Local cross-correlation model of stereo correspondence

As the disparity gradient of a stimulus increases, human observers' ability to solve the correspondence problem and thereby estimate the disparities becomes poorer. It finally fails altogether when a critical gradient-the disparity-gradient limit (Burt & Julesz, 1980) - is reached. We investigated the cause of the disparity-gradient limit. As part of this work, we developed a local cross-correlator similar to ones proposed in the computer vision literature and similar to the disparity-energy model of neurons in area VI. Like humans, the cross-correlator exhibits poorer performance as the disparity gradient increases. We also conducted a psychophysical experiment in which observers were presented sawtooth waveforms defined by disparity. They made spatial phase discriminations. We presented different corrugation spatial frequencies and amplitudes, and measured observers' ability to discriminate the two phases. Coherence thresholds (the proportion of signal dots at threshold relative to the total number of dots in the stimulus) were well predicted by the disparity gradient and not by either the spatial frequency or amplitude of the corrugation waveform. Thus, human observers and a local cross-correlator exhibit similar behavior, which suggests that humans use such an algorithm to estimate disparity. As a consequence, disparity estimation is done with local estimates of constant disparity (piecewise frontal), which places a constraint on the highest possible stereo resolution.