Efficient encoding of stereo information produces sparser responses to natural binocular images

Li and Atick proposed a theory of efficient stereo coding in which the two eyes’ signals are transformed into uncorrelated binocular summation and differencing channels (Li & Atick (1994) Network, 5, 157-174; Li (1995) in The Neurobiology of Compuation: The Proceedings of the Third Annual Computation and Neural Systems Conference, J. Bower (ed) (Boston: Kluwer), 397-402). May, Zhaoping and Hibbard recently provided striking psychophysical evidence in support of this theory (May, Zhaoping & Hibbard (2012) Current Biology, 22(1), 28-32). Here, we assess the implications of this decorrelation stage for the subsequent encoding of binocular information. We applied Independent Component Analysis (ICA) to image patches sampled from (i) the left and right images of natural binocular pairs and (ii) the same images transformed into summation and differencing channels, with appropriate gain-control applied to the two channels. In both cases, the resulting ICA filters were pairs of Gabor-like receptive fields. In comparison to the results for untransformed images, ICA applied to the summation and differencing channels resulted in a modest, but significant increase in the kurtosis of responses. Efficient coding thus produces a sparser representation of natural binocular images.