Edge localization in images by symmetrical wavelet transforms
Mingui Sun, Ching-Chung Li, Robert J. Sclabassi · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1993
The performance of a wavelet-based edge detector is characterized by a set of digital filters that implement the wavelet transform. In this paper we clarify the issue whether an implementation filter can be made symmetric or antisymmetric with respect to the origin while still maintaining the desired spatial localization. It is shown that, by analyzing the asymptotical convergence of the filter coefficients, these two conditions are not compatible if the filter possesses an antisymmetry. However, when the filter is symmetric with respect to the origin, the optimal spatial localization can be obtained.