A preference for phase-based disparity in a neuromorphic implementation of the binocular energy model

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.