Geodesic Estimation in Elliptical Distributions

Berkane, Maia; Oden, Kevin; Bentler, Peter M.

doi:10.1006/jmva.1997.1690

Cited by 33 publications

(35 citation statements)

References 9 publications

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“…Mitchell (1989) derived the Fisher-Rao metric for general multivariate elliptical distributions, with the multivariate normal distribution as a special case. A closed expression for the associated GD, in the case of elliptical distributions differing only in their dispersion matrix, was obtained by James (1973) and Berkane et al (1997) (see also Calvo and Oller, 2002). We have derived a closed-form expression for the GD between MGGDs in the case of a fixed MGGD shape parameter and have proposed a suitable approximation to the geodesics on the manifold of MGGDs with varying shape parameters 2 .…”

Section: Introductionmentioning

confidence: 99%

Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination

Verdoolaege

Scheunders

2011

Int J Comput Vis

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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 KullbackLeibler 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.

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Section: Introductionmentioning

confidence: 99%

Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination

Verdoolaege

Scheunders

2011

Int J Comput Vis

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“…Consequently, for fixed shape parameters, the GD between G 0 distributions can be computed according to (7). Note that when M tends toward infinity, the G 0 pdf converges toward the Gaussian pdf and the coefficient b h = 1/4 is retrieved [6]. Note also that it does not depend on the scale parameter m.…”

Section: Geodesic Distance For Fixed Shape Parametersmentioning

confidence: 89%

“…For the G 0 distribution, a closed form of the geodesic distance (GD) [6] is established for fixed shape parameters and an approximation of the GD is given for the general case by assuming the geodesic coordinate functions as straight lines. A multi-model approach is then proposed for the classification of texture images.…”

Section: Introductionmentioning

confidence: 99%

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

Bombrun¹,

Berthoumieu²,

Lasmar³

et al. 2011

2011 18th IEEE International Conference on Image Processing

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This paper presents a new texture retrieval algorithm based on elliptical distributions for the modeling of wavelet subbands. 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 G 0 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 G 0 modeling for spatial one achieves higher recognition rates than other approaches.

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“…For this later one, the multivariate Laplace is a special case, and the multivariate G 0 distribution. For both models, a closed form of the geodesic distance (GD) [7] has been established for fixed shape parameters and an approximation of the GD has been given for the general case by assuming the geodesic coordinate functions as straight lines [8] [9]. Unfortunately, most of the time, only approximations of the GD can be derived for non trivial multivariate distributions (MGGD, G 0 , .…”

Section: Introductionmentioning

confidence: 99%

Multivariate texture retrieval using the Kullback-Leibler divergence between bivariate generalized Gamma times an Uniform distribution

Bombrun

Berthoumieu

2012

2012 19th IEEE International Conference on Image Processing

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This paper presents a new multivariate elliptical distribution, namely the multivariate generalized Gamma times an Uniform (MGΓU) distribution. Because it generalizes the multivariate generalized Gaussian distribution (MGGD), the MGΓU distribution is able to fit a wider range of signals. For the bivariate case, we provide a closed-form of the KullbackLeibler divergence (KLD). We propose the MGΓU distribution for modeling chrominance wavelet coefficients and exercise it in a texture retrieval experiment.A comparative study between some multivariate models on the VisTex and Outex image database is conducted and reveals that the use of the MGΓU distribution of chromiance wavelet coefficient allows an indexing gain compared to other classical approaches such as MGGD and Copula based model).

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Geodesic Estimation in Elliptical Distributions

Cited by 33 publications

References 9 publications

Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination

Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination

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

Multivariate texture retrieval using the Kullback-Leibler divergence between bivariate generalized Gamma times an Uniform distribution

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