MULTIVARIATE TEXTURE DISCRIMINATION USING A PRINCIPAL GEODESIC CLASSIFIER A.Shabbir 1, 2 and G.Verdoolaege 1, 3 1 Department of Applied Physics, Ghent University, B-9000 Ghent, Belgium 2 Max Planck Institute for Plasma Physics, D-85748 Garching, Germany 3 Laboratory for Plasma Physics – Royal Military Academy (LPP – ERM/KMS), B-1000 Brussels, Belgium ABSTRACT A new texture discrimination method is presented for classification and retrieval of colored textures represented in the wavelet domain. The interband correlation structure is modeled by multivariate probability models which constitute a Riemannian manifold. The presented method considers the shape of the class on the manifold by determining the principal geodesic of each class. The method, which we call principal geodesic classification, then determines the shortest distance from a test texture to the principal geodesic of each class. We use the Rao geodesic distance (GD) for calculating distances on the manifold. We compare the performance of the proposed method with distance-to-centroid and k- nearest neighbor classifiers and of the GD with the Euclidean distance. The principal geodesic classifier coupled with the GD yields better results, indicating the usefulness of effectively and concisely quantifying the variability of the classes in the probabilistic feature space. Index Terms— Texture classification, principal geodesic analysis, geodesic distance 1. INTRODUCTION Several texture discrimination techniques have shown the wavelet representation to be a well suited domain for characterizing textures [1,2,3]. Hence, wavelet decomposition is often conducted for the generation of a set of features (signature) that accurately characterize the texture image. In many discrimination methods, each wavelet subband is modelled by a probability density function (PDF). The distribution parameters are estimated, composing the signature of the texture. The next step entails the use of an appropriate similarity measure for assessing the similarity of two textures based on their respective signatures. The Euclidean distance (ED) and the Kullback-Leibler divergence (KLD) between probability distributions have yielded acceptable performances in various texture retrieval contexts [1,2]. However, the ED is not a natural similarity measure between probability distributions and the KLD is in fact not even a true distance measure. The Rao geodesic distance (GD) derived from the Fisher information has outperformed KLD and Euclidean in many contexts [2,3]. Therefore, in this work, the GD between multivariate probability distributions has been used, as it provides a natural similarity measure between PDFs. Numerous univariate models, such as the generalised Gaussian [1] and Weibull [4], have been proposed for characterizing wavelet subbands. However, these models are inadequate for modelling the correlation between color bands and thus do not completely capture the rich texture information. In this work, we employ the multivariate Laplacian and Gaussian probability distributions for joint modeling of the spectral bands, while assuming independence amongst the wavelet subbands corresponding to the same color. Texture retrieval techniques frequently compute the distance between the unlabelled (query) texture image and the nearest texture in the training set [1,2,5], seldom taking into account the underlying shape and variability of the class. In this paper, we present a new scheme for texture discrimination based on the calculation of the minimum geodesic distance between the unlabelled texture and the principal geodesic (principal direction) for each class. The principal direction, also called the first ‘principal component’, of the class is the direction in which the class members exhibit most variance. For data lying in Euclidean space, principal component analysis (PCA) [6] provides an efficient 3550 978-1-4799-8339-1/15/$31.00 ©2015 IEEE ICIP 2015