Exploring multivariate generalized gamma manifold for color texture retrieval

•Color textures are represented on the copula-based Multivariate Generalized Gamma distribution manifold.•Give a geometric perspective to the space of Multivariate Generalized Gamma distribution by treating it as a statistical manifold.•Piecewise affine approximation is based on optimization techniques and neural networks to solve the geodesic equations.•Graph-based method to approximate the whole manifold, using the Fast-Marching method.•Geometric thinking leads to the improvement of the way to consider the statistical modeling of images. This work proposes a novel method for color-textured image retrieval on a Multivariate Generalized Gamma Distribution manifold (MGΓD). Thanks to the Gaussian copula theory, we define the expression of MGΓD, which efficiently models the statistical dependence structure between dual-tree complex wavelet transform (DTCWT) of the color components. The major contribution of this paper is to provide a geometric perspective to the MGΓD by treating it as a Riemannian manifold while proposing the geodesic distance (GD) as a measure of Riemannian similarity on it. Based on information geometry tools, we conduct a geometrical study of the MGΓD manifold, allowing us to derive two suitable approximations of the GD. The experiments are performed on five well-known color texture databases, considering the content-based image retrieval (CBIR) framework and using the RGB color space. The obtained results demonstrate the efficiency of the geometric interpretation through the proposed GD as a natural and intuitive similarity measure on the studied statistical manifold.