Full-wave and half-wave processes in second-order motion and texture

A theory of human second-order motion perception is proposed and further applied to the discrimination of texture slant. The computational algorithms for deriving the direction of left-right motion from a sequence of images are equivalent to the algorithms for deriving the direction of slant (e.g. from top left to bottom right or top right to bottom left) in a single 2D image. There is a broad range of phenomena for which Fourier analysis of the image plus a few simple rules gives a good account of human perception. The problem with this first-order analysis is that there exists a broad class of 'microbalanced' stimuli in which the motion or slant is completely obvious to human subjects but is invisible to first-order analysis. Microbalanced stimuli require second-order analysis which consists of non-linear preprocessing (spatiotemporal filtering followed by rectification of the input signal) before standard motion or slant analysis. To determine whether the second-order rectification is half-wave or full-wave, we construct two special microbalanced stimulus types: 'half-wave stimuli' whose motion (or texture slant) is interpretable by a half-wave rectifying system but not by full-wave or a first-order (Fourier) analysis and 'full-wave stimuli' which are interpretable only after full-wave rectification. Such experiments show that second-order texture-slant perception utilizes both half-wave and full-wave processes, second-order motion-direction discrimination depends predominantly on full-wave rectification and second-order spatial interactions such as lateral contrast-contrast inhibition and second-order Mach bands are exclusively full-wave.