Valero Laparra
University of Valencia
Empirical statistical analysis of phases in Gabor filtered natural images
Thursday 07th of February 2013 at 12:00pm
560 Evans
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)(video)
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