A New Local Optimal Spline Wavelet for Image Edge Detection

Dujuan Zhou, Zizhao Yuan, Zhanchuan Cai (), Defu Zhu and Xiaojing Shen
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Dujuan Zhou: School of Computer Science and Engineering, Macau University of Science and Technology, Taipa, Macau, China
Zizhao Yuan: School of Mathematics, Physics and Civil Engineering, Beijing Institute of Technology, Zhuhai 519088, China
Zhanchuan Cai: School of Computer Science and Engineering, Macau University of Science and Technology, Taipa, Macau, China
Defu Zhu: Key Laboratory of In-Situ Property-Improving Mining of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China
Xiaojing Shen: Faculty of Data Science, City University of Macau, Macau, China

Mathematics, 2024, vol. 13, issue 1, 1-22

Abstract: Wavelet-based edge detection methods have evolved significantly over the years, contributing to advances in image processing, computer vision, and pattern recognition. This paper proposes a new local optimal spline wavelet (LOSW) and the dual wavelet of the LOSW. Then, a pair of dual filters can be obtained, which can provide distortion-free signal decomposition and reconstruction, while having stronger denoising and feature capture capabilities. The coefficients of the pair of dual filters are calculated for image edge detection. We propose a new LOSW-based edge detection algorithm (LOSW-ED), which introduces a structural uncertainty–aware modulus maxima (SUAMM) to detect highly uncertain edge samples, ensuring robustness in complex and noisy environments. Additionally, LOSW-ED unifies multi-structure morphology and modulus maxima to fully exploit the complementary properties of low-frequency (LF) and high-frequency (HF) components, enabling multi-stage differential edge refinement. The experimental results show that the proposed LOSW and LOSW-ED algorithm has better performance in noise suppression and edge structure preservation.

Keywords: local optimal spline wavelet; wavelet transforms; modulus maxima; uncertainty; multi-structure morphology; edge detection; wavelet reconstruction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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