Recursive implementations of temporal filters for image motion computation

Efficient algorithms for image motion computation are important for compute r vision applications and the modelling of biological vision systems. Inten sity-based image motion computation proceeds in two stages: the convolution of linear spatiotemporal filter kernels with the image sequence, followed by the non-linear combination of the filter outputs. If the spatiotemporal extent of the filter kernels is large, then the convolution stage can be ve ry intensive computationally. One effective means of reducing the storage r equired and computation involved in implementing the temporal convolutions is the introduction of recursive filtering. Non-recursive methods require t he number of frames of the image sequence stored at any given time to be eq ual to the temporal extent of the slowest temporal filter. In contrast, rec ursive methods encode recent stimulus history implicitly in the values of a small number of variables updated through a series of feedback equations. Recursive filtering reduces the number of values stored in memory during co nvolution and the number of mathematical operations involved in computing t he filters' outputs. This paper extends previous recursive implementations of gradient- and correlation-based motion analysis algorithms [Fleet DJ, La ngley K (1995) IEEE PAMI 17: 61-67; Clifford CWG, Ibbotson MR, Langley K (1 997) Vis Neurosci 14: 741-749], describing a recursive implementation of ca usal band-pass temporal filters suitable for use in energy- and phase-based algorithms for image motion computation. It is shown that the filters' tem poral frequency tuning curves fit psychophysical estimates of the temporal properties of human visual filters [Hess RF, Snowden RJ (1992) Vision Res 3 2: 47-60].