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5 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 - 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.

3 - 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.

4 - 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.

5 - 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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