Human visual coding and the third-order statistics of natural scenes
Mitchell Thomson
Many studies have investigated the possibility of a `perceptual match'
between the properties of the human visual system and those of natural
scenes, but these analyses have so far been largely restricted to
second-order statistical measures. Demonstrations of phase
randomization and phase quantization imply that it is the organization
of the Fourier phase spectrum which is the critical determinant of
perceived scene structure. Second-order image-analysis techniques are
effectively phase-blind; to quantify phase relationships one must
compute higher-order statistics of image data. It can be shown that
the triple correlation function determines a bandlimited image of
fixed position uniquely and completely, and third-order image measures
can predict human performance in psychophysical image-discrimination
tasks. The present work extends existing 1-D results to 2-D image
data: a third-order coherence measure was computed for a variety of
natural images before and after Fourier-phase randomization. A
wavelet-based technique was used to assess the effect on this
coherence measure of processing the images through independent
spatial-frequency channels. The results suggest that although a
constant-octave-band representation may encode equal energy in equal
octaves, it does not encode equal (third-order) structure in equal
octaves: the predicted optimal pattern of spatial-frequency tuning
appears instead rather more similar to existing experimental data on
cortical-cell bandwidths.
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