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

Geert Verdoolaege (UGent) and Paul Scheunders
(2011) INTERNATIONAL JOURNAL OF COMPUTER VISION. 95(3). p.265-286
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Abstract
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.
Keywords
RETRIEVAL, DISTANCE, IMAGE, ELLIPTIC DISTRIBUTIONS, TENSOR, PROBABILITY, ESTIMATORS, DENSITY, SURFACE, SPHERE, Geodesic distance, Multivariate generalized Gaussian distribution, Texture discrimination, Multicomponent images

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MLA
Verdoolaege, Geert, and Paul Scheunders. “Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination.” INTERNATIONAL JOURNAL OF COMPUTER VISION, vol. 95, no. 3, 2011, pp. 265–86, doi:10.1007/s11263-011-0448-9.
APA
Verdoolaege, G., & Scheunders, P. (2011). Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination. INTERNATIONAL JOURNAL OF COMPUTER VISION, 95(3), 265–286. https://doi.org/10.1007/s11263-011-0448-9
Chicago author-date
Verdoolaege, Geert, and Paul Scheunders. 2011. “Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination.” INTERNATIONAL JOURNAL OF COMPUTER VISION 95 (3): 265–86. https://doi.org/10.1007/s11263-011-0448-9.
Chicago author-date (all authors)
Verdoolaege, Geert, and Paul Scheunders. 2011. “Geodesics on the Manifold of Multivariate Generalized Gaussian Distributions with an Application to Multicomponent Texture Discrimination.” INTERNATIONAL JOURNAL OF COMPUTER VISION 95 (3): 265–286. doi:10.1007/s11263-011-0448-9.
Vancouver
1.
Verdoolaege G, Scheunders P. Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination. INTERNATIONAL JOURNAL OF COMPUTER VISION. 2011;95(3):265–86.
IEEE
[1]
G. Verdoolaege and P. Scheunders, “Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination,” INTERNATIONAL JOURNAL OF COMPUTER VISION, vol. 95, no. 3, pp. 265–286, 2011.
@article{1934322,
  abstract     = {{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.}},
  author       = {{Verdoolaege, Geert and Scheunders, Paul}},
  issn         = {{0920-5691}},
  journal      = {{INTERNATIONAL JOURNAL OF COMPUTER VISION}},
  keywords     = {{RETRIEVAL,DISTANCE,IMAGE,ELLIPTIC DISTRIBUTIONS,TENSOR,PROBABILITY,ESTIMATORS,DENSITY,SURFACE,SPHERE,Geodesic distance,Multivariate generalized Gaussian distribution,Texture discrimination,Multicomponent images}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{265--286}},
  title        = {{Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination}},
  url          = {{http://doi.org/10.1007/s11263-011-0448-9}},
  volume       = {{95}},
  year         = {{2011}},
}
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