相关论文: On spatial thinning-replacement processes based on…

Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…

We introduce a dynamical system based on the vertices of Voronoi tessellations. This dynamical system acts on finite or discrete point sets in the plane, taking a point set to the vertex set of its Voronoi tessellation. We explore the…

Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…

Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…

High energy experimental data can be viewed as a sampling of the relevant phase space. We point out that one can apply Voronoi tessellations in order to understand the underlying probability distributions in this phase space. Interesting…

The Voronoi tessellation is a natural way of space segmentation, which has many applications in various fields of science and technology, as well as in social sciences and visual art. The varieties of the Voronoi tessellation methods are…

The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern "random", Poisson-Voronoi tessellations (PVT), or "non-random", Non Poisson-Voronoi…

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…

Voronoi tessellations are used to partition the Euclidean space into polyhedral regions, which are called Voronoi cells. Labeling the Voronoi cells with the class information, we can map any classification problem into a Voronoi…

The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial…

The large-scale matter distribution represents a complex network of structure elements such as voids, clusters, filaments, and sheets. This network is spanned by a point distribution. The global properties of the point process can be…

This study proposes an innovative approach to analyze spatial patterns of behavior by integrating information in weighted Voronoi diagrams. The objective of the research is to analyze the temporal distribution of an experimental subject in…

We introduce a new class of dynamic point process models with simple and intuitive dynamics that are based on the Voronoi tessellations generated by the processes. Under broad conditions, these processes prove to be ergodic and produce, on…

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…

The purpose of this note is to clarify the effect of the finite size of spherical particles upon the characteristics of their spatial distribution through a random Poisson process (RPP). This information is of special interest when using…

Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a…

Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…

This note describes a simple method to draw random points such that the cells of the corresponding Voronoi tesselation (approximately) satisfy a desired size distribution, for instance, follow a power law. The method is illustrated and…

We consider the Voronoi tessellation associated to a stationary simple point process on $\mathbb{R}^d$ with finite and positive intensity. We introduce the Delaunay triangulation as its dual graph, i.e.~the graph with vertex set given by…

Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…