Principal geodesic distance on a multivariate generalized gaussian manifold

Geert Verdoolaege; Aqsa Shabbir

doi:10.1007/978-3-319-25040-3_41

Principal geodesic distance on a multivariate generalized gaussian manifold

Geert Verdoolaege, Aqsa Shabbir

Laboratory for Plasma Physics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We present a new texture discrimination method for textured color images in the wavelet domain. In each wavelet subband, the correlation between the color bands is modeled by a multivariate generalized Gaussian distribution with fixed shape parameter (Gaussian, Laplacian). On the corresponding Riemannian manifold, the shape of texture clusters is characterized by means of principal geodesic analysis, specifically by the principal geodesic along which the cluster exhibits its largest variance. Then, the similarity of a texture to a class is defined in terms of the Rao geodesic distance on the manifold from the texture’s distribution to its projection on the principal geodesic of that class. This similarity measure is used in a classification scheme, referred to as principal geodesic classification (PGC). It is shown to perform significantly better than several other classifiers.

Original language	English
Title of host publication	Geometric Science of Information - 2nd International Conference, GSI 2015, Proceedings
Editors	Frank Nielsen, Frank Nielsen, Frank Nielsen, Frederic Barbaresco, Frederic Barbaresco, Frank Nielsen
Publisher	Springer
Pages	379-386
Number of pages	8
ISBN (Print)	9783319250397, 9783319250397
DOIs	https://doi.org/10.1007/978-3-319-25040-3_41
Publication status	Published - 2015
Event	2nd International Conference on Geometric Science of Information, GSI 2015 - Palaiseau, France Duration: 28 Oct 2015 → 30 Oct 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9389
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	2nd International Conference on Geometric Science of Information, GSI 2015
Country/Territory	France
City	Palaiseau
Period	28/10/15 → 30/10/15

Keywords

Principal geodesic analysis
Rao geodesic distance
Texture classification

Access to Document

10.1007/978-3-319-25040-3_41

Cite this

Verdoolaege, G., & Shabbir, A. (2015). Principal geodesic distance on a multivariate generalized gaussian manifold. In F. Nielsen, F. Nielsen, F. Nielsen, F. Barbaresco, F. Barbaresco, & F. Nielsen (Eds.), Geometric Science of Information - 2nd International Conference, GSI 2015, Proceedings (pp. 379-386). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9389). Springer. https://doi.org/10.1007/978-3-319-25040-3_41

Verdoolaege, Geert ; Shabbir, Aqsa. / Principal geodesic distance on a multivariate generalized gaussian manifold. Geometric Science of Information - 2nd International Conference, GSI 2015, Proceedings. editor / Frank Nielsen ; Frank Nielsen ; Frank Nielsen ; Frederic Barbaresco ; Frederic Barbaresco ; Frank Nielsen. Springer, 2015. pp. 379-386 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Principal geodesic distance on a multivariate generalized gaussian manifold",

abstract = "We present a new texture discrimination method for textured color images in the wavelet domain. In each wavelet subband, the correlation between the color bands is modeled by a multivariate generalized Gaussian distribution with fixed shape parameter (Gaussian, Laplacian). On the corresponding Riemannian manifold, the shape of texture clusters is characterized by means of principal geodesic analysis, specifically by the principal geodesic along which the cluster exhibits its largest variance. Then, the similarity of a texture to a class is defined in terms of the Rao geodesic distance on the manifold from the texture{\textquoteright}s distribution to its projection on the principal geodesic of that class. This similarity measure is used in a classification scheme, referred to as principal geodesic classification (PGC). It is shown to perform significantly better than several other classifiers.",

keywords = "Principal geodesic analysis, Rao geodesic distance, Texture classification",

author = "Geert Verdoolaege and Aqsa Shabbir",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 2nd International Conference on Geometric Science of Information, GSI 2015 ; Conference date: 28-10-2015 Through 30-10-2015",

year = "2015",

doi = "10.1007/978-3-319-25040-3\_41",

language = "English",

isbn = "9783319250397",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

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Verdoolaege, G & Shabbir, A 2015, Principal geodesic distance on a multivariate generalized gaussian manifold. in F Nielsen, F Nielsen, F Nielsen, F Barbaresco, F Barbaresco & F Nielsen (eds), Geometric Science of Information - 2nd International Conference, GSI 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9389, Springer, pp. 379-386, 2nd International Conference on Geometric Science of Information, GSI 2015, Palaiseau, France, 28/10/15. https://doi.org/10.1007/978-3-319-25040-3_41

Principal geodesic distance on a multivariate generalized gaussian manifold. / Verdoolaege, Geert; Shabbir, Aqsa.
Geometric Science of Information - 2nd International Conference, GSI 2015, Proceedings. ed. / Frank Nielsen; Frank Nielsen; Frank Nielsen; Frederic Barbaresco; Frederic Barbaresco; Frank Nielsen. Springer, 2015. p. 379-386 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9389).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We present a new texture discrimination method for textured color images in the wavelet domain. In each wavelet subband, the correlation between the color bands is modeled by a multivariate generalized Gaussian distribution with fixed shape parameter (Gaussian, Laplacian). On the corresponding Riemannian manifold, the shape of texture clusters is characterized by means of principal geodesic analysis, specifically by the principal geodesic along which the cluster exhibits its largest variance. Then, the similarity of a texture to a class is defined in terms of the Rao geodesic distance on the manifold from the texture’s distribution to its projection on the principal geodesic of that class. This similarity measure is used in a classification scheme, referred to as principal geodesic classification (PGC). It is shown to perform significantly better than several other classifiers.

AB - We present a new texture discrimination method for textured color images in the wavelet domain. In each wavelet subband, the correlation between the color bands is modeled by a multivariate generalized Gaussian distribution with fixed shape parameter (Gaussian, Laplacian). On the corresponding Riemannian manifold, the shape of texture clusters is characterized by means of principal geodesic analysis, specifically by the principal geodesic along which the cluster exhibits its largest variance. Then, the similarity of a texture to a class is defined in terms of the Rao geodesic distance on the manifold from the texture’s distribution to its projection on the principal geodesic of that class. This similarity measure is used in a classification scheme, referred to as principal geodesic classification (PGC). It is shown to perform significantly better than several other classifiers.

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Verdoolaege G, Shabbir A. Principal geodesic distance on a multivariate generalized gaussian manifold. In Nielsen F, Nielsen F, Nielsen F, Barbaresco F, Barbaresco F, Nielsen F, editors, Geometric Science of Information - 2nd International Conference, GSI 2015, Proceedings. Springer. 2015. p. 379-386. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-25040-3_41

Principal geodesic distance on a multivariate generalized gaussian manifold

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