Publications about Bimodal

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4 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 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.

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.

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