Searching for filters with 'interesting' output distributions: an uninteresting direction to explore?

Abstract

It has been independently proposed, by Barlow, Field, Intrator and co-workers, that the receptive fields of neurons in V1 are optimized to generate 'sparse', Kurtotic, or 'interesting' output probability distributions. We investigate the empirical evidence for this further and argue that filters can produce 'interesting' output distributions simply because natural images have variable local intensity variance. If the proposed filters have zero DC, then the probability distribution of filter outputs (and hence the output Kurtosis) is well predicted simply from these effects of variable local variance. This suggests that finding filters with high output Kurtosis does not necessarily signal interesting image structure. It is then argued that finding filters that maximize output Kurtosis generates filters that are incompatible with observed physiology. In particular the optimal difference-of-Gaussian (DOG) filter should have the smallest possible scale, an on-centre off-surround cell should have a negative DC, and that the ratio of centre width to surround width should approach unity. This is incompatible with the physiology. Further, it is also predicted that oriented filters should always be oriented in the vertical direction, and of all the filters tested, the filter with the highest output Kurtosis has the lowest signal-to-noise ratio (the filter is simply the difference of two neighbouring pixels). Whilst these observations are not incompatible with the brain using a sparse representation, it does argue that little significance should be placed on finding filters with highly Kurtotic output distributions. It is therefore argued that other constraints are required in order to understand the development of visual receptive fields.