Lionel Bombrun

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.

Wavelet-Based Texture Features for the Classification of Age Classes in a Maritime Pine Forest

This letter evaluates the potential of wavelet-based texture modeling for the classification of stand age in a managed maritime pine forest using very high resolution panchromatic and multispectral PLEIADES data. A cross-validation approach based on stand age reference data is used to compare classification performances obtained from different multivariate models (multivariate Gaussian, spherically invariant random vector (SIRV)-based models, and Gaussian copulas) and from co-occurrence matrices. Results show that the multivariate modeling of the spatial dependence of wavelet coefficients (particularly when using the Gaussian SIRV model) outperforms the use of features derived from co-occurrence matrices. Simultaneously adding features representing the color dependence and leveling the dominant orientation in anisotropic forest stands enhances the classification performances. These results confirm the ability of such wavelet-based multivariate models to efficiently capture the textural properties of very high resolution forest data and open up perspectives for their use in the mapping of monospecific forest structure variables.

Multivariate texture retrieval using the SIRV representation and the geodesic distance

This paper presents a new wavelet based retrieval approach based on Spherically Invariant Random Vector (SIRV) modeling of wavelet subbands. Under this multivariate model, wavelet coefficients are considered as a realization of a random vector which is a product of the square root of a scalar random variable (called multiplier) with an independent Gaussian vector. We propose to work on the joint distribution of the scalar multiplier and the multivariate Gaussian process. For measuring similarity between two texture images, the geodesic distance is provided for various multiplier priors. A comparative study between the proposed method and conventional models on the VisTex image database is conducted and indicates that SIRV modeling combined with geodesic distance achieves higher recognition rates than classical approaches.

Supervised Classification of Very High Resolution Optical Images Using Wavelet-Based Textural Features

In this paper, we explore the potentialities of using wavelet-based multivariate models for the classification of very high resolution optical images. A strategy is proposed to apply these models in a supervised classification framework. This strategy includes a content-based image retrieval analysis applied on a texture database prior to the classification in order to identify which multivariate model performs the best in the context of application. Once identified, the best models are further applied in a supervised classification procedure by extracting texture features from a learning database and from regions obtained by a presegmentation of the image to classify. The classification is then operated according to the decision rules of the chosen classifier. The use of the proposed strategy is illustrated in two real case applications using Pléiades panchromatic images: the detection of vineyards and the detection of cultivated oyster fields. In both cases, at least one of the tested multivariate models displays higher classification accuracies than gray-level cooccurrence matrix descriptors. Its high adaptability and the low number of parameters to be set are other advantages of the proposed approach.

Performance of the maximum likelihood estimators for the parameters of multivariate generalized Gaussian distributions

This paper studies the performance of the maximum likelihood estimators (MLE) for the parameters of multivariate generalized Gaussian distributions. When the shape parameter belongs to ]0, 1[, we have proved that the scatter matrix MLE exists and is unique up to a scalar factor. After providing some elements about this proof, an estimation algorithm based on a Newton-Raphson recursion is investigated. Some experiments illustrate the convergence speed of this algorithm. The bias and consistency of the scatter matrix estimator are then studied for different values of the shape parameter. The performance of the shape parameter estimator is finally addressed by comparing its variance to the Cramér-Rao bound.

Gaussian Distributions on Riemannian Symmetric Spaces: Statistical Learning With Structured Covariance Matrices

The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing challenge is to develop Riemannian-geometric tools which are adapted to structured covariance matrices. This paper proposes to meet this challenge by introducing a new class of probability distributions, Gaussian distributions of structured covariance matrices. These are Riemannian analogs of Gaussian distributions, which only sample from covariance matrices having a preassigned structure, such as complex, Toeplitz, or block-Toeplitz. The usefulness of these distributions stems from three features: 1) they are completely tractable, analytically, or numerically, when dealing with large covariance matrices; 2) they provide a statistical foundation to the concept of structured Riemannian barycentre (i.e., Fréchet or geometric mean); and 3) they lead to efficient statistical learning algorithms, which realise, among others, density estimation and classification of structured covariance matrices. This paper starts from the observation that several spaces of structured covariance matrices, considered from a geometric point of view, are Riemannian symmetric spaces. Accordingly, it develops an original theory of Gaussian distributions on Riemannian symmetric spaces, of their statistical inference, and of their relationship to the concept of Riemannian barycentre. Then, it uses this original theory to give a detailed description of Gaussian distributions of three kinds of structured covariance matrices, complex, Toeplitz, and block-Toeplitz. Finally, it describes algorithms for density estimation and classification of structured covariance matrices, based on Gaussian distribution mixture models.

Texture Classification Using Rao’s Distance on the Space of Covariance Matrices

The current paper introduces new prior distributions on the zero-mean multivariate Gaussian model, with the aim of applying them to the classification of covariance matrices populations. These new prior distributions are entirely based on the Riemannian geometry of the multivariate Gaussian model. More precisely, the proposed Riemannian Gaussian distribution has two parameters, the centre of mass \(\bar{Y}\) and the dispersion parameter \(\sigma \). Its density with respect to Riemannian volume is proportional to \(\exp (-d^2(Y; \bar{Y}))\), where \(d^2(Y; \bar{Y})\) is the square of Rao’s Riemannian distance. We derive its maximum likelihood estimators and propose an experiment on the VisTex database for the classification of texture images.

An M-Estimator for Robust Centroid Estimation on the Manifold of Covariance Matrices

This letter introduces a new robust estimation method for the central value of a set of

Texture image classification with Riemannian fisher vectors issued from a Laplacian model

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Texture image classification with Riemannian fisher vectors

covariance matrices. This estimator, called Hubers centroid, is described starting from the expression of two well-known methods that are the center of mass and the median. In addition, a computation algorithm based on the gradient descent is proposed. Moreover, Hubers centroid performances are analyzed on simulated data to identify the impact of outliers on the estimation process. In the end, the algorithm is applied to brain decoding, based on magnetoencephalography data. For both simulated and real data, the covariance matrices are considered as realizations of Riemannian Gaussian distributions and the results are compared to those given by the center of mass and the median.