The computation of deformation and rotation in stereopsis

Recent work [12] has proposed that tracking phase differences through the resolutions of bandpass filtering created via Hilbert transform pairs can be used to obtain unrotated stereoscopic disparities both horizontally and vertically. These ideas are now extended to incorporate the deformation arising from a stereoscopic transformation. From an ordered arrangement of directionally selective quadrature filters with both finite orientation and spatial frequency bandwidths, we create a further Hilbert transform pair from the energy responses of filters similarly located in space, but with different orientation preferences. From this response an estimate of both orientational disparity and orientational diffrequency is finally computed. The latter term is shown to approximate the anisotropic deformation arising from surface slant. We show using this representation that the surface slant can be approximated by differences in spatial frequency and that the diffrequency and deformation hypotheses are equivalent.