Two-step method for assessing dissimilarity of random sets

TL;DR

This paper introduces a new statistical approach to compare two random sets based on boundary curvature, perimeter, and area ratios, with theoretical justification, simulation validation, and real tissue data application.

Contribution

It presents a novel two-step method for assessing dissimilarity of random sets focusing on boundary shape and size ratios, supported by theoretical and empirical validation.

Findings

Method effectively distinguishes tissue types based on shape and size features.

Simulation confirms the method's accuracy and robustness.

Application to real data demonstrates practical utility.

Abstract

The paper concerns a new statistical method for assessing dissimilarity of two random sets based on one realisation of each of them. The method focuses on shapes of the components of the random sets, namely on the curvature of their boundaries together with the ratios of their perimeters and areas. Theoretical background is introduced and then, the method is described, justified by a simulation study and applied to real data of two different types of tissue - mammary cancer and mastopathy.