Tropical Geometry Based Edge Detection Using Min-Plus and Max-Plus Algebra

• URL: http://arxiv.org/abs/2505.18625v1
• Date: Sat, 24 May 2025 10:19:27 GMT
• Title: Tropical Geometry Based Edge Detection Using Min-Plus and Max-Plus Algebra
• Authors: Shivam Kumar Jha S, Jaya NN Iyer,
• Abstract summary: This paper proposes a tropical geometry-based edge detection framework that reformulates convolution and gradient computations using min-plus and max-plus algebra.<n>The tropical formulation emphasizes dominant intensity variations, contributing to sharper and more continuous edge representations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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