Adaptive edge detection: a new criterion and its recursive implementation

A good edge detection method is always a good trade-off between noise restraining and signal preserving. This paper presents a new criterion for optimal edge detection, which is under a general gradient edge model. The noise restraining ability and edge localization precision are combined for a criterion with distinct physical meaning. We deduce some nonlinear shift-variant filters that can be implemented recursively as usual IIR filters. It also can be proven that the first and second order linear shift-invariant approximations are Shen's (1992) and Canny-Deriche's (1986, 1987) operators respectively.