A spatio-temporal generalization of Canny´s edge detector

Moving step edges are modeled as the product of a deterministic function in space and a stochastic function in time which captures the edge shapes and the temporal uncertainties, respectively. Under J. Canny´s (IEEE Trans. on Pattern Analysis and Machine Intelligence, vol.PAMI-8, p.679-98, Nov. 1986) original optimality criteria, a set of optimal edge detectors is derived. They are in a product form, i.e., a product of a spatial function and a temporal function. The spatial function is Canny´s edge detector in one dimension and the temporal function can be well approximated by the exponential function. Generalizing Canny´s edge detector to the temporal domain is not only theoretically interesting, but also practically useful. The generalization of Canny´s edge detectors provides better immunity to noise and can serve as one of the tools in understanding the temporal behavior of moving edges. They have been used in a data-fusion framework to detect moving edges and their normal velocities simultaneously. For completeness, the authors derive some properties of the optimal edge detectors and compare them with Gabor filters