Yannick Berthoumieu

Parameter Estimation For Multivariate Generalized Gaussian Distributions

Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution (MGGD) has been receiving much attention in signal and image processing applications. Considering the estimation issue of the MGGD parameters, the main contribution of this paper is to prove that the maximum likelihood estimator (MLE) of the scatter matrix exists and is unique up to a scalar factor, for a given shape parameter β ∈ (0,1). Moreover, an estimation algorithm based on a Newton-Raphson recursion is proposed for computing the MLE of MGGD parameters. Various experiments conducted on synthetic and real data are presented to illustrate the theoretical derivations in terms of number of iterations and number of samples for different values of the shape parameter. The main conclusion of this work is that the parameters of MGGDs can be estimated using the maximum likelihood principle with good performance.

Gaussian Copula Multivariate Modeling for Texture Image Retrieval Using Wavelet Transforms

In the framework of texture image retrieval, a new family of stochastic multivariate modeling is proposed based on Gaussian Copula and wavelet decompositions. We take advantage of the copula paradigm, which makes it possible to separate dependence structure from marginal behavior. We introduce two new multivariate models using, respectively, generalized Gaussian and Weibull densities. These models capture both the subband marginal distributions and the correlation between wavelet coefficients. We derive, as a similarity measure, a closed form expression of the Jeffrey divergence between Gaussian copula-based multivariate models. Experimental results on well-known databases show significant improvements in retrieval rates using the proposed method compared with the best known state-of-the-art approaches.

Multiscale skewed heavy tailed model for texture analysis

This paper deals with texture analysis based on multiscale stochastic modeling. In contrast to common approaches using symmetric marginal probability density functions of subband coefficients, experimental manipulations show that the symmetric shape assumption is violated for several texture classes. From this fact, we propose in this paper to exploit this shape property to improve texture characterization. We present Asymmetric Generalized Gaussian density as a model to represent detail subbands resulting from multiscale decomposition. A fast estimation method is presented and closed-form of Kullback-Leibler divergence is provided in order to validate the model into a retrieval scheme. The experimental results indicate that this model achieves higher recognition rates than the conventional approach of using the Generalized Gaussian model where asymmetry was not considered.

Copulas based multivariate gamma modeling for texture classification

This paper deals with texture modeling for classification or retrieval systems using multivariate statistical features. The proposed features are defined by the hyperparameters of a copula-based multivariate distribution characterizing the coefficients provided by image decomposition in scale and orientation. As it belongs to the multivariate stochastic models, the copulas are useful to describe pairwise non-linear association in the case of multivariate non-Gaussian density. In this paper, we propose the d-variate Gaussian copula associated to univariate Gamma densities for modeling the texture. Experiments were conducted on the VisTex database aiming to compare the recognition rates of the proposed model with the univariate generalized Gaussian model, the univariate Gamma model, and the generalized Gaussian copula-based multivariate model.

Consistent estimation of autoregressive parameters from noisy observations based on two interacting Kalman filters

The estimation of the parameters of an autoregressive process (AR) from noisy observations is still a challenging problem. In this paper, we propose to sequentially estimate both the signal and the parameters, avoiding a non-linear approach such as the extended Kalman filter. The method is based on two conditionally linked Kalman filters running in parallel. Once a new observation is available, the first filter uses the latest estimated AR parameters to estimate the signal, while the second filter uses the estimated signal to update the AR parameters. This approach can be viewed as a recursive instrumental variable-based method and hence has the advantage of providing consistent estimates of the parameters from noisy observations. A comparative study with existing algorithms illustrates the performances of the proposed method when the additive noise is either white or coloured.

Seismic Fault Preserving Diffusion

This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non linear diffusion filtering leading to a better detection of seismic faults. The non linear diffusion approaches are based on the definition of a partial differential equation that allows us to simplify the images without blurring relevant details or discontinuities. Computing the structure tensor which provides information on the local orientation of the geological layers, we propose to drive the diffusion along these layers using a new approach called SFPD (Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor are fixed according to a confidence measure that takes into account the regularity of the local seismic structure. Results on both synthesized and real 3-D blocks show the efficiency of the proposed approach.

Estimating local multiple orientations

This paper focuses on the estimation of local orientation in an image where several orientations exist at the same location and at the same scale. Within this framework, Isotropic and Recursive Oriented Network (IRON), an operator based on an oriented network of parallel lines is introduced. IRON uses only a few parameters. Beyond the choice of a specific line homogeneity feature, the size and the shape of the network can be tuned. These parameters allow us to adapt our operator to the image studied. The implementation we propose for the network is recursive, relying on the rotation of the image instead of the rotation of the operator. IRON can proceed on a small computing support, and thus provides a local estimation of orientations. Herein, we test IRON on both synthetic and real images. Compared to some other orientation estimation methods such as Gabor filters or Steerable filters, our operator detects multiple orientations with both better accuracy and noise robustness, at a competitive computational cost thanks to its recursivity. Moreover, IRON offers better selectivity, particularly at small scale.

Spectral–Spatial Classification of Hyperspectral Images Using ICA and Edge-Preserving Filter via an Ensemble Strategy

To obtain accurate classification results of hyperspectral images, both spectral and spatial information should be fully exploited in the classification process. In this paper, we propose a novel method using independent component analysis (ICA) and edge-preserving filtering (EPF) via an ensemble strategy for the classification of hyperspectral data. First, several subsets are randomly selected from the original feature space. Second, ICA is used to extract spectrally independent components followed by an effective EPF method, to produce spatial features. Two strategies (i.e., parallel and concatenated) are presented to include the spatial features in the analysis. The spectral-spatial features are then classified with a random forest or a rotation forest classifier. Experimental results on two real hyperspectral data sets demonstrate the effectiveness of the proposed methods. A sensitivity analysis of the new classifiers is also performed.

Multivariate texture retrieval using the geodesic distance between elliptically distributed random variables

This paper presents a new texture retrieval algorithm based on elliptical distributions for the modeling of wavelet sub-bands. For measuring similarity between two texture images, the geodesic distance (GD) is considered. A closed form for fixed shape parameters and an approximation when assuming the geodesic coordinate functions as straight lines are given. Taken into various elliptical choices, the multivariate Laplace and G0 distributions are introduced for modeling respectively the color cue and spatial dependencies of the wavelet coefficients. A multi-model classification approach is then proposed to combine the similarity measures. A comparative study between some multivariate models on the VisTex image database is conducted and reveals that the combination of the multivariate Laplace modeling for the color dependency and the multivariate G0 modeling for spatial one achieves higher recognition rates than other approaches.

2-D Wavelet Packet Spectrum for Texture Analysis

This brief derives a 2-D spectrum estimator from some recent results on the statistical properties of wavelet packet coefficients of random processes. It provides an analysis of the bias of this estimator with respect to the wavelet order. This brief also discusses the performance of this wavelet-based estimator, in comparison with the conventional 2-D Fourier-based spectrum estimator on texture analysis and content-based image retrieval. It highlights the effectiveness of the wavelet-based spectrum estimation.