Related papers: The Voronoi tessellation method in astronomy
The adhesion approximation is a simple analytical model suggested for explanation of the major geometrical features of the observed structure in the galaxy distribution on scales from 1 to (a few)x100/h Mpc. It is based on Burgers' equation…
Encoder-Decoder networks such as U-Nets have been applied successfully in a wide range of computer vision tasks, especially for image segmentation of different flavours across different fields. Nevertheless, most applications lack of a…
High-z Type Ia supernovae are expected to be gravitationally lensed by the foreground distribution of large-scale structure. The resulting magnification of supernovae is statistically measurable, and the angular correlation of the…
Characterizing the spacing of primary dendrite arms in directionally-solidified microstructures is an important step for developing process-structure-property relationships by enabling the quantification of (i) the influence of processing…
In this paper we present formulae for chord length distribution in the framework of Poissonian Voronoi Tessellation (PVT) and non Poissonian Voronoi Tessellation (NPVT). The introduction of the scale parameter in the obtained distributions…
Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for…
We present new techniques to perform adaptive spatial binning of two-dimensional (2D) data to reach a chosen constant signal-to-noise ratio per bin. These methods are required particularly for the proper analysis of Integral Field…
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define…
Weak gravitational lensing provides a unique method to map directly the distribution of dark matter in the universe and to measure cosmological parameters. This cosmic-shear technique is based on the measurement of the weak distortions that…
On megaparsec scales the Universe is permeated by an intricate filigree of clusters, filaments, sheets and voids, the Cosmic Web. For the understanding of its dynamical and hierarchical history it is crucial to identify objectively its…
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…
Tessellations are valuable both conceptually and for analysis in the study of the large-scale structure of the universe. They provide a conceptual model for the 'cosmic web,' and are of great use to analyze cosmological data. Here we…
Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up…
Swarm robotics, or very large-scale robotics (VLSR), has many meaningful applications for complicated tasks. However, the complexity of motion control and energy costs stack up quickly as the number of robots increases. In addressing this…
A jammed packing of frictionless spheres at zero temperature is perfectly specified by the network of contact forces from which mechanical properties can be derived. However, we can alternatively consider a packing as a geometric structure,…
The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi…
We measure the Voronoi density probability distribution function (PDF) for both dark matter and halos in N-body simulations. For the dark matter, Voronoi densities represent the matter density field smoothed on a uniform mass scale, which…
Unlike other schemes that locally violate the essential stability properties of the analytic parabolic and elliptic problems, Voronoi finite volume methods (FVM) and boundary conforming Delaunay meshes provide good approximation of the…
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…
This paper presents a novel approach to the analysis of spatial behavior distribution, utilizing weighted Voronoi diagrams. The objective is to map and understand how an experimental subject moves and spends time in various areas of a given…