Binocular fusion takes place over a limited region smaller than one degree of visual angle (Panum's fusional area), which is on the order of the range of preferred disparities measured in populations of disparity-tuned neurons in the visual cortex. However, the actual range of binocular disparities encountered in natural scenes extends over tens of degrees. This discrepancy suggests that there must be a mechanism for detecting whether the stimulus disparity is inside or outside the range of the preferred disparities in the population. Here, we compare the efficacy of several features derived from the population responses of phase-tuned disparity energy neurons in differentiating between in-range and out-of-range disparities. Interestingly, some features that might be appealing at first glance, such as the average activation across the population and the difference between the peak and average responses, actually perform poorly. On the other hand, normalizing the difference between the peak and average responses results in a reliable indicator. Using a probabilistic model of the population responses, we improve classification accuracy by combining multiple features. A decision rule that combines the normalized peak to average difference and the peak location significantly improves performance over decision rules based on either measure in isolation. In addition, classifiers using normalized difference are also robust to mismatch between the image statistics assumed by the model and the actual image statistics.

The relative depth of objects causes small shifts in the left and right retinal positions of these objects, called binocular disparity. This letter describes an electronic implementation of a single binocularly tuned complex cell based on the binocular energy model, which has been proposed to model disparity-tuned complex cells in the mammalian primary visual cortex. Our system consists of two silicon retinas representing the left and right eyes, two silicon chips containing retinotopic arrays of spiking neurons with monocular Gabor-type spatial receptive fields, and logic circuits that combine the spike outputs to compute a disparity-selective complex cell response. The tuned disparity can be adjusted electronically by introducing either position or phase shifts between the monocular receptive field profiles. Mismatch between the monocular receptive field profiles caused by transistor mismatch can degrade the relative responses of neurons tuned to different disparities. In our system, the relative responses between neurons tuned by phase encoding are better matched than neurons tuned by position encoding. Our numerical sensitivity analysis indicates that the relative responses of phase-encoded neurons that are least sensitive to the receptive field parameters vary the most in our system. We conjecture that this robustness may be one reason for the existence of phase-encoded disparity-tuned neurons in biological neural systems.