Modeling magnitudes of Gabor coefficients: The β-Rayleigh distribution

Generalized Gaussian (GG) densities have been recently proposed to model both real and imaginary parts of Gabor coefficients. However, when matching faces, most systems make use of magnitude information only, due to its smooth behavior with displacements. The first goal of this paper is to propose a novel statistical model for the magnitude of Gabor coefficients, supposed that both real and imaginary parts are GG distributed. The proposed model, namely the ß-Rayleigh distribution, R_ß(¿), is a generalization of the standard Rayleigh, R(¿), density. The Kullback Leibler (KL) divergence is used to measure the fitting accuracy of the model, showing the benefits of R_ß(¿) over standard R(¿). The second goal of the paper tackles the selection of distance measures for Gabor features comparison, a topic that has received little attention in the literature. Inspired by the proposed statistical model, different ¿_ß norms are tested on the XM2VTS database, showing interesting results that confirm that classical distances used in Gabor-based recognition systems do not provide the best performance.