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Poisson Voronoi tessellations have been used in modeling many types of systems across different sciences, from geography and astronomy to telecommunications. The existing literature on the statistical properties of Poisson Voronoi cells is…
The regeneration of forest resources is one of the main objectives of modern forest management. The present book is based on my personal PhD thesis and aims to identify detailed features of the regeneration process and the characteristics…
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.…
Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial…
Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set…
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…
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…
Voronoi treemaps are used to depict nodes and their hierarchical relationships simultaneously. However, in addition to the hierarchical structure, data attributes, such as co-occurring features or similarities, frequently exist. Examples…
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…
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…
Representing a scanned map of the real environment as a topological structure is an important research topic in robotics. Since topological representations of maps save a huge amount of map storage space and online computing time, they are…
Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three dimensional…
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…
Space partitioning methods such as random forests and the Mondrian process are powerful machine learning methods for multi-dimensional and relational data, and are based on recursively cutting a domain. The flexibility of these methods is…
Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide…
Given two sets of training samples, general method is to estimate the density function and classify the test sample according to higher values of estimated densities. Natural way to estimate the density should be histogram tending to…
The spatial preferential attachment (SPA) is a model for complex networks. In the SPA model, nodes are embedded in a metric space, and each node has a sphere of influence whose size increases if the node gains an in-link, and otherwise…
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 area query, to find all elements contained in a specified area from a certain set of spatial objects, is a very important spatial query widely required in various fields. A number of approaches have been proposed to implement this…
With recent developments in remote sensing technologies, plot-level forest resources can be predicted utilizing airborne laser scanning (ALS). The prediction is often assisted by mostly vertical summaries of the ALS point clouds. We present…