SEARCHING FOR FILTERS WITH INTERESTING OUTPUT DISTRIBUTIONS - AN UNINTERESTING DIRECTION TO EXPLORE

It has been independently proposed, by Barlow, Field, Intrator and co- workers, that the receptive fields of neurons in V1 are optimized to g enerate 'sparse', Kurtotic, or 'interesting' output probability distri butions. We investigate the empirical evidence for this further and ar gue 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 f ilter outputs (and hence the output Kurtosis) is well predicted simply from these effects of variable local variance. This suggests that fin ding Alters with high output Kurtosis does not necessarily signal inte resting image structure. It is then argued that finding filters that m aximize output Kurtosis generates filters that are incompatible with o bserved 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 wi th the physiology. Further, it is also predicted that oriented filters should always be oriented in the vertical direction, and of all the f ilters tested, the Alter with the highest output Kurtosis has the lowe st signal-to-noise ratio (the filter is simply the difference of two n eighbouring pixels). Whilst these observations are not incompatible wi th 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 ar e required in order to understand the development of visual receptive fields.