Random Tessellations -- An Overview of Models

TL;DR

This paper provides a comprehensive overview of random tessellation models in stochastic geometry, covering their formulation, types, simulation methods, and model fitting techniques.

Contribution

It systematically reviews various classes of random tessellations, including Voronoi, hyperplane, and STIT models, highlighting their geometric properties and simulation approaches.

Findings

Overview of random tessellation mechanisms

Discussion of simulation and model fitting methods

Classification of tessellation model types

Abstract

Random tessellations are a prominent class of models in stochastic geometry. In this chapter, we give an overview of mechanisms that have been used to formulate random tessellation models. First, the notion of a random tessellation and basic geometric characteristics of random tessellations are introduced. Then, several model classes are presented. This includes, but is not limited to, Voronoi tessellations and their weighted generalizations, hyperplane tessellations, and STIT tessellations. Simulation of the tessellation models and approaches for model fitting are also discussed.