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A novel texture classification method of matching co- occurrence matrices (CMs) on statistical manifold is presented. The manifold framework is stemmed from the assumption that the co-occurred pixel pairs of a texture image under a specific parameter setting is a realization of underlying probability distribution. The dissimilarity between texture images can be evaluated by the divergence between corresponding probabilistic generating models. The model divergence can be approximately quantified by the geodesic distance between the embedded CMs on a geodesically complete statistical manifold with the proposed techniques: the CM embedding and compactification. Texture classification can be then performed by matching the embedded CMs on a compactified statistical manifold. The method can be applied to a compactified product manifold for matching CM sets as multiple parameter settings are considered. The proposed method is straightforward without learning step. Experiments are carried out on two subsets of the Brodatz and the VisTex databases. The results show that our method can get the higher classification accuracy than that of Haralick feature-based method. Moreover, the proposed similarity measure for matching also gains the better classification performance than the sum of squared distance (SSD) and intersection, which are two popular similarity measures usually adopted for co-occurrence histogram (CH) comparison.