Publications about Wavelet packet

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• 7 Conference articles
• 3 Technical and Research Reports

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7 Conference articles

1 - Nonlinear models for the statistics of adaptive wavelet packet coefficients of texture. J. Aubray and I. H. Jermyn and J. Zerubia. In Proc. European Signal Processing Conference (EUSIPCO), Florence, Italy, September 2006. Keywords : Texture, Adaptive, Wavelet packet, Nonlinear, Bimodal, Statistics. @INPROCEEDINGS{aubray_eusipco06, author = {Aubray, J. and Jermyn, I. H. and Zerubia, J.}, title = {Nonlinear models for the statistics of adaptive wavelet packet coefficients of texture}, year = {2006}, month = {September}, booktitle = {Proc. European Signal Processing Conference (EUSIPCO)}, address = {Florence, Italy}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_aubray_eusipco06.pdf}, keyword = {Texture, Adaptive, Wavelet packet, Nonlinear, Bimodal, Statistics} } Abstract : Probabilistic adaptive wavelet packet models of texture pro- vide new insight into texture structure and statistics by focus- ing the analysis on significant structure in frequency space. In very adapted subbands, they have revealed new bimodal statistics, corresponding to the structure inherent to a texture, and strong dependencies between such bimodal sub- bands, related to phase coherence in a texture. Existing models can capture the former but not the latter. As a first step to- wards modelling the joint statistics, and in order to simplify earlier approaches, we introduce a new parametric family of models capable of modelling both bimodal and unimodal subbands, and of being generalized to capture the joint statistics. We show how to compute MAP estimates for the adaptive basis and model parameters, and apply the models to Brodatz textures to illustrate their performance.

2 - Texture-adaptive mother wavelet selection for texture analysis. G.C.K. Abhayaratne and I. H. Jermyn and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Genoa, Italy, September 2005. Keywords : Texture, Wavelet packet, Adaptive, Mother. @INPROCEEDINGS{abhayaratne_icip05, author = {Abhayaratne, G.C.K. and Jermyn, I. H. and Zerubia, J.}, title = {Texture-adaptive mother wavelet selection for texture analysis}, year = {2005}, month = {September}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Genoa, Italy}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Abhayaratne05icip.pdf}, keyword = {Texture, Wavelet packet, Adaptive, Mother} } Abstract : Classification results obtained using wavelet-based texture analysis techniques vary with the choice of mother wavelet used in the methodology. We discuss the use of mother wavelet filters as parameters in a probabilistic approach to texture analysis based on adaptive biorthogonal wavelet packet bases. The optimal choice for the mother wavelet filters is estimated from the data, in addition to the other model parameters. The model is applied to the classification of single texture images and mosaics of Brodatz textures, the results showing improvement over the performance of standard wavelets for a given filter length.

3 - Multimodal statistics of adaptive wavelet packet coefficients: experimental evidence and theory. R. Cossu and I. H. Jermyn and J. Zerubia. In Proc. Physics in Signal and Image Processing, Toulouse, France, January 2005. Keywords : Bimodal, Statistics, Wavelet packet, Adaptive, Texture. @INPROCEEDINGS{cossu_psip05, author = {Cossu, R. and Jermyn, I. H. and Zerubia, J.}, title = {Multimodal statistics of adaptive wavelet packet coefficients: experimental evidence and theory}, year = {2005}, month = {January}, booktitle = {Proc. Physics in Signal and Image Processing}, address = {Toulouse, France}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Cossu05psip.pdf}, keyword = {Bimodal, Statistics, Wavelet packet, Adaptive, Texture} } Abstract : In recent work, it was noted that although the subband histograms for standard wavelet coefcients take on a generalized Gaussian form, this is no longer true for wavelet packet bases adapted to a given texture. Instead, three types of subband statistics are observed: Gaussian, generalized Gaussian, and interestingly, in some subbands, bi- or multi-modal histograms. Motivated by this observation, we provide additional experimental conrmation of the existence of multimodal subbands, and provide a theoretical explanation for their occurrence. The results reveal the connection of such subbands with the characteristic structure in a texture, and thus confirm the importance of such subbands for image modelling and applications.

4 - Texture discrimination using multimodal wavelet packet subbands. R. Cossu and I. H. Jermyn and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Singapore, October 2004. Keywords : Bimodal, Adaptive, probabilistic, Wavelet packet, Texture. @INPROCEEDINGS{cossu_icip04, author = {Cossu, R. and Jermyn, I. H. and Zerubia, J.}, title = {Texture discrimination using multimodal wavelet packet subbands}, year = {2004}, month = {October}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Singapore}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Cossu04icip.pdf}, keyword = {Bimodal, Adaptive, probabilistic, Wavelet packet, Texture} } Abstract : The subband histograms of wavelet packet bases adapted to individual texture classes often fail to display the leptokurtotic behaviour shown by the standard wavelet coefcients of `natural' images. While many subband histograms remain leptokurtotic in adaptive bases, some subbands are Gaussian. Most interestingly, however, some subbands show multimodal behaviour, with no mode at zero. In this paper, we provide evidence for the existence of these multimodal subbands and show that they correspond to narrow frequency bands running throughout images of the texture. They are thus closely linked to the texture's structure. As such, they seem likely to possess superior descriptive and discriminative power as compared to unimodal subbands. We demonstrate this using both Brodatz and remote sensing images.

5 - Texture analysis using adaptative biorthogonal wavelet packets. G.C.K. Abhayaratne and I. H. Jermyn and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Singapore, October 2004. Keywords : Adaptive, Wavelet packet, Biorthogonal, Texture, Statistics. @INPROCEEDINGS{Abhayratne_icip04, author = {Abhayaratne, G.C.K. and Jermyn, I. H. and Zerubia, J.}, title = {Texture analysis using adaptative biorthogonal wavelet packets}, year = {2004}, month = {October}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Singapore}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Abhayaratne04icip.pdf}, keyword = {Adaptive, Wavelet packet, Biorthogonal, Texture, Statistics} } Abstract : We discuss the use of adaptive biorthogonal wavelet packet bases in a probabilistic approach to texture analysis, thus combining the advantages of biorthogonal wavelets (FIR, linear phase) with those of a coherent texture model. The computation of the probability uses both the primal and dual coefcients of the adapted biorthogonal wavelet packet basis. The computation of the biorthogonal wavelet packet coefcients is done using a lifting scheme, which is very efficient. The model is applied to the classification of mosaics of Brodatz textures, the results showing improvement over the performance of the corresponding orthogonal wavelets.

6 - Texture analysis using probabilistic models of the unimodal and multimodal statistics of adaptative wavelet packet coefficients. R. Cossu and I. H. Jermyn and J. Zerubia. In Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Montreal, Canada, May 2004. Keywords : Bimodal, Adaptive, Wavelet packet, Texture, Gaussian mixture, Statistics. @INPROCEEDINGS{cossu04a, author = {Cossu, R. and Jermyn, I. H. and Zerubia, J.}, title = {Texture analysis using probabilistic models of the unimodal and multimodal statistics of adaptative wavelet packet coefficients}, year = {2004}, month = {May}, booktitle = {Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, address = {Montreal, Canada}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Cossu04icassp.pdf}, keyword = {Bimodal, Adaptive, Wavelet packet, Texture, Gaussian mixture, Statistics} } Abstract : Although subband histograms of the wavelet coefficients of natural images possess a characteristic leptokurtotic form, this is no longer true for wavelet packet bases adapted to a given texture. Instead, three types of subband statistics are observed: Gaussian, leptokurtotic, and interestingly, in some subbands, multimodal histograms. These subbands are closely linked to the structure of the texture, and guarantee that the most probable image is not flat. Motivated by these observations, we propose a probabilistic model that takes them into account. Adaptive wavelet packet subbands are modelled as Gaussian, generalized Gaussian, or a constrained Gaussian mixture. We use a Bayesian methodology, finding MAP estimates for the adaptive basis, for subband model selection, and for subband model parameters. Results confirm the effectiveness of the proposed approach, and highlight the importance of multimodal subbands for texture discrimination and modelling.

7 - Texture Analysis: An Adaptive Probabilistic Approach. K. Brady and I. H. Jermyn and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Barcelona, Spain, September 2003. Keywords : Adaptive, Wavelet packet, Statistics, Texture. @INPROCEEDINGS{Brady03, author = {Brady, K. and Jermyn, I. H. and Zerubia, J.}, title = {Texture Analysis: An Adaptive Probabilistic Approach}, year = {2003}, month = {September}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Barcelona, Spain}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Brady03icip.pdf}, keyword = {Adaptive, Wavelet packet, Statistics, Texture} } Abstract : Two main issues arise when working in the area of texture segmentation: the need to describe the texture accurately by capturing its underlying structure, and the need to perform analyses on the boundaries of textures. Herein, we tackle these problems within a consistent probabilistic framework. Starting from a probability distribution on the space of infinite images, we generate a distribution on arbitrary finite regions by marginalization. For a Gaussian distribution, the computational requirement of diagonalization and the modelling requirement of adaptivity together lead naturally to adaptive wavelet packet models that capture the ‘significant amplitude features’ in the Fourier domain. Undecimated versions of the wavelet packet transform are used to diagonalize the Gaussian distribution efficiently, albeit approximately. We describe the implementation and application of this approach and present results obtained on several Brodatz texture mosaics.

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3 Technical and Research Reports

1 - Models of the Unimodal and Multimodal Statistics of Adaptive Wavelet Packet Coefficients. R. Cossu and I. H. Jermyn and K. Brady and J. Zerubia. Research Report 5122, INRIA, France, February 2004. Keywords : Wavelet packet, Texture. @TECHREPORT{5122, author = {Cossu, R. and Jermyn, I. H. and Brady, K. and Zerubia, J.}, title = {Models of the Unimodal and Multimodal Statistics of Adaptive Wavelet Packet Coefficients}, year = {2004}, month = {February}, institution = {INRIA}, type = {Research Report}, number = {5122}, address = {France}, url = {https://hal.inria.fr/inria-00071461}, pdf = {https://hal.inria.fr/file/index/docid/71461/filename/RR-5122.pdf}, ps = {https://hal.inria.fr/docs/00/07/14/61/PS/RR-5122.ps}, keyword = {Wavelet packet, Texture} } Résumé : De récents travaux ont montré que bien que les histogrammes de sous-bandes pour les coefficients d'ondelettes standards ont une forme de gaussienne généralisée, ce n'est plus vrai pour les bases de paquets d'ondelettes adaptés à une certaine texture. Trois types de statistiques sont alors observés pour les sous-bandes: gaussienne, gaussienne generalisée et dans certaines sous-bandes des histogrammes multimodaux sans mode en zéro. Dans ce rapport, nous démontrons que ces sous-bandes sont étroitement liées à la structure de la texture et sont ainsi primordiales dans les applications dans lesquelles la texture joue un rôle important. Fort de ces observations, nous étendons l'approche de modélisation de textures proposée par en incluant ces sous-bandes. Nous modifions l'hypothèse gaussienne pour inclure les gaussiennes généralisées et les mixtures de gaussiennes contraintes. Nous utilisons une méthodologie bayésienne, définissant des estimateurs MAP pour la base adaptative, pour la sélection du modèle de la sous-bande et pour les paramètres de ce modèle. Les résultats confirment l'efficacité de la méthode proposée et soulignent l'importance des sous-bandes multimodales pour la discrimination et la modélisation de textures. Abstract : In recent work, it was noted that although the subband histograms for standard wavelet coefficients take on a generalized Gaussian form, this is no longer true for wavelet packet bases adapted to a given texture. Instead, three types of subband statistics are observed: Gaussian, generalized Gaussian, and most interestingly, in some subbands, multimodal histograms with no mode at zero. As will be demonstrated in this report, these latter subbands are closely linked to the structure of the texture, and are thus likely to be important for many applications in which texture plays a role. Motivated by these observations, we extend the approach to texture modelling proposed by to include these subbands. We relax the Gaussian assumption to include generalized Gaussians and constrained Gaussian mixtures. We use a Bayesian methodology, finding MAP estimates for the adaptive basis, for subband model selection, and for subband model parameters. Results confirm the effectiveness of the proposed approach, and highlight the importance of multimodal subbands for texture discrimination and modelling.

2 - A Probabilistic Framework for Adaptive Texture Description. K. Brady and I. H. Jermyn and J. Zerubia. Research Report 4920, INRIA, France, September 2003. Keywords : Segmentation, Texture, Wavelet packet. @TECHREPORT{4920, author = {Brady, K. and Jermyn, I. H. and Zerubia, J.}, title = {A Probabilistic Framework for Adaptive Texture Description}, year = {2003}, month = {September}, institution = {INRIA}, type = {Research Report}, number = {4920}, address = {France}, url = {https://hal.inria.fr/inria-00071659}, pdf = {https://hal.inria.fr/file/index/docid/71659/filename/RR-4920.pdf}, ps = {https://hal.inria.fr/docs/00/07/16/59/PS/RR-4920.ps}, keyword = {Segmentation, Texture, Wavelet packet} } Résumé : Ce rapport présente le développement d'un nouveau cadre probabiliste cohérent pour la description adaptative de texture. En partant d'une distribution de probabilité sur un espace d'images infinies, nous générons une distribution sur des régions finies par marginalisation. Pour une distribution gaussienne, les contraintes de calcul imposées par la diagonalisation nous conduisent naturellement à des modèles utilisant des paquets d'ondelettes adaptatifs. Ces modèles reflètent les principales périodicités présentes dans les textures et permettent également d'avoir des corrélations à longue portée tout en préservant l'indépendance des coefficients des paquets d'ondelettes. Nous avons appliqué notre méthode à la segmentation. Deux types de données figurent dans notre ensemble de test: des mosaïques synthétiques de Brodatz et des images satellitaires haute résolution. Dans le cas des textures synthétiques, nous utilisons la version non-décimée de la transformée en paquets d'ondelettes afin de diagonaliser la distribution gaussienne de manière efficace, bien qu'approximative. Cela nous permet d'effectuer une classification de la mosaique pixel par pixel. Une étape de régularisation est ensuite effectuée afin d'arriver à un résultat de segmentation final plus lisse. Afin d'obtenir les meilleurs résultats possibles dans le cas de données réelles, la moyenne de la distribution est ensuite introduite dans le modèle. L'approximation faite pour la classification des mosaiques de textures synthetiques a été testée sur des images réelles, mais les résultats obtenus n'étaient pas satisfaisants. C'est pourquoi nous avons introduit, pour ce type de données, une technique de classification heuristique basée sur la transformée en paquets d'ondelettes décimée. Les résultats de segmentation sont ensuite régularisés à l'aide de la même méthode que dans le cas synthétique. Nous présentons les résultats pour chaque type de données et concluons par une discussion. Abstract : This report details the development of a probabilistic framework for adaptive texture description. Starting with a probability distribution on the space of infinite images, we generate a distribution on finite regions by marginalisation. For a Gaussian distribution, the computational requirement of diagonalisation leads naturally to adaptive wavelet packet models which capture the principal periodicities present in the textures and allow long-range correlations while preserving the independence of the wavelet packet coefficients. These models are then applied to the task of segmentation. Two data types are included in our test bed: synthetic Brodatz mosaics and high-resolution satellite images. For the case of the synthetic textures, undecimated versions of the wavelet packet transform are used to diagonalise the Gaussian distribution efficiently, albeit approximately. This enables us to perform a pixelwise classification of the mosaics. A regularisation step is then implemented in order to arrive at a smooth final segmentation. In order to obtain the best possible results for the real dataset, the mean of the distribution is included in the model. The approximation made for the classification of the synthetic texture mosaics is tested on the remote sensing images, but it produces unsatisfactory results. Therefore we introduce a heuristic classification technique for this dataset, based on a decimated wavelet packet transform. The resulting segmentation is then regularised using the same method as in the synthetic case. Results are presented for both types of data and a discussion follows.

3 - Satellite image deconvolution using complex wavelet packets. A. Jalobeanu and L. Blanc-Féraud and J. Zerubia. Research Report 3955, Inria, June 2000. Keywords : Deconvolution, Bayesian estimation, Wavelet packet. @TECHREPORT{jalo00, author = {Jalobeanu, A. and Blanc-Féraud, L. and Zerubia, J.}, title = {Satellite image deconvolution using complex wavelet packets}, year = {2000}, month = {June}, institution = {Inria}, type = {Research Report}, number = {3955}, url = {https://hal.inria.fr/inria-00072694}, pdf = {https://hal.inria.fr/file/index/docid/72694/filename/RR-3955.pdf}, ps = {https://hal.inria.fr/docs/00/07/26/94/PS/RR-3955.ps}, keyword = {Deconvolution, Bayesian estimation, Wavelet packet} } Résumé : La déconvolution des images satellitaires floues et bruitées est un problème inverse mal posé. L'inversion directe entraîne une amplification inacceptable du bruit. Généralement, soit le problème est régularisé lors de l'inversion, soit le bruit est filtré après déconvolution et décomposition dans le domaine de la transformée en ondelettes. Nous avons developpé dans ce rapport la deuxième solution, en seuillant les coefficients d'une nouvelle transformée en paquets d'ondelettes complexes, les fonctions de seuillage étant estimées de manière automatique. L'utilisation de paquets d'ondelettes complexes rend cette méthode invariante par translation, et tient compte des directions, tout en restant d'une complexité O(N). Les résultats obtenus présentent à la fois des textures nettes et un très bon rapport signal/bruit dans les zones homogènes. Par rapport aux algorithmes concurrents, la méthode que nous proposons est plus rapide, invariante par rotation, et tient compte de la directionnalité des détails et des textures de l'image pour mieux les restaurer. Les images déconvoluées de cette manière peuvent être utilisées telles quelles (la restauration peut être intégrée directement dans la chaîne d'acquisition). Mais elles peuvent également constituer le point de départ d'une méthode de régularisation adaptative, permettant d'obtenir des contours plus francs. Abstract : The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. The direct inversion leads to unacceptable noise amplificatio- n. Usually, either the problem is regularized during the inversion process, or the noise is filtered after deconvolution and decomposition in the wavelet transform domain. Herein, we have developed the second solution, by thresholding the coefficients of a new complex wavelet packet transform; the thresholding functions are automatically estimated. The use of complex wavelet packets enables translation invariance, and takes into account the directions, while remaining of complexity O(N). The obtained results exhibit both correctly restored textures and a high SNR in homogeneous areas. Compared to concurrent algorithms, the proposed method is faster, rotation invariant and takes into account the directions of the details and textures of the image to restore them better. The images deconvolved this way can be used as they are (the restoration step proposed here can be directly inserted in the acquisition chain). But they also can provide a starting point of an adaptive regularization method, enabling one to obtain sharper edges.

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