Two-Step Method for Assessing Similarity of Random Sets

Vesna Gotovac Đogaš; Kateřina Helisová; Bogdan Radović; Jakub Staněk; Markéta Zikmundová; Kateřina Brejchová

doi:10.5566/ias.2600

Authors

Vesna Gotovac Đogaš University of Split
Kateřina Helisová Czech Technical University in Prague
Bogdan Radović Czech Technical University in Prague
Jakub Staněk Charles University
Markéta Zikmundová University of Chemistry and Technology Prague
Kateřina Brejchová Czech Technical University in Prague

DOI:

https://doi.org/10.5566/ias.2600

Keywords:

connected component, curvature, similarity, $N$-distance, random set

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.

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