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The binocular energy model and V1 neurons signal disparity in half-matched stereograms.

Depth perception from binocular disparity depends upon correctly matching image features seen by the left and right eyes. A local cross-correlation between left and right images, similar to the operation of the binocular energy model, is a good candidate mechanism. Recently, Doi et al. (2011, 2013, 2014) showed that human observers can detect depth in "half-matched" stereograms containing equal numbers of correlated and anti-correlated dots. These stimuli have a binocular correlation of 0 for all disparities, leading Doi et al. to argue that a correlation computation cannot explain human performance. However, these stimuli do contain local fluctuations in correlation. We explore whether it is possible account for these responses with the binocular energy model, and have begun testing the predictions in disparity-selective neurons from V1. In half-matched stereograms the standard binocular energy model responds equally to all disparities. Simply adding an expansive nonlinearity on the output of a model complex cell renders it disparity selective. At the preferred disparity, local fluctuations in correlation produce a greater variance in the output of an energy model, compared to a non-preferred disparity. When passed through the nonlinearity, this greater variance results in a greater mean. The strength of disparity selectivity decreases with dot density (low density produces greater fluctuations). We examined this in disparity selective neurons in monkey V1. In neurons showing attenuated responses to anticorrelated stimuli, we find robust disparity selectivity at low dot densities. At high dot densities disparity selectivity is much weaker, but remains significant. A single computation - the binocular energy model followed by an output nonlinearity, can explain depth perception in both correlated and "half-matched" random dot stereograms. A key property of this simple model, that disparity selectivity depends on dot density (only in half-matched stereograms), is true in appropriately selected disparity selective V1 neurons. Meeting abstract presented at VSS 2015.