A New Local Optimal Spline Wavelet for Image Edge Detection
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...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/1/42 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850072347777695744 |
|---|---|
| author | Dujuan Zhou Zizhao Yuan Zhanchuan Cai Defu Zhu Xiaojing Shen |
| author_facet | Dujuan Zhou Zizhao Yuan Zhanchuan Cai Defu Zhu Xiaojing Shen |
| author_sort | Dujuan Zhou |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5e0bab5bb1bc45d19ac280a0978f4f3c |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-5e0bab5bb1bc45d19ac280a0978f4f3c2025-08-20T02:47:06ZengMDPI AGMathematics2227-73902024-12-011314210.3390/math13010042A New Local Optimal Spline Wavelet for Image Edge DetectionDujuan Zhou0Zizhao Yuan1Zhanchuan Cai2Defu Zhu3Xiaojing Shen4School of Computer Science and Engineering, Macau University of Science and Technology, Taipa, Macau, ChinaSchool of Mathematics, Physics and Civil Engineering, Beijing Institute of Technology, Zhuhai 519088, ChinaSchool of Computer Science and Engineering, Macau University of Science and Technology, Taipa, Macau, ChinaKey Laboratory of In-Situ Property-Improving Mining of Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, ChinaFaculty of Data Science, City University of Macau, Macau, ChinaWavelet-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.https://www.mdpi.com/2227-7390/13/1/42local optimal spline waveletwavelet transformsmodulus maximauncertaintymulti-structure morphologyedge detection |
| spellingShingle | Dujuan Zhou Zizhao Yuan Zhanchuan Cai Defu Zhu Xiaojing Shen A New Local Optimal Spline Wavelet for Image Edge Detection Mathematics local optimal spline wavelet wavelet transforms modulus maxima uncertainty multi-structure morphology edge detection |
| title | A New Local Optimal Spline Wavelet for Image Edge Detection |
| title_full | A New Local Optimal Spline Wavelet for Image Edge Detection |
| title_fullStr | A New Local Optimal Spline Wavelet for Image Edge Detection |
| title_full_unstemmed | A New Local Optimal Spline Wavelet for Image Edge Detection |
| title_short | A New Local Optimal Spline Wavelet for Image Edge Detection |
| title_sort | new local optimal spline wavelet for image edge detection |
| topic | local optimal spline wavelet wavelet transforms modulus maxima uncertainty multi-structure morphology edge detection |
| url | https://www.mdpi.com/2227-7390/13/1/42 |
| work_keys_str_mv | AT dujuanzhou anewlocaloptimalsplinewaveletforimageedgedetection AT zizhaoyuan anewlocaloptimalsplinewaveletforimageedgedetection AT zhanchuancai anewlocaloptimalsplinewaveletforimageedgedetection AT defuzhu anewlocaloptimalsplinewaveletforimageedgedetection AT xiaojingshen anewlocaloptimalsplinewaveletforimageedgedetection AT dujuanzhou newlocaloptimalsplinewaveletforimageedgedetection AT zizhaoyuan newlocaloptimalsplinewaveletforimageedgedetection AT zhanchuancai newlocaloptimalsplinewaveletforimageedgedetection AT defuzhu newlocaloptimalsplinewaveletforimageedgedetection AT xiaojingshen newlocaloptimalsplinewaveletforimageedgedetection |