A Finite Mixture of Weibull-Based Statistical Model for Texture Retrieval in the Complex Wavelet Domain

This paper presents a new statistical model for texture retrieval in the complex wavelet domain. For this purpose, a finite mixture of Weibull distributions (MoWbl) is proposed to characterize the statistical distribution of magnitudes of complex wavelet coefficients. Despite the ability of the mixture model on capturing a wide range of distribution shapes, choosing an appropriate number of mixture components is a challenging task. To this end, we adopt an unsupervised learning of the model parameters based on the Figueiredo-Jain algorithm and maximum-likelihood estimates. As found in all retrieval statistical-based frameworks, the presence of a similarity measure is trivial. Generally, the failure of a retrieval mixture based system is closely related to the choice of the similarity measure that relies mainly on approximations of some divergences and distances. To overcome this limitation, we propose a canonical form of Weibull distribution which allows us to develop an analytic expression of Cauchy-Schwarz divergence (CSD) for MoWbl distributions. Experiments, conducted on three popular datasets, show that the proposed model yields better performance in terms of goodness-of-fit, retrieval, and execution time compared to some related statistical models for texture retrieval.