Phase-differencing in stereo vision: Solving the localisation problem

Complex Gabor filters with phases in quadrature are often used to model even- and odd-symmetric simple cells in the primary visual cortex. In stereo vision, the phase difference between the responses of the left and right views can be used to construct a disparity or depth map. Various constraints can be applied in order to construct smooth maps, but this leads to very imprecise depth transitions. In this theoretical paper we show, by using lines and edges as image primitives, the origin of the localisation problem. We also argue that disparity should be attributed to lines and edges, rather than trying to construct a 3D surface map in cortical area V1. We derive allowable translation ranges which yield correct disparity estimates, both for left-view centered vision and for cyclopean vision.