Non-Fourier motion analysis

It has been realized for some time that the visual system performs at least two general sorts of motion processing. First-order motion processing applies some variant of standard motion analysis (i.e. spatiotemporal Fourier energy analysis) directly to stimulus luminance, whereas second-order motion processing applies standard motion analysis to one or another grossly non-linear transformation of stimulus luminance. We have developed a method for disentangling the different sorts of mechanisms that may operate in human vision to detect second-order motion. This method hinges on an empirical condition called transition invariance that may or may not be satisfied by a family psi of textures. Any failure of this condition indicates that more than one mechanism is involved in detecting the motion of stimuli composed of the textures in psi. We have shown that the family of sinusoidal gratings oriented orthogonally to the direction of motion and varying in contrast and spatial frequency is transition invariant. We modelled the results in terms of a single-channel motion computation. We have new results indicating that a specific class of textures differing in texture element density and texture element contrast decisively fails the test of transition invariance. These findings suggest that in addition to the single second-order motion channel required by our earlier results there exists at least one other second-order motion channel. We argue that the preprocessing transformation used by this channel is a pointwise non-linearity that maps stimulus contrasts of absolute value less than some relatively high threshold tau onto 0, but increases with magnitude of c-tau for contrasts. c of absolute value greater than tau.