Entropy reduction and decorrelation in visual coding by oriented neural receptive fields

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Abstract
Image coding is optimally efficient if the coefficients of the representation are nonredundant, in the Shannon sense that their mutual information is zero. In that case, the code coefficients are uncorrelated and they form a statistically independent ensemble, so that the conditional probability of one coefficient's value, given any other coefficient's value, is the same as its unconditional probability: P(x/y) = P(x). In order for each coefficient to capture a unique property of the image that cannot be captured by any other coefficient, the expansion functions employed in the code must be linearly independent. In order for the code coefficients to have zero mutual information, the code primitives must be orthogonal so that their projections onto each other are always zero. In biological visual systems, although it is clear that some forms of efficiency (such as speed) are desirable, it is not obvious whether coding efficiency as measured by mutual information among the neurons is a factor which explains any of their properties. The center/surround receptive field profiles of neurons in the retina and geniculate are far from an orthogonal set, but a given neuron can still be regarded as a decorrelator of the incoming signal in the sense that it responds primarily to changes in the image (changes in space, time, chrominance, etc.) At the level of the brain's visual cortex, the introduction of the new variable of orientation selectivity can be regarded not only as a means for providing orientation labels for image structure, but also more basically as an effective decorrelator of the neural representation.(ABSTRACT TRUNCATED AT 250 WORDS)