Color Texture Discrimination using the Principal Geodesic Distance on a Multivariate Generalized Gau

28/10/2015
Publication GSI2015
OAI : oai:www.see.asso.fr:11784:14303
DOI : http://dx.doi.org/10.1007/978-3-319-25040-3_41You do not have permission to access embedded form.

Résumé

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.

Color Texture Discrimination using the Principal Geodesic Distance on a Multivariate Generalized Gau

Média

Voir la vidéo

Métriques

185
4
3.2 Mo
 application/pdf
bitcache://b08b6d00d43dddeb7c9637d88a7a215a56c19dd6

Licence

Creative Commons Attribution-ShareAlike 4.0 International

Sponsors

Organisateurs

logo_see.gif
logocampusparissaclay.png

Sponsors

entropy1-01.png
springer-logo.png
lncs_logo.png
Séminaire Léon Brillouin Logo
logothales.jpg
smai.png
logo_cnrs_2.jpg
gdr-isis.png
logo_gdr-mia.png
logo_x.jpeg
logo-lix.png
logorioniledefrance.jpg
isc-pif_logo.png
logo_telecom_paristech.png
csdcunitwinlogo.jpg
<resource  xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
                xmlns="http://datacite.org/schema/kernel-4"
                xsi:schemaLocation="http://datacite.org/schema/kernel-4 http://schema.datacite.org/meta/kernel-4/metadata.xsd">
        <identifier identifierType="DOI">10.23723/11784/14303</identifier><creators><creator><creatorName>Geert Verdoolaege</creatorName></creator><creator><creatorName>Aqsa Shabbir</creatorName></creator></creators><titles>
            <title>Color Texture Discrimination using the Principal Geodesic Distance on a Multivariate Generalized Gau</title></titles>
        <publisher>SEE</publisher>
        <publicationYear>2015</publicationYear>
        <resourceType resourceTypeGeneral="Text">Text</resourceType><subjects><subject>Texture classification</subject><subject>Rao geodesic distance</subject><subject>Principal geodesic analysis</subject></subjects><dates>
	    <date dateType="Created">Sun 8 Nov 2015</date>
	    <date dateType="Updated">Wed 31 Aug 2016</date>
            <date dateType="Submitted">Sat 17 Feb 2018</date>
	</dates>
        <alternateIdentifiers>
	    <alternateIdentifier alternateIdentifierType="bitstream">b08b6d00d43dddeb7c9637d88a7a215a56c19dd6</alternateIdentifier>
	</alternateIdentifiers>
        <formats>
	    <format>application/pdf</format>
	</formats>
	<version>24694</version>
        <descriptions>
            <description descriptionType="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.

</description>
        </descriptions>
    </resource>
.

FACULTY OF ENGINEERING AND ARCHITECTURE Color Texture Discrimination using the Principal Geodesic Distance on a Multivariate Generalized Gaussian Manifold Geert Verdoolaege1,2 and Aqsa Shabbir1,3 1Department of Applied Physics, Ghent University, Ghent, Belgium 2Laboratory for Plasma Physics, Royal Military Academy (LPP–ERM/KMS), Brussels, Belgium 3Max-Planck-Institut für Plasmaphysik, D-85748 Garching, Germany Geometric Science of Information Paris, October 28–30, 2015 Overview 1 Color texture 2 Geometry of wavelet distributions 3 Principal geodesic classification 4 Classification experiments 5 Conclusions 2 Overview 1 Color texture 2 Geometry of wavelet distributions 3 Principal geodesic classification 4 Classification experiments 5 Conclusions 3 VisTex database 128 × 128 subimages extracted from RGB images from 40 classes (textures) 4 CUReT database 200 × 200 RGB images from 61 classes with varying illumination and viewpoint 5 Texture modeling Structure at various scales Stochasticity Correlations between colors, neighboring pixels, etc. ⇒ Multivariate wavelet distributions 6 Overview 1 Color texture 2 Geometry of wavelet distributions 3 Principal geodesic classification 4 Classification experiments 5 Conclusions 7 Generalized Gaussian distributions Univariate: generalized Gaussian distribution (zero mean): p(x|α, β) = β 2αΓ(1/β) exp − |x| α β m-variate multivariate generalized Gaussian (MGGD, zero-mean): p(x|Σ, β) = Γ m 2 π m 2 Γ m 2β 2 m 2β β |Σ| 1 2 exp − 1 2 x Σ−1 x β Shape parameter β = 1: Gaussian; β = 1/2: Laplace (heavy tails) 8 MGGD geometry: coordinate system (Σ1, β1) → (Σ2, β2): find K such that K Σ1K = Im, K Σ2K ≡ Φ2 ≡ diag(λ1 2, . . . , λp 2), λi 2 eigenvalues of Σ−1 1 Σ2 In fact, ∀ Σ(t), t ∈ [0, 1]: K Σ(t)K ≡ Φ(t) ≡ diag(λ1 2, . . . , λp 2), λi 2 eigenvalues of Σ−1 1 Σ(t) ri(t) ≡ ln[λi(t)] M. Berkane et al., J. Multivar. Anal., 63, 35–46, 1997 G. Verdoolaege and P. Scheunders, J. Math. Imaging Vis., 43, 180–193, 2012 9 MGGD geometry: Fisher information metric gββ(β) = 1 β2 1 + m 2β 2 Ψ1 m 2β + m β ln(2) + Ψ m 2β + m 2β [ln(2)]2 + Ψ 1 + m 2β ln(4) + Ψ 1 + m 2β + Ψ1 1 + m 2β gβi(β) = − 1 2β 1 + ln(2) + Ψ 1 + m 2β gii(β) = 3bh − 1 4 bh ≡ 1 4 m + 2β m + 2 gij(β) = bh − 1 4 , i = j 10 MGGD geometry: geodesics and exponential map Geodesic equations for fixed β: ri (t) ≡ ln(λi 2) t Geodesic distance: GD(Σ1, Σ2) =   3bh − 1 4 i (ri 2)2 + 2 bh − 1 4 i