A new wavelet-based edge detector via constrained optimization

This report proposes a new wavelet–based approach to solving the edge detection problem. The proposed scheme adopts Canny’s three criteria [3] as a guide to derive a wavelet–style edge filter such that the edge points of an image can be detected efficiently and accurately at different scales. Since Canny’s criteria are suitable for those edge detectors that detect local extremes, the desired wavelet is therefore chosen to be anti–symmetric. In order to reconstruct the original image, the dual of the desired wavelet is also required. Basically, the pair of wavelets are represented as linear combinations of translations of a scaling function. By introducing a constrained optimization process, the set of expansion coefficients of the desired wavelet and its dual as well, can be determined. In order to implement the desired edge detector, a continuous wavelet has to be converted into the discrete form. For this purpose, the format of the discrete wavelet transform has to be developed. Since the proposed edge filter is wavelet–based, the inherent multiresolution nature of wavelet transform provides more flexibility in the analysis of images. Also, since an optimization process is introduced in the filter derivation process, the performance of the proposed filter is better than that of Mallat–Zhong’s edge detector. In real implementation, the experimental results show that the proposed approach is indeed superb.