Empirical statistical analysis of phases in Gabor filtered natural images

Valero Laparra

University of Valencia
560 Evans Hall

The talk will show the results of an empirical statistical analysis of images processed by complex Gabor-like filters. The analysis intends to be a compilation of statistical facts, which could be use to better model the human visual system by including phase information. It is widely accepted that a model of the human visual system should contain a first linear stage where the image is processed by Gabor-like filters, and a second step where coefficients are non-linearly combined. A lot of effort has been put in modeling this non-linear combination. Most models employ the absolute value of the coefficients and ignore the sign (or phase) [1-5]. The first contributions in modeling the phase were mainly based on phase congruence [6,7]. In [8] a great contribution was done mainly proposing a multidimensional phase distribution model which we employ in our analysis. Our analysis is motivated from the experience we acquired in the complex ICA context [9]. We started to model simultaneously modulus and phase and we realized that more analysis of the empirical behaviour should be done. Analyzing marginal, conditional and multidimensional empirical distributions we found interesting behaviours. For instance non trivial dependencies between moduli and phases are observed, thus the coefficients show eliptically asymmetric distribution. Also, there is more intrascale than interscale dependency, thus extending the phase congruence point of view. [1] O. Schwartz and E.P. Simoncelli. Natural signal statistics and sensory gain control. Nature neuroscience, (2001) [2] U. Koster and A. Hyvarinen. A two-layer ICA-like model estimated by score matching. Lecture Notes in Computer Science, (2007) [3] J. Eichhorn, F. Sinz, and M. Bethge. Natural Image Coding in V1: How Much Use Is Orientation Selectivity? PLoS Computational Biology, (2009) [4] J. Malo and V. Laparra. Psychophysically Tuned Divisive Normalization factorizes the PDF of Natural Images Neural Computation, (2010) [5] S. Lyu and E.P. Simoncelli. Nonlinear extraction of independent components of natural images using radial gaussianization. Neural Computation, (2009) [6] M.C. Morrone and D.C. Burr. Feature detection in human vision: A phase-dependent energy model. Proceedings of the Royal Society, London B, (1988) [7] P. Kovesi. Phase congruency: A low-level image invariant Psychological Research, (2000) [8] C. Cadieu. Probabilistic Models of Phase Variables for Visual Representation and Neural Dynamics. PhD Thesis (2009) [9] V. Laparra, M. Gutmann, J. Malo, & A. Hyvärinen. Complex-valued independent component analysis of natural images International Conference on Artificial Neural Networks, (2011)