A spatio-temporal generalization of Canny's edge detector

Abstract

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. >