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A New Local Optimal Spline Wavelet for Image Edge Detection

Author

Listed:
  • Dujuan Zhou

    (School of Computer Science and Engineering, Macau University of Science and Technology, Taipa, Macau, China
    School of Mathematics, Physics and Civil Engineering, Beijing Institute of Technology, Zhuhai 519088, China
    These authors contributed equally to this work.)

  • Zizhao Yuan

    (School of Mathematics, Physics and Civil Engineering, Beijing Institute of Technology, Zhuhai 519088, China
    These authors contributed equally to this work.)

  • 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
    Galuminium Group Co., Ltd., Guangzhou 510450, China)

  • Xiaojing Shen

    (Faculty of Data Science, City University of Macau, Macau, China)

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.

Suggested Citation

  • Dujuan Zhou & Zizhao Yuan & Zhanchuan Cai & Defu Zhu & Xiaojing Shen, 2024. "A New Local Optimal Spline Wavelet for Image Edge Detection," Mathematics, MDPI, vol. 13(1), pages 1-22, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:42-:d:1553982
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