Biological computation of image motion from flows over boundaries

A theory of early motion processing in the human and primate visual system is presented which is based on the idea that spatio-temporal retinal image data is represented in primary visual cortex by a truncated 3D Taylor expansion that we refer to as a jet vector. This representation allows all the concepts of differential geometry to be applied to the analysis of visual information processing. We show in particular how the generalised Stokes theorem can be used to move from the calculation of derivatives of image brightness at a point to the calculation of image brightness differences on the boundary of a volume in space-time and how this can be generalised to apply to integrals of products of derivatives. We also provide novel interpretations of the roles of direction selective, bi-directional and pan-directional cells and of type I and type II cells in V5/MT.