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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.18625 |
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| _version_ | 1866912392443592704 |
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| author | S, Shivam Kumar Jha Iyer, Jaya NN |
| author_facet | S, Shivam Kumar Jha Iyer, Jaya NN |
| contents | This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra. The tropical formulation emphasizes dominant intensity variations, contributing to sharper and more continuous edge representations. Three variants are explored: an adaptive threshold-based method, a multi-kernel min-plus method, and a max-plus method emphasizing structural continuity. The framework integrates multi-scale processing, Hessian filtering, and wavelet shrinkage to enhance edge transitions while maintaining computational efficiency. Experiments on MATLAB built-in grayscale and color images suggest that tropical formulations integrated with classical operators, such as Canny and LoG, can improve boundary detection in low-contrast and textured regions. Quantitative evaluation using standard edge metrics indicates favorable edge clarity and structural coherence. These results highlight the potential of tropical algebra as a scalable and noise-aware formulation for edge detection in practical image analysis tasks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tropical Geometry Based Edge Detection Using Min-Plus and Max-Plus Algebra S, Shivam Kumar Jha Iyer, Jaya NN Algebraic Geometry Computer Vision and Pattern Recognition 14T90, 14-04 This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra. The tropical formulation emphasizes dominant intensity variations, contributing to sharper and more continuous edge representations. Three variants are explored: an adaptive threshold-based method, a multi-kernel min-plus method, and a max-plus method emphasizing structural continuity. The framework integrates multi-scale processing, Hessian filtering, and wavelet shrinkage to enhance edge transitions while maintaining computational efficiency. Experiments on MATLAB built-in grayscale and color images suggest that tropical formulations integrated with classical operators, such as Canny and LoG, can improve boundary detection in low-contrast and textured regions. Quantitative evaluation using standard edge metrics indicates favorable edge clarity and structural coherence. These results highlight the potential of tropical algebra as a scalable and noise-aware formulation for edge detection in practical image analysis tasks. |
| title | Tropical Geometry Based Edge Detection Using Min-Plus and Max-Plus Algebra |
| topic | Algebraic Geometry Computer Vision and Pattern Recognition 14T90, 14-04 |
| url | https://arxiv.org/abs/2505.18625 |