Searching for Lters with \interesting" Output Distributions: an Uninteresting Direction to Explore?

It has been proposed that the receptive elds of neurons in V1 are optimised to generate \sparse", Kurtotic, or \interesting" output probability We investigate the empirical evidence for this further and argue that lters can produce \interesting" output distributions simply because natural images have variable local intensity variance. If the proposed lters have zero D.C., then the probability distribution of lter outputs (and hence the output Kurtosis) is well predicted simply from these eeects of variable local variance. This suggests that nding lters with high output Kurtosis does not necessarily signal interesting image structure. It is then argued that nding lters that maximise output Kurtosis generates lters that are incompatible with observed physiology. In particular the optimal diierence{of{Gaussian (DOG) lter should have the smallest possible scale, an on{ centre oo{surround cell should have a negative D.C., 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 lters should always be oriented in the vertical direction, and of all the lters tested, the lter with the highest output Kurtosis has the lowest signal to noise (the lter is simply the diierence of two neighbouring pixels). Whilst these observations are not incompatible with the brain using a sparse representation, it does argue that little signiicance should be placed on nding lters with highly Kurtotic output distributions. It is therefore argued that other constraints are required in order to understand the development of visual receptive elds.