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

arXiv: https://arxiv.org/abs/2505.18625 · HTML: https://mlsanity.com/paper/2505.18625/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 28 references that are in the map.
- First posted on arXiv 24 May 2025.

## Builds on (most cited first, 1 of 1)

- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)

## Abstract (arXiv)

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.