Vertical and Horizontal Disparities from Phase

We apply the notion that phase differences can be used to interpret disparity between a pair of stereoscopic images. Indeed, phase relationships can also be used to obtain probabilistic measures both edges and corners, as well as the directional instantaneous frequency of an image field. The method of phase differences is shown to be equivalent to a Newton-Raphson root finding iteration through the resolutions of band-pass filtering. The method does, however, suffer from stability problems, and in particular stationary phase and aliasing. The stability problems associated with this technique are implicitly derived from the mechanism used to interpet disparity, which in general requires an assumption of linear phase and the local instantaneous frequency. We present two techniques. Firstly, we use the centre frequency of the applied band-pass filter to interpret disparity. This interpretation, however, suffers heavily from phase error and requires considerable damping prior to convergence. Secondly, we use the derivative of phase to obtain the instantaneous frequency from an image, which is then used to improve the disparity estimate. These ideas are extended into 2-D where it is possible to extract both vertical and horizontal disparities.