Physiological computation of binocular disparity

We previously proposed a physiologically realistic model for stereo vision based on the quantitative binocular receptive field profiles mapped by Freeman and coworkers. Here we present several new results about the model that shed light on the physiological processes involved in disparity computation. First, we show that our model can be extended to a much more general class of receptive field profiles than the commonly used Gabor functions. Second, we demonstrate that there is, however, an advantage of using the Gabor filters: similar to our perception, the stereo algorithm with the Gabor filters has a small bias towards zero disparity. Third, we prove that the complex cells as described by Freeman et al. compute disparity by effectively summing up two related cross products between the band-pass filtered left and right retinal image patches. This operation is related to cross-correlation but it overcomes some major problems with the standard correlator. Fourth, we demonstrate that as few as two complex cells at each spatial location are sufficient for a reasonable estimation of binocular disparity. Fifth, we find that our model can be significantly improved by considering the fact that complex cell receptive field are, on average, larger than those of simple cells. This fact is incorporated into the model by averaging over several quadrature pairs of simple cells with nearby and overlapping receptive fields to construct a model complex cell. The disparity tuning curve of the resulting complex cell is much more reliable than the constructed from a single quadrature pair of simple cells used previously, and the computed disparity maps for random dot stereograms with the new algorithm are very similar to human perception, with sharp transitions at disparity boundaries. Finally, we show that under most circumstances our algorithm works equally well with either of the two well-known receptive field models in the literature.