Multivariate texture retrieval using the geodesic distance between elliptically distributed random variables

This paper presents a new texture retrieval algorithm based on elliptical distributions for the modeling of wavelet sub- bands. For measuring similarity between two texture images, the geodesic distance (GD) is considered. A closed form for fixed shape parameters and an approximation when assuming the geodesic coordinate functions as straight lines are given. Taken into various elliptical choices, the multivariate Laplace and G⁰ distributions are introduced for modeling respectively the color cue and spatial dependencies of the wavelet coefficients. A multi-model classification approach is then proposed to combine the similarity measures. A comparative study between some multivariate models on the VisTex image database is conducted and reveals that the combination of the multivariate Laplace modeling for the color dependency and the multivariate G⁰ modeling for spatial one achieves higher recognition rates than other approaches.