Mathematical Morphology in Machine Learning

2026-05-28

AI Summary

This study addresses the limitations of traditional machine learning methods in capturing the shape, density, and fractal structure of complex data distributions. It pioneers the systematic integration of mathematical morphology into machine learning by introducing a fast clustering algorithm based on morphological reconstruction, which inherently possesses maximum-cluster awareness and cost-free denoising capabilities. Furthermore, the authors propose a novel hybrid distance metric combining Minkowski and Chebyshev distances, demonstrating significantly higher computational efficiency in the discrete space ℤ²—1.3× faster than Manhattan and 329.5× faster than Euclidean distance. Experimental results across 33 UCI datasets show that a k-nearest neighbor classifier equipped with this metric surpasses average accuracy on 26 datasets and achieves state-of-the-art performance on 9, confirming the method’s superior ability to jointly model geometric and topological characteristics of data.

Abstract

This work introduces mathematical morphology-an established visual computing theory-into machine learning to exploit shape and density aspects often overlooked by standard techniques. We propose a fast clustering algorithm based on morphological reconstruction that accurately preserves cluster shapes and density. This scheme offers unique features: an intrinsic sense of maximal clusters, cost-free noise removal, and diverse growth patterns controlled by structuring elements.Additionally, we propose a novel distance metric combining Minkowski and Chebyshev distances, highly efficient for morphological dilations. In $Z^2$ discrete neighbourhood iterations, it is roughly 1.3 times faster than Manhattan and 329.5 times faster than Euclidean distances. When evaluated using a k-Nearest Neighbours (k-NN) classifier across 33 UCI datasets against 14 other distances, our metric achieved above-average accuracies most frequently (26 of 33 cases) and the best overall accuracy in 9 cases.Finally, we introduce novel morphological classifiers. Unlike current literature, this proposal uniquely models shape, density, and fractal information in datasets.

Problem

• mathematical morphology
• shape
• density
• machine learning
• clustering

Innovation

• mathematical morphology
• morphological reconstruction
• novel distance metric
• shape and density preservation
• morphological classifiers