an optimal partition. In particular, this functional owns a data term specific to textures. We use a packet wavelet transform to analyze the textures, these ones being characterized by their energy distribution in each sub-band of the decomposition. The partial differential equations (PDE) related to the minimization of the functional are embeded in a dynamical scheme. Given an initial interface set (zero level set), the different terms of the PDE's govern the motion of interfaces such that, at convergence, we get an optimal partition as defined above. Each interface is guided by external forces (regularity of the interface), and internal ones (data term and partition constraints). We have conducted several experiments on both synthetic and real images. |
|
2 - On Bayesian Estimation in Manifolds. I. H. Jermyn. Research Report 4607, Inria, France, November 2002. Keywords : Rare event, Bayesian estimation, Invariant.
@TECHREPORT{4607,
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{Jermyn, I. H.}, |
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{On Bayesian Estimation in Manifolds}, |
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{Rare event, Bayesian estimation, Invariant} |
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Résumé :
Il est fréquemment dit que les estimées au sens du maximum a posteriori (MAP) et du minimum de l'erreur quadratique moyenne (MMSE) d'un paramètre continu ne sont pas invariantes relativement aux «reparamètrisations» de l'espace des paramètres . Ce rapport clarifie les questions autour de ce problème, en soulignant la différence entre l'invariance aux changements de coordonnées, qui est une condition sine qua non pour un problème mathématiq- uement bien défini, et l'invariance aux difféomorphismes, qui est une question significative, et fournit une solution. On montre d'abord que la présence d'une structure métrique sur peut être utilisée pour définir les estimées aux sens du MAP et du MMSE qui sont invariantes aux changements de coordonnées, et on explique pourquoi cela est la fa on naturelle et nécessaire pour le faire. Le problème de l'estimation et les quantités géométriques qui y sont associées sont tous définis d'une fa on clairement invariante aux changements de coordonnées. On montre que la même estimée au sens du MAP est obtenue en utilisant soit la `maximisation d'une densité' soit une fonction de perte delta, définie de fa on invariante. Puis, on discute le choix d'une métrique pour . En imposant un critère d'invariance qui est naturel dans le cadre bayesien, on montre que ce choix est unique. Il ne correspond pas nécessairement à un choix de coordonnées. L'estimée au sens du MAP qui en résulte coincide avec l'estimée fondée sur la longueur minimum de message (MML), mais la demonstration n'utilise pas de discrétisation ou d'approximation. |
Abstract :
It is frequently stated that the maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimates of a continuous parameter are not invariant to arbitrary «reparametrizations» of the parameter space . This report clarifies the issues surrounding this problem, by pointing out the difference between coordinate invariance, which is a sine qua non for a mathematically well-defined problem, and diffeomorphism invariance, which is a substantial issue, and provides a solution. We first show that the presence of a metric structure on can be used to define coordinate-invari- ant MAP and MMSE estimates, and we argue that this is the natural and necessary way to proceed. The estimation problem and related geometrical quantities are all defined in a manifestly coordinate-invariant way. We show that the same MAP estimate results from `density maximization' or from using an invariantly-defined delta function loss. We then discuss the choice of a metric structure on . By imposing an invariance criterion natural within a Bayesian framework, we show that this choice is essentially unique. It does not necessarily correspond to a choice of coordinates. The resulting MAP estimate coincides with the minimum message length (MML) estimate, but no discretization or approximation is used in its derivation. |
|
3 - Analyse Intra-urbaine à partir d'Images Satellitaires par une Approche de Fusion de Données sur la Ville de Mexico. O. Viveros-Cancino and X. Descombes and J. Zerubia. Research Report 4578, Inria, France, October 2002. Keywords : Data fusion, Markov Fields, Texture, Urban areas, Confusion matrix.
@TECHREPORT{4578,
|
author |
= |
{Viveros-Cancino, O. and Descombes, X. and Zerubia, J.}, |
title |
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{Analyse Intra-urbaine à partir d'Images Satellitaires par une Approche de Fusion de Données sur la Ville de Mexico}, |
year |
= |
{2002}, |
month |
= |
{October}, |
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{Inria}, |
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url |
= |
{https://hal.inria.fr/inria-00072010}, |
pdf |
= |
{https://hal.inria.fr/file/index/docid/72010/filename/RR-4578.pdf}, |
ps |
= |
{https://hal.inria.fr/docs/00/07/20/10/PS/RR-4578.ps}, |
keyword |
= |
{Data fusion, Markov Fields, Texture, Urban areas, Confusion matrix} |
} |
Résumé :
Ce document présente une analyse intra-urbaine afin d'améliorer la détection des différents tissus urbains avec une application sur la ville de Mexico. La méthode de fission-fusion est proposée ainsi qu'une méthode pour fusionner les classes existantes. Les deux méthodes se composent des étapes suivantes : premièrement, une analyse de texture, nommée étape de fission, est faite pour mieux décrire l'image, ensuite, une classification supervisée, nommée étape de fusion, est faite sur les paramètres issus de l'analyse de texture à partir des valeurs de qualité, notamment la valeur Kappa calculée sur la matrice de confusion. Ces étapes sont réalisées sur des images optiques (SPOT) et radar (ERS) de la ville de Mexico et sont suivies d'un régularisation. |
Abstract :
In this research report we present an intra-urban analysis to improve urban texture extraction. Two methods are proposed : a fission-fusion method and another method which fuses already existing classes. Both methods consist of two steps. The first step, called fission, performs a texture analysis which looks for structures with different parameters. The second step, called fusion, involves a supervised classification using quality parameters, in particular the kappa value which is computed from the confusion matrix. These two steps are carried out on SPOT and radar images of Mexico city. A regularization step is then performed which completes our analysis. |
|
4 - Gamma-Convergence of Discrete Functionals with non Convex Perturbation for Image Classification. G. Aubert and L. Blanc-Féraud and R. March. Research Report 4560, Inria, France, September 2002. Keywords : Generalised Gaussians, Classification, Regularization.
@TECHREPORT{4560,
|
author |
= |
{Aubert, G. and Blanc-Féraud, L. and March, R.}, |
title |
= |
{Gamma-Convergence of Discrete Functionals with non Convex Perturbation for Image Classification}, |
year |
= |
{2002}, |
month |
= |
{September}, |
institution |
= |
{Inria}, |
type |
= |
{Research Report}, |
number |
= |
{4560}, |
address |
= |
{France}, |
url |
= |
{https://hal.inria.fr/inria-00072028}, |
pdf |
= |
{https://hal.inria.fr/file/index/docid/72028/filename/RR-4560.pdf}, |
ps |
= |
{https://hal.inria.fr/docs/00/07/20/28/PS/RR-4560.ps}, |
keyword |
= |
{Generalised Gaussians, Classification, Regularization} |
} |
Résumé :
Ce rapport contient la justification mathématique du modèle variationnel proposé en traitement d'image pour la classification supervisée. A partir des travaux effectués en mécanique des fluides pour les transitions de phase, nous avons développé un modèle de classification par minimisation d'une suite de fonctionnelles. Le résultat est une image de classes formée de régions homogènes séparées par des contours réguliers. Ce modèle diffère de ceux utilisés en mécanique des fluides car la perturbation utilisée n'est pas quadratique mais correspond à une fonction de régularisation d'image préservant les contours. La gamma-convergence de cette nouvelle suite de fonctionnelles est prouvée. |
Abstract :
The purpose of this report is to show the theoretical soundness of a variation- al method proposed in image processing for supervised classification. Based on works developed for phase transitions in fluid mechanics, the classification is obtained by minimizing a sequence of functionals. The method provides an image composed of homogeneous regions with regular boundaries, a region being defined as a set of pixels belonging to the same class. In this paper, we show the gamma-convergence of the sequence of functionals which differ from the ones proposed in fluid mechanics in the sense that the perturbation term is not quadratic but has a finite asymptote at infinity, corresponding to an edge preserving regularization term in image processing. |
|
5 - Mathematical Statement to one Dimensional Phase Unwrapping : a Variational Approach. C. Lacombe and G. Aubert and L. Blanc-Féraud. Research Report 4521, Inria, France, July 2002. Keywords : Sobolev space, Bounded Variation Space, Synthetic Aperture Radar (SAR), Interferometry, Phase unwrapping.
@TECHREPORT{4521,
|
author |
= |
{Lacombe, C. and Aubert, G. and Blanc-Féraud, L.}, |
title |
= |
{Mathematical Statement to one Dimensional Phase Unwrapping : a Variational Approach}, |
year |
= |
{2002}, |
month |
= |
{July}, |
institution |
= |
{Inria}, |
type |
= |
{Research Report}, |
number |
= |
{4521}, |
address |
= |
{France}, |
url |
= |
{https://hal.inria.fr/inria-00072067}, |
pdf |
= |
{https://hal.inria.fr/file/index/docid/72067/filename/RR-4521.pdf}, |
ps |
= |
{https://hal.inria.fr/docs/00/07/20/67/PS/RR-4521.ps}, |
keyword |
= |
{Sobolev space, Bounded Variation Space, Synthetic Aperture Radar (SAR), Interferometry, Phase unwrapping} |
} |
Résumé :
Beaucoup d'alogorithmes de déroulement de phase ont été développés et formulés dans le domaine discret durant ces dix dernières années. Nous proposons ici, une formulation variationnelle pour résoudre le problème. Cette étude dans le domaine continu va nous permettre d'imposer quelques contraintes sur la régularité de la solution et de les implémenter efficacement. Cette méthode est présentée dans le cas unidimensionnel, et servira de base pour nos développement futurs pour le cas réel en 2D. |
Abstract :
Over the past ten years, many phase unwrapping algorithms have been developed and formulated in a discrete setting. Here we propose a variational formulatio- n to solve the problem. This continuous framework will allow us to impose some constraints on the smoothness of the solution and to implement them efficiently. This method is presented in the one dimensional case, and will serve as a basis for future developments in the real 2D case. |
|
6 - Signed Distance Functions and Viscosity Solutions of Discontinuous Hamilton-Jacobi Equations. J.F. Aujol and G. Aubert. Research Report 4507, Inria, France, July 2002. Keywords : Partial differential equation, Signed distance function, Hamilton-Jacobi equation, Skeleton.
@TECHREPORT{4507,
|
author |
= |
{Aujol, J.F. and Aubert, G.}, |
title |
= |
{Signed Distance Functions and Viscosity Solutions of Discontinuous Hamilton-Jacobi Equations}, |
year |
= |
{2002}, |
month |
= |
{July}, |
institution |
= |
{Inria}, |
type |
= |
{Research Report}, |
number |
= |
{4507}, |
address |
= |
{France}, |
url |
= |
{https://hal.inria.fr/inria-00072081}, |
pdf |
= |
{https://hal.inria.fr/file/index/docid/72081/filename/RR-4507.pdf}, |
ps |
= |
{https://hal.inria.fr/docs/00/07/20/81/PS/RR-4507.ps}, |
keyword |
= |
{Partial differential equation, Signed distance function, Hamilton-Jacobi equation, Skeleton} |
} |
Résumé :
Dans ce travail, nous commençons par revoir quelques propriétés de la fonction distance signée. En particulier, nous examinons le squelette d'une courbe de ^2, et nous obtenons une description complète de sa fermeture. Nous donnons aussi une condition suffisante pour que l'adhérence du squelette soit de mesure de Lebesgue nulle. Nous menons alors une étude complète de l'EDP: du/dt +sign(u_0(x))(|Du|-1)=0 , cette dernière étant reliée étroitement à la fonction distance signée. Les articles spécialisés ne fournissent pas de résultats mathématiques pour ce genre d'EDP. En effet, nous sommes confrontés à un Hamiltonien discontinu. Nous nous intéressons ensuite à une classe d'EDP plus générale: du/dt +sign(u_0(x))H(Du)=0 , où H est un opérateur convexe. En se plaçant dans le cadre d'hypothèses techniques raisonnables, nous obtenons le même genre de résultats que précédemment. A notre connaissance, il s'agit de résultats nouveaux pour des opérateurs hamiltoniens discontinus. |
Abstract :
In this paper, we first review some properties of the signed distance function. In particular, we examine the skeleton of a curve in ^2 and get a complete description of its closure. We also give a sufficient condition for the closure of the skeleton to be of zero Lebesgue's measure. We then make a complete study of the PDE: du/dt +sign(u_0(x))(|Du|-1)=0 , which is closely related to the signed distance function. The existing literature provides no mathematical results for such PDEs. Indeed, we face the difficulty of considering a discontinuous Hamiltonian operator with respect to the space variable. We state an existence and uniqueness theorem, giving in particular an explicit Hopf-Lax formula for the solution as well as its asymptotic behaviour. This generalizes classical results for continous Hamitonian. We then get interested in a more general class of PDEs: du/dt +sign(u_0(x))H(D- u)=0, with H convex Under some technical but reasonable assumptions, we obtain the same kind of results. As far as we know, they are new for discontinuous Hamiltonians. |
|
7 - Building Extraction from Digital Elevation Model. M. Ortner and X. Descombes and J. Zerubia. Research Report 4517, Inria, France, July 2002. Keywords : Buildings, Digital Elevation Model (DEM), RJMCMC.
@TECHREPORT{4517,
|
author |
= |
{Ortner, M. and Descombes, X. and Zerubia, J.}, |
title |
= |
{Building Extraction from Digital Elevation Model}, |
year |
= |
{2002}, |
month |
= |
{July}, |
institution |
= |
{Inria}, |
type |
= |
{Research Report}, |
number |
= |
{4517}, |
address |
= |
{France}, |
url |
= |
{https://hal.inria.fr/inria-00072071}, |
pdf |
= |
{https://hal.inria.fr/file/index/docid/72071/filename/RR-4517.pdf}, |
ps |
= |
{https://hal.inria.fr/docs/00/07/20/71/PS/RR-4517.ps}, |
keyword |
= |
{Buildings, Digital Elevation Model (DEM), RJMCMC} |
} |
Résumé :
L'objectif de ce travail est de d'extraire des bâtiments sur des Modèles Numériques d'Elévation (MNE).Pour ce faire, nous introduisons un processus ponctuel dont les points représentent les bâtiments. La densité de ce processus ponctuel se divise en deux parties : la première est un modèle a priori utilisant des interactions entre les points pour introduire la connaissance que l'on a de la structure des bâtiments en zone urbaine, la seconde est un terme d'attache aux données pour assurer la cohérence entre les réalisations du processus ponctuel et le Modèle Numérique d'Elévation. Nous calculons ensuite une estimée de la zone urbaine à partir de cette densité en utilisant une simulation de Monte Carlo par Chaine de Markov et, en particulier, un algorithme de Metropolis Hastings Green, qui est une extension de l'algorithme de simulation de processus ponctuels proposé par Geyer et Møller.Nous proposons des résultats sur des données réelles fournies par l'IGN. |
Abstract :
We aim to extract buildings from Digital Elevation Models. To achieve this goal, we define a point process whose points represent buildings. We then define a density for this point process which is split into two parts. When written as an energy this density consists of two fields : an internal field that allows us to model the prior knowledge we have on patterns of buildings in urban areas, and an external field that makes the point process fit the data, ie. the Digital Elevation Model. Once we have defined this artificial likehood, we use a Metropolis Hastings Green sampler, which is an extension of Geyer and Møller algorithm to sample point processes. This gives an estimate of the observed urban area.We present results on real data provided by the French Mapping Institute (IGN). |
|
8 - A Comparative Study of Point Processes for Line Network Extraction in Remote Sensing. C. Lacoste and X. Descombes and J. Zerubia. Research Report 4516, Inria, France, July 2002. Keywords : Stochastic geometry, Marked point process, Road network, Line networks, RJMCMC.
@TECHREPORT{4516,
|
author |
= |
{Lacoste, C. and Descombes, X. and Zerubia, J.}, |
title |
= |
{A Comparative Study of Point Processes for Line Network Extraction in Remote Sensing}, |
year |
= |
{2002}, |
month |
= |
{July}, |
institution |
= |
{Inria}, |
type |
= |
{Research Report}, |
number |
= |
{4516}, |
address |
= |
{France}, |
url |
= |
{http://hal.inria.fr/inria-00072072}, |
pdf |
= |
{http://hal.inria.fr/docs/00/07/20/72/PDF/RR-4516.pdf}, |
ps |
= |
{http://hal.inria.fr/docs/00/07/20/72/PS/RR-4516.ps}, |
keyword |
= |
{Stochastic geometry, Marked point process, Road network, Line networks, RJMCMC} |
} |
Résumé :
Nous présentons, dans ce rapport, une étude comparative entre plusieurs modèles d'extraction de réseaux linéiques, issus de la géométrie stochastique. Nous nous pla ons dans le cadre des processus ponctuels marqués spécifiés par une densité par rapport au processus de Poisson homogène. L'objectif de cette étude est de déterminer quelle type de densité a priori est la plus adaptée à cette probématique de détection de réseaux linéiques, et plus particulièrement de réseaux routiers. Nous reprenons le Candy modèle, introduit dans [21] pour l'extraction de réseaux routiers, et nous l'utilisons comme modèle de référence. Ce modèle est basé sur l'idée qu'un réseau routier peut être assimilé à une réalisation d'un processus Markov objet, où les objets correspondent à des segments en interaction. Nous proposons deux variantes de ce modèle qui font intervenir des coefficients mesurant la qualité des interactions entre objets. La première est une généralisation du Candy modèle et la seconde correspond à une adaptation du modèle IDQ, proposé dans [13] pour l'extraction de bâtiments dans les modèles numériques d'élévation. Nous réalisons l'optimisation de chaque modèle par un recuit simulé sur un algorithme MCMC à sauts réversibles. Les résultats expérimentaux obtenus pour les trois modèles, sur des images satellitaires ou aériennes, permettent de vérifier l'intérêt de l'intégration de la qualité des interactions dans la densité a priori. |
Abstract :
We present in this report a comparative study between models of line network extraction, within a stochastic geometry framework. We rely on the theory of marked point processes specified by a density with respect to the uniform Poisson process. We aim to determine which prior density is the most relevant for road network detection. The Candy model, introduced in [21] for the extraction of road networks, is used as a reference model. This model is based on the idea that a road network can be thought of as a realization of a Markov object process, where the objects correspond to interacting line segments. We have developed two variants of this model which use quality coefficients for interactions. The first of these two variants is a generalization of the Candy model and the second one is an adaptation of the IDQ model proposed in [13] for the problem of building extraction from digital elevation models. The optimization is achieved by a simulated annealing with a RJMCMC algorithm. The experimental results, obtained for each model on aerial or satellite images, show the interest of adding quality coefficients for interactions in the prior density. |
|
9 - Analyse de Texture Hyperspectrale par Modélisation Markovienne. G. Rellier and X. Descombes and F. Falzon and J. Zerubia. Research Report 4479, INRIA, France, June 2002. Keywords : Classification, Markov Fields, Texture, Hyperspectral imaging.
@TECHREPORT{4479,
|
author |
= |
{Rellier, G. and Descombes, X. and Falzon, F. and Zerubia, J.}, |
title |
= |
{Analyse de Texture Hyperspectrale par Modélisation Markovienne}, |
year |
= |
{2002}, |
month |
= |
{June}, |
institution |
= |
{INRIA}, |
type |
= |
{Research Report}, |
number |
= |
{4479}, |
address |
= |
{France}, |
url |
= |
{https://hal.inria.fr/inria-00072109}, |
pdf |
= |
{https://hal.inria.fr/file/index/docid/72109/filename/RR-4479.pdf}, |
ps |
= |
{https://hal.inria.fr/docs/00/07/21/09/PS/RR-4479.ps}, |
keyword |
= |
{Classification, Markov Fields, Texture, Hyperspectral imaging} |
} |
Résumé :
L'analyse de texture est l'objet de nombreuses recherches dans le domaine de l'imagerie mono et multispectrale. En parallèle, sont apparus ces dernières années de nouveaux instruments spectro-imageurs ayant un grand nombre de canaux (supérieur à 10), fournissant des images appelées hyperspectrales qui sont une représentation du paysage échantillonnée à la fois spatialement et spectralement. Le but de ce travail est de réaliser une analyse de texture qui se déroule conjointement dans ces deux espaces discrets. Pour ce faire, on utilise une modélisation probabiliste vectorielle de la texture via un champ de Markov gaussien. Les paramètres de ce champ permettent la caractérisation de différentes textures présentes dans les images hyperspec- trales. L'application visée dans cette étude étant la classification du tissu urbain, qui est mal caractérisée par la seule radiométrie, on utilise ces paramètres comme de nouvelles bandes afin d'effectuer la classification par le critère du Maximum de Vraisemblance. Les résultats sur des images AVIRIS montrent une nette amélioration de la classification due à l'utilisatio- n de l'information de texture. |
Abstract :
Texture analysis has been widely investigated in monospectral and multispectr- al imagery domain. In the same time, new image sensors with a large number of bands (more than 10) have been designed. They are able to provide images with both fine spectral and spatial sampling, called hyperspectral images. The aim of this work is to perform a joint texture analysis in both discrete spaces. To achieve this goal, we have a probabilistic vectorial texture modeling, with Gauss-Markov Random Field. The MRF parameters allow for the characterisation of different hyperspectral textures. A likely application of this work being the classification of urban areas, which are not well characterized by radiometry alone, we use these parameters as new features is a Maximum Likelihood classification algorithm. The results obtain on AVIRIS hyperspectral images show better classifications when using texture information. |
|
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2 Collection articles or Books chapters |
1 - Markov random fields in image processing, application to remote sensing and astrophysics. J. Zerubia and A. Jalobeanu and Z. Kato. In Journal de Physique, EDP Sciences, Vol. IV (12), 2002. Keywords : Markov Fields, Satellite images, Astrophysics.
@INCOLLECTION{jzjalokato2002,
|
author |
= |
{Zerubia, J. and Jalobeanu, A. and Kato, Z.}, |
title |
= |
{Markov random fields in image processing, application to remote sensing and astrophysics}, |
year |
= |
{2002}, |
booktitle |
= |
{Journal de Physique, EDP Sciences}, |
volume |
= |
{IV}, |
number |
= |
{12}, |
url |
= |
{http://jp4.journaldephysique.org/articles/jp4/abs/2002/01/jp4pr1p117/jp4pr1p117.html}, |
keyword |
= |
{Markov Fields, Satellite images, Astrophysics} |
} |
|
2 - An application of marked point process to the extraction of linear networks for images. R. Stoica and X. Descombes and M.N.M. Van Lieshout and J. Zerubia. In Spatial statitics through applications, Publ. WITPress, 2002. Keywords : Line networks, Road network, Object extraction, Satellite images, Marked point process.
@INCOLLECTION{stoicaXDlivre,
|
author |
= |
{Stoica, R. and Descombes, X. and Van Lieshout, M.N.M. and Zerubia, J.}, |
title |
= |
{An application of marked point process to the extraction of linear networks for images}, |
year |
= |
{2002}, |
booktitle |
= |
{Spatial statitics through applications}, |
publisher |
= |
{WITPress}, |
url |
= |
{http://www.witpress.com/books/978-1-85312-649-9}, |
pdf |
= |
{http://oai.cwi.nl/oai/asset/10645/10645A.pdf}, |
keyword |
= |
{Line networks, Road network, Object extraction, Satellite images, Marked point process} |
} |
|
top of the page
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