Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination

We consider the Rao geodesic distance (GD) based on the Fisher information as a similarity measure on the manifold of zero-mean multivariate generalized Gaussian distributions (MGGD). The MGGD is shown to be an adequate model for the heavy-tailed wavelet statistics in multicomponent images, such as color or multispectral images. We discuss the estimation of MGGD parameters using various methods. We apply the GD between MGGDs to color texture discrimination in several classification experiments, taking into account the correlation structure between the spectral bands in the wavelet domain. We compare the performance, both in terms of texture discrimination capability and computational load, of the GD and the Kullback-Leibler divergence (KLD). Likewise, both uni- and multivariate generalized Gaussian models are evaluated, characterized by a fixed or a variable shape parameter. The modeling of the interband correlation significantly improves classification efficiency, while the GD is shown to consistently outperform the KLD as a similarity measure

Multivariate texture discrimination based on geodesics to class centroids on a generalized Gaussian Manifold

A texture discrimination scheme is proposed wherein probability distributions are deployed on a probabilistic manifold for modeling the wavelet statistics of images. We consider the Rao geodesic distance (GD) to the class centroid for texture discrimination in various classification experiments. We compare the performance of GD to class centroid with the Euclidean distance in a similar context, both in terms of accuracy and computational complexity. Also, we compare our proposed classification scheme with the k-nearest neighbor algorithm. Univariate and multivariate Gaussian and Laplace distributions, as well as generalized Gaussian distributions with variable shape parameter are each evaluated as a statistical model for the wavelet coefficients. The GD to the centroid outperforms the Euclidean distance and yields superior discrimination compared to the k-nearest neighbor approach

Соціально-педагогічна діяльність щодо формування психолого-педагогічної культури батьків в умовах ЗНЗ

A procedure is developed to quantify and improve the signal-to-noise ratio (SNR) of Magnetic Resonance images. The image SNR is quanti ed using the correlation function of two independent acquisitions of an image. To test the performance of the quantification, SNR measurement data are fitted to theoretically expected curves. The proposed correlation technique is also used to improve the SNR by estimating the amplitude of the signal spectrum. The technique is applied to a set of MR images and its performance, in terms of gain in SNR, contrast-to-noise ratio (CNR) and resolution loss, is compared to that of classical noise filters. The SNR as well as the CNR is found to be improved signi cantly with minor loss of resolution. Finally, it is shown that the correlation technique can be implemented in a highly efficient way in almost any acquisition procedure of

Decay of the Sinai Well in D dimensions

We study the decay law of the Sinai Well in $D$ dimensions and relate the behavior of the decay law to internal distributions that characterize the dynamics of the system. We show that the long time tail of the decay is algebraic ($1/t$), irrespective of the dimension $D$.Comment: 14 pages, Figures available under request. Revtex. Submitted to Phys. Rev. E.,e-mail: [email protected]

Classifying hyperspectral airborne imagery for vegetation survey along coastlines

This paper studies the potential of airborne hyperspectral imagery for classifying vegetation along the Belgian coastlines. Here, the aim is to build vegetation maps using automatic classification. Besides a general linear multiclass classifier (Linear Discriminant Analysis), several strategies for combining binary classifiers are proposed: one based on a hierarchical decision tree, one based on the Hamming distance between the codewords obtained by binary classifiers and one based on the coupling of posterior probabilities. In addition, a new procedure is proposed for spatial classification smoothing. This procedure takes into account spatial information by letting the decision for classification of a pixel depend on the classification probabilities of neighboring pixels. This is shown to render smoother classification images