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.