Velocity Computation from Measures of Spatiotemporal Gradients at Multiple Orientations

Abstract

Current models of speed and direction of motion which use measures of spatiotemporal gradients can suffer from ill-conditioning. This problem arises either because local measures of the derivatives of image brightness take zero values or because the motion equations cannot be solved for one-dimensional (1-D) signals in two-dimensional (2-D) images—the aperture problem. One way around this predicament is to select image points or introduce constants to deal with ill-conditioned calculations. Here we describe an analytic method that combines measures of speed in a range of directions to provide a well-conditioned measure of velocity at all points in the moving stimulus. This approach is a natural extension of a one-dimensional model which has been successful in predicting perceived motion in a variety of 1-D spatiotemporal motion patterns (Johnston, McOwan and Buxton 1992 Proceedings of the Royal Society of London, Series B 250 297 – 306). Speed is computed with the use of biologically plausible filters that are derivatives of Gaussians in the spatial domain and log Gaussians in the temporal domain. Measures of speed and inverse speed are computed for a range of orientations consistent with the number of direction columns in MT/V5. The pattern of velocities measured over this set of orientations is then used to recover the speed and direction of motion of the stimulus. The model can correctly compute the velocity of moving 1-D patterns, such as gratings, patterns that prove a problem for many current 2-D motion models as they form degenerate cases, as well as the motion of rigid 2-D patterns.