On idempotence and related requirements in edge detection

The energy feature detectors described by R. Owens et al. (1989) are good candidates for idempotent edge detectors. However, some of them (in particular, the Gabor energy feature detector) suffer from a serious defect that is absent in gradient-type operators: their sensitivity to gray-level shift in the original image. This leads to errors in the localization of step edges. The Fourier phase and amplitude conditions outlined by M.C. Morrone and D.C. Burr (1988) for the class of energy feature detectors guarantee a zero DC level when the convolution masks are taken in L¹; therefore, the resulting energy feature detector is invariant under grey-level shift in the original image. Also, the properties of the underlying edge model are invariant under a smoothing of the image by a Gaussian or any function in L¹ having zero Fourier phase. In particular, such a smoothing does not deteriorate the idempotence of the edge detector. Some concrete examples of energy feature detectors satisfying the Morrone conditions are described