A New Class Biorthogonal Spline Wavelet for Image Edge Detection
Dujuan Zhou, Zizhao Yuan
TL;DR
The paper tackles robust edge detection in the presence of noise and uncertain regional structures by introducing a new biorthogonal cubic special spline wavelet (BCSSW) built via the Cohen-Daubechies-Feauveau framework and a cubic special spline, yielding improved compactness, symmetry, and frequency behavior. It couples BCSSW with an edge detector (EDBSW) that leverages structural uncertainty-aware modulus maxima and a multi-structure anti-noise morphology, integrated through a fusion-reconstruction pipeline. Key contributions include the BCSSW construction and filter design, a structural-uncertainty modulus-maxima framework with adaptive thresholding, a multi-structure anti-noise operator, and a context-weighted fusion strategy for refined edge maps. Experimental results on BSDS500 and MVTec demonstrate superior noise robustness, sharper and more continuous edges, and better preservation of structural details compared to traditional operators and various wavelets, highlighting practical benefits for real-world image analysis.
Abstract
Spline wavelets have shown favorable characteristics for localizing in both time and frequency. In this paper, we propose a new biorthogonal cubic special spline wavelet (BCSSW), based on the Cohen-Daubechies-Feauveau wavelet construction method and the cubic special spline algorithm. BCSSW has better properties in compact support, symmetry, and frequency domain characteristics. However, current mainstream detection operators usually ignore the uncertain representation of regional pixels and global structures. To solve these problems, we propose a structural uncertainty-aware and multi-structure operator fusion detection algorithm (EDBSW) based on a new BCSSW spline wavelet. By constructing a spline wavelet that efficiently handles edge effects, we utilize structural uncertainty-aware modulus maxima to detect highly uncertain edge samples. The proposed wavelet detection operator utilizes the multi-structure morphological operator and fusion reconstruction strategy to effectively address anti-noise processing and edge information of different frequencies. Numerous experiments have demonstrated its excellent performance in reducing noise and capturing edge structure details.