Computational analysis of non-Fourier motion

Non-Fourier motion is now commonplace in research on visual motion perception, yet lacks a computational framework. This paper examines this issue based on the observation that many non-Fourier motion stimuli have a simple characterization in the frequency domain, in terms of oriented power distributions that lie along lines (or planes) that do not pass through the origin. This provides a unifying theoretical framework for a very diverse class of non-Fourier phenomena. It also allows us to examine some central issues concerning the computational nature of non-Fourier models, and naturally occurring sources of non-Fourier motion. For example, it is shown that the orientation of power in frequency domain corresponds to the velocity of a multiplicative envelope, and may arise as a restricted form of lighting effects, translucency or occlusion. We also show that both the location and orientation of spectral power may be extracted from the phase and amplitude output of band-pass filters, consonant with existing non-Fourier models.