Identification et simulation d'une classe de processus stables autosimilaires a accroissements stationnaires
Http Www Theses Fr, 2001
Cette these est consacree a l'etude d'une classe de processus symetriques -stables, a val... more Cette these est consacree a l'etude d'une classe de processus symetriques -stables, a valeurs reelles, h-autosimilaires a accroissements stationnaires indexes par r d (ss h-sssi). En particulier, on s'interesse a l'estimation du parametre de hurst h, 0 < h < 1, et de l'indice de stabilite , 0 < < 2. Ce manuscrit se compose de trois parties. La premiere partie porte sur l'identification de deux classes de processus ss, 1 < < 2, a valeurs reelles h-sssi : les processus a moyenne mobile et ceux obtenus comme une transformee de fourier, dits processus harmonisables. Leur parametre de hurst h est estime au moyen de variations d'ordre p des accroissements du processus, pour tout 0 < p <. On donne en outre une estimation theorique des normes l p() du processus suivant une direction sur la sphere unite de r d. La deuxieme partie propose une estimation jointe des parametres h et de ces memes processus au moyen de variations quadratiques. Pour cela, on introduit un principe de localisation qui permet de tronquer les grands sauts d'une mesure aleatoire stable sur un domaine borne. Grace a ce principe, il devient possible d'utiliser des variations quadratiques de coefficients d'ondelettes du processus stable etudie. On donne des estimateurs de l'indice de stabilite d'une mesure aleatoire ss ainsi que de l'ordre d'operateurs pseudo-differentiels associes, d'ou l'on deduit l'estimation du parametre d'autosimilarite h. La troisieme partie porte sur la simulation du processus a moyenne mobile x. Pour un domaine d'etude et une precision fixes, on donne un mode de construction d'un processus simule qui est aussi proche que souhaite du processus x en norme l p. A partir d'une analyse multiresolution de x, ce processus simule est obtenu comme somme finie d'ondelettes adaptees pour laquelle les grands sauts de la mesure de poisson sous-jacente ont ete tronques.
In this paper, we propose a flexible noise model for multi-dimensional map synthesis. This model ... more In this paper, we propose a flexible noise model for multi-dimensional map synthesis. This model allows the generation of a very varied range of maps, that can be used as perturbation functions, for the generation of color textures, or as bump or displacement maps, for geometric deformation of surface or volume objects. We demonstrate that, because the noise construction is random and procedural, the maps we generate can be as big as desired, without tiling effects, and whose aspect can be easily changed by slightly modifying the values of the model’s parameters. Finally, we furnish a model-based software, called TAON (“The Art Of Noise”), for the generation of any desired map, to be used in an image synthesis process.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Copyright
In this paper, a class of Gaussian processes, having locally the same fractal properties as fract... more In this paper, a class of Gaussian processes, having locally the same fractal properties as fractional Brownian motion, is studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. A time dependency of the integrand of the classical Wiener integral, associated with the fractional Brownian motion, is introduced. We show how to identify the asymptotic expansion for high frequencies of these integrands on one sample path. Then, the identiÿcation of the ÿrst terms of this expansion is used to solve some ÿltering problems. Furthermore, rates of convergence of the estimators are then given.
We study the Gaussian random elds indexed by R d whose covariance is de ned in all generality as ... more We study the Gaussian random elds indexed by R d whose covariance is de ned in all generality as the parametrix of an elliptic pseudo-di erential operator with minimal regularity asumption on the symbol. We construct new wavelet bases adapted to these operators the decomposition of the eld on this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the eld in term of the properties of the principal symbol of the pseudodi erential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.
Three different approaches to colour texture analysis are tested on the classification of images ... more Three different approaches to colour texture analysis are tested on the classification of images from the VisTex and Outex databases. All the methods tested are based on extensions of the cooccurrence matrix method. The first method is a multispectral extension since cooccurrence matrices are computed both between and within the colour bands. The second uses joint colour-texture features: colour features are added to grey scale texture features in the entry of the classifier. The last uses grey scale texture features computed on a previously quantized colour image. Results show that the multispectral method gives the best percentages of good classification (VisTex: 97.9%, Outex: 94.9%). The joint colour-texture method is not far from it (VisTex: 96.8%, Outex: 91.0%), but the quantization method is not very good (VisTex:83.6%, Outex:68.4%). Each method is decomposed to try to understand each one deeper, and computation time is estimated to show that multispectral method is fast enoug...
Identiication of Filtered White Noises and of Elliptic Gaussian Random Processes
In this paper , two classes of Gaussian Processes having locally the same fractal properties as F... more In this paper , two classes of Gaussian Processes having locally the same fractal properties as Fractional Brownian Motion are studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. In the rst class (i.e. Filtered White Noises), a time dependency of the integrand of the classical Wiener Integral associated to the Fractional Brownian Motion is introduced. We show how to identify the asymptotic expansion for high frequencies of these integrands on one sample path. Then the identiication of the rst terms of this expansion is used to solve some \\ltering" problems. Furthermore rates of convergence of the estimators are then given. In the second class (i.e. Elliptic Gaussian Random Processes), spatial modulations in the symbol of the pseudo-diierential operator characterizing the reproducing spaces of the processes is introduced. At last identiication results for the symbol of the Elliptic Gaussian Random Processes are deduced from...
Identifying the multifractional function of a Gaussian process
Statistics Probability Letters, Aug 1, 1998
... b, Département de Mathématiques Université de Versailles-St Quentin en Yvelines 45, avenue de... more ... b, Département de Mathématiques Université de Versailles-St Quentin en Yvelines 45, avenue des Etats-Unis, 78035 Versailles, France. c, CERMICS ENPC France. d, Laboratoire de Biométrie INRA, Domaine de Vilvert 78350 Jouy-en-Josas, France. ...
Analyse multi-échelle des champs gaussiens markoviens d’ordre p indexés par [0,1]. (Multiscale analysis of p-order Markov Gaussian fields, indexed by [0,1])
Comptes Rendus De L Academie Des Sciences Series I Mathematics, 1991
Hydrodynamical limit for the asymmetric zero-range process
Annales De L I H P Probabilites Et Statistiques, 1988
On reprend une methode, utilisee precedemment, basee sur les proprietes de l'equation aux der... more On reprend une methode, utilisee precedemment, basee sur les proprietes de l'equation aux derivees partielles limite non lineaire du premier ordre et on montre qu'elle s'applique aux processus de zero-range asymetrique, l'equation limite etant de meme type
Identification et simulation d'une classe de processus stables autosimilaires a accroissements stationnaires
Http Www Theses Fr, 2001
Cette these est consacree a l'etude d'une classe de processus symetriques -stables, a val... more Cette these est consacree a l'etude d'une classe de processus symetriques -stables, a valeurs reelles, h-autosimilaires a accroissements stationnaires indexes par r d (ss h-sssi). En particulier, on s'interesse a l'estimation du parametre de hurst h, 0 < h < 1, et de l'indice de stabilite , 0 < < 2. Ce manuscrit se compose de trois parties. La premiere partie porte sur l'identification de deux classes de processus ss, 1 < < 2, a valeurs reelles h-sssi : les processus a moyenne mobile et ceux obtenus comme une transformee de fourier, dits processus harmonisables. Leur parametre de hurst h est estime au moyen de variations d'ordre p des accroissements du processus, pour tout 0 < p <. On donne en outre une estimation theorique des normes l p() du processus suivant une direction sur la sphere unite de r d. La deuxieme partie propose une estimation jointe des parametres h et de ces memes processus au moyen de variations quadratiques. Pour cela, on introduit un principe de localisation qui permet de tronquer les grands sauts d'une mesure aleatoire stable sur un domaine borne. Grace a ce principe, il devient possible d'utiliser des variations quadratiques de coefficients d'ondelettes du processus stable etudie. On donne des estimateurs de l'indice de stabilite d'une mesure aleatoire ss ainsi que de l'ordre d'operateurs pseudo-differentiels associes, d'ou l'on deduit l'estimation du parametre d'autosimilarite h. La troisieme partie porte sur la simulation du processus a moyenne mobile x. Pour un domaine d'etude et une precision fixes, on donne un mode de construction d'un processus simule qui est aussi proche que souhaite du processus x en norme l p. A partir d'une analyse multiresolution de x, ce processus simule est obtenu comme somme finie d'ondelettes adaptees pour laquelle les grands sauts de la mesure de poisson sous-jacente ont ete tronques.
In this paper, we propose a flexible noise model for multi-dimensional map synthesis. This model ... more In this paper, we propose a flexible noise model for multi-dimensional map synthesis. This model allows the generation of a very varied range of maps, that can be used as perturbation functions, for the generation of color textures, or as bump or displacement maps, for geometric deformation of surface or volume objects. We demonstrate that, because the noise construction is random and procedural, the maps we generate can be as big as desired, without tiling effects, and whose aspect can be easily changed by slightly modifying the values of the model’s parameters. Finally, we furnish a model-based software, called TAON (“The Art Of Noise”), for the generation of any desired map, to be used in an image synthesis process.
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Copyright
In this paper, a class of Gaussian processes, having locally the same fractal properties as fract... more In this paper, a class of Gaussian processes, having locally the same fractal properties as fractional Brownian motion, is studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. A time dependency of the integrand of the classical Wiener integral, associated with the fractional Brownian motion, is introduced. We show how to identify the asymptotic expansion for high frequencies of these integrands on one sample path. Then, the identiÿcation of the ÿrst terms of this expansion is used to solve some ÿltering problems. Furthermore, rates of convergence of the estimators are then given.
We study the Gaussian random elds indexed by R d whose covariance is de ned in all generality as ... more We study the Gaussian random elds indexed by R d whose covariance is de ned in all generality as the parametrix of an elliptic pseudo-di erential operator with minimal regularity asumption on the symbol. We construct new wavelet bases adapted to these operators the decomposition of the eld on this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the eld in term of the properties of the principal symbol of the pseudodi erential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.
Three different approaches to colour texture analysis are tested on the classification of images ... more Three different approaches to colour texture analysis are tested on the classification of images from the VisTex and Outex databases. All the methods tested are based on extensions of the cooccurrence matrix method. The first method is a multispectral extension since cooccurrence matrices are computed both between and within the colour bands. The second uses joint colour-texture features: colour features are added to grey scale texture features in the entry of the classifier. The last uses grey scale texture features computed on a previously quantized colour image. Results show that the multispectral method gives the best percentages of good classification (VisTex: 97.9%, Outex: 94.9%). The joint colour-texture method is not far from it (VisTex: 96.8%, Outex: 91.0%), but the quantization method is not very good (VisTex:83.6%, Outex:68.4%). Each method is decomposed to try to understand each one deeper, and computation time is estimated to show that multispectral method is fast enoug...
Identiication of Filtered White Noises and of Elliptic Gaussian Random Processes
In this paper , two classes of Gaussian Processes having locally the same fractal properties as F... more In this paper , two classes of Gaussian Processes having locally the same fractal properties as Fractional Brownian Motion are studied. Our aim is to give estimators of the relevant parameters of these processes from one sample path. In the rst class (i.e. Filtered White Noises), a time dependency of the integrand of the classical Wiener Integral associated to the Fractional Brownian Motion is introduced. We show how to identify the asymptotic expansion for high frequencies of these integrands on one sample path. Then the identiication of the rst terms of this expansion is used to solve some \\ltering" problems. Furthermore rates of convergence of the estimators are then given. In the second class (i.e. Elliptic Gaussian Random Processes), spatial modulations in the symbol of the pseudo-diierential operator characterizing the reproducing spaces of the processes is introduced. At last identiication results for the symbol of the Elliptic Gaussian Random Processes are deduced from...
Identifying the multifractional function of a Gaussian process
Statistics Probability Letters, Aug 1, 1998
... b, Département de Mathématiques Université de Versailles-St Quentin en Yvelines 45, avenue de... more ... b, Département de Mathématiques Université de Versailles-St Quentin en Yvelines 45, avenue des Etats-Unis, 78035 Versailles, France. c, CERMICS ENPC France. d, Laboratoire de Biométrie INRA, Domaine de Vilvert 78350 Jouy-en-Josas, France. ...
Analyse multi-échelle des champs gaussiens markoviens d’ordre p indexés par [0,1]. (Multiscale analysis of p-order Markov Gaussian fields, indexed by [0,1])
Comptes Rendus De L Academie Des Sciences Series I Mathematics, 1991
Hydrodynamical limit for the asymmetric zero-range process
Annales De L I H P Probabilites Et Statistiques, 1988
On reprend une methode, utilisee precedemment, basee sur les proprietes de l'equation aux der... more On reprend une methode, utilisee precedemment, basee sur les proprietes de l'equation aux derivees partielles limite non lineaire du premier ordre et on montre qu'elle s'applique aux processus de zero-range asymetrique, l'equation limite etant de meme type
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