Relationship between phase and energy methods for disparity computation

The phase and energy methods for computing binocular disparity maps from stereograms are motivated differently, have different physiological relevances, and involve different computational steps. Nevertheless, we demonstrate that at the final stages where disparity values are made explicit, the simplest versions of the two methods are exactly equivalent. The equivalence also holds when the quadrature-pair construction in the energy method is replaced with a more physiologically plausible phase-averaging step. The equivalence fails, however, when the phase-difference receptive field model is replaced by the position-shift model. Additionally, intermediate results from the two methods are always quite distinct. In particular, the energy method generates a distributed disparity representation similar to that found in the visual cortex, while the phase method does not. Finally, more elaborate versions of the two methods are in general not equivalent. We also briefly compare these two methods with some other stereo models in the literature.