paper announcement: Local correlations, information redundancy, and the sufficient pixel depth in natural images

[Yury Petrov]

I would like to post the following article here. This paper will be
published in the Journal of Optical Society of America A in January.
The manuscript is available from

http://www.physiol.ox.ac.uk/~yp/DOCS/InfRedNatSc.pdf

and

http://www.physiol.ox.ac.uk/~yp/DOCS/InfRedNatSc.ps

Thank you,
Yury Petrov

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Local correlations, information redundancy, and the sufficient pixel
depth in natural images

Yury Petrov
University Laboratory of Physiology, Oxford University, Oxford, OX1 3PT, UK

L. Zhaoping
Department of Psychology, UCL, London, WC1H 0AP, UK


A mathematical framework which enables the factorisation of a joint
probability distribution into its localised components for a two-dimensional
array of pixels is presented. The factorisation was used to estimate the
contribution to mutual information due to two- (I2) and three-pixel (I3)
luminance correlations for a large ensemble of natural images analysed at
various spatial scales and pixel depths b. It is shown that both I2 and I3
saturate around b = 6 bits/pixel. Three-pixel correlations are shown to
produce only a marginal increase of information redundancy (4%) over two-
pixel correlations (50%). Implications for neural representation in visual
cortex are discussed.