Classification of realisations of random sets

TL;DR

This paper introduces a classification approach for realisations of random sets using geometric similarity measures, validated through simulations and applied to histological image classification.

Contribution

It proposes a novel classification methodology based on empirical geometric distances, applicable to both simulated data and real histological images.

Findings

Effective classification of random set realisations demonstrated.

Geometric similarity measures successfully distinguish tissue types.

Method shows promise for medical image analysis.

Abstract

In this paper, the classification task for a family of sets representing the realisation of some random set models is solved. Both unsupervised and supervised classification methods are utilised using the similarity measure between two realisations derived as empirical estimates of $\mathcal N$-distances quantified based on geometric characteristics of the realisations, namely the boundary curvature and the perimeter over area ratios of obtained samples of connected components from the realisations. To justify the proposed methodology, a simulation study is performed using random set models. The methods are used further for classifying histological images of mastopathy and mammary cancer tissue.