Timothy Saint, 12/16/03
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Fun with: ICA, divisive normalization, color in V1, and the 
efficient coding hypothesis.
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Abstract:
In 1997, Bell & Sejnowski pointed out that if you use ICA on a 
collection of natural images, you get a set of filters that look 
qualitatively like the receptive fields of V1 simple cells: localized 
in space, tuned for orientation and spatial frequency, and looking more 
or less like oriented gabors. This work was done with black and white 
images; do the filters still make decent models for V1 simple cells if 
you incorporate color as well? A recent paper on color processing in V1 
(Johnson et al. 2001) allows a comparison. The authors of that paper 
show that color-sensitive neurons in V1 receive doubly-opponent cone 
inputs; furthermore, they show that V1 cells can be grouped into three 
classes: color sensitive, luminance sensitive, and color luminance 
sensitive. It turns out that ICA filters also receive doubly-opponent 
'cone' inputs - but they cannot be classified along the same lines as 
V1 simple cells. However, this problem can be eliminated by adding a 
stage of divisive normalization (a la Simoncelli and Schwarz 2001); 
other aspects of the modeling are also improved by adding divisive 
normalization.