A New Class Biorthogonal Spline Wavelet for Image Edge Detection

TL;DR

This paper introduces a novel biorthogonal cubic spline wavelet designed for improved image edge detection, emphasizing better support, symmetry, and frequency features, and proposes a new detection algorithm that effectively manages noise and structural uncertainties.

Contribution

It presents a new biorthogonal cubic spline wavelet and a structural uncertainty-aware detection algorithm, enhancing edge detection performance in noisy images.

Findings

Improved noise reduction in edge detection.

Enhanced capture of edge structure details.

Effective handling of uncertain and multi-frequency edges.

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.