A Mathematical Survey of Image Deep Edge Detection Algorithms: From Convolution to Attention
Edge detection, a cornerstone of computer vision, identifies intensity discontinuities in images, enabling applications from object recognition to autonomous navigation. This survey presents a mathematically grounded analysis of edge detection’s evolution, spanning traditional gradient-based methods...
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MDPI AG
2025-07-01
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| author | Gang Hu |
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| description | Edge detection, a cornerstone of computer vision, identifies intensity discontinuities in images, enabling applications from object recognition to autonomous navigation. This survey presents a mathematically grounded analysis of edge detection’s evolution, spanning traditional gradient-based methods, convolutional neural networks (CNNs), attention-driven architectures, transformer-backbone models, and generative paradigms. Beginning with Sobel and Canny’s kernel-based approaches, we trace the shift to data-driven CNNs like Holistically Nested Edge Detection (HED) and Bidirectional Cascade Network (BDCN), which leverage multi-scale supervision and achieve ODS (Optimal Dataset Scale) scores 0.788 and 0.806, respectively. Attention mechanisms, as in EdgeNAT (ODS 0.860) and RankED (ODS 0.824), enhance global context, while generative models like GED (ODS 0.870) achieve state-of-the-art precision via diffusion and GAN frameworks. Evaluated on BSDS500 and NYUDv2, these methods highlight a trajectory toward accuracy and robustness, yet challenges in efficiency, generalization, and multi-modal integration persist. By synthesizing mathematical formulations, performance metrics, and future directions, this survey equips researchers with a comprehensive understanding of edge detection’s past, present, and potential, bridging theoretical insights with practical advancements. |
| format | Article |
| id | doaj-art-bd6b4ba9844e48a9be98918bac31dbd1 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-bd6b4ba9844e48a9be98918bac31dbd12025-08-20T03:36:27ZengMDPI AGMathematics2227-73902025-07-011315246410.3390/math13152464A Mathematical Survey of Image Deep Edge Detection Algorithms: From Convolution to AttentionGang Hu0Department of Computer Information Systems, SUNY Buffalo State University, Buffalo, NY 14222, USAEdge detection, a cornerstone of computer vision, identifies intensity discontinuities in images, enabling applications from object recognition to autonomous navigation. This survey presents a mathematically grounded analysis of edge detection’s evolution, spanning traditional gradient-based methods, convolutional neural networks (CNNs), attention-driven architectures, transformer-backbone models, and generative paradigms. Beginning with Sobel and Canny’s kernel-based approaches, we trace the shift to data-driven CNNs like Holistically Nested Edge Detection (HED) and Bidirectional Cascade Network (BDCN), which leverage multi-scale supervision and achieve ODS (Optimal Dataset Scale) scores 0.788 and 0.806, respectively. Attention mechanisms, as in EdgeNAT (ODS 0.860) and RankED (ODS 0.824), enhance global context, while generative models like GED (ODS 0.870) achieve state-of-the-art precision via diffusion and GAN frameworks. Evaluated on BSDS500 and NYUDv2, these methods highlight a trajectory toward accuracy and robustness, yet challenges in efficiency, generalization, and multi-modal integration persist. By synthesizing mathematical formulations, performance metrics, and future directions, this survey equips researchers with a comprehensive understanding of edge detection’s past, present, and potential, bridging theoretical insights with practical advancements.https://www.mdpi.com/2227-7390/13/15/2464edge detectioncomputer visionconvolutional neural networks (CNNs)attention mechanismstransformergenerative models |
| spellingShingle | Gang Hu A Mathematical Survey of Image Deep Edge Detection Algorithms: From Convolution to Attention Mathematics edge detection computer vision convolutional neural networks (CNNs) attention mechanisms transformer generative models |
| title | A Mathematical Survey of Image Deep Edge Detection Algorithms: From Convolution to Attention |
| title_full | A Mathematical Survey of Image Deep Edge Detection Algorithms: From Convolution to Attention |
| title_fullStr | A Mathematical Survey of Image Deep Edge Detection Algorithms: From Convolution to Attention |
| title_full_unstemmed | A Mathematical Survey of Image Deep Edge Detection Algorithms: From Convolution to Attention |
| title_short | A Mathematical Survey of Image Deep Edge Detection Algorithms: From Convolution to Attention |
| title_sort | mathematical survey of image deep edge detection algorithms from convolution to attention |
| topic | edge detection computer vision convolutional neural networks (CNNs) attention mechanisms transformer generative models |
| url | https://www.mdpi.com/2227-7390/13/15/2464 |
| work_keys_str_mv | AT ganghu amathematicalsurveyofimagedeepedgedetectionalgorithmsfromconvolutiontoattention AT ganghu mathematicalsurveyofimagedeepedgedetectionalgorithmsfromconvolutiontoattention |