Tropical Geometry Based Edge Detection Using Min-Plus and Max-Plus Algebra
This work addresses edge detection for image analysis tasks, offering a scalable and noise-aware formulation that is incremental, building on classical operators like Canny and LoG.
The paper tackles edge detection in images by reformulating convolution and gradient computations using tropical algebra, resulting in improved boundary detection in low-contrast and textured regions with favorable edge clarity and structural coherence.
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.