相关论文: Bregman Voronoi Diagrams: Properties, Algorithms a…

In this paper, we propose a novel space partitioning strategy for implicit hierarchy visualization such that the new plot not only has a tidy layout similar to the treemap, but also is flexible to data changes similar to the Voronoi…

Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algorithms for approximate solutions are based on constructing…

Classical linear metric learning methods have recently been extended along two distinct lines: deep metric learning methods for learning embeddings of the data using neural networks, and Bregman divergence learning approaches for extending…

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…

Detachment and fracture are central to many tissue-level processes, but they are challenging to simulate with Voronoi-type models that typically assume a confluent tissue. Here we analyze the finite Voronoi model, a nonconfluent extension…

In quantum information theory, a geometric approach, known as "quantum information geometry," has been considered as a powerful method. In this thesis, we give a computational geometric interpretation to the geometric structure of a quantum…

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…

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…

Voronoi and related diagrams have technological applications, for example, in motion planning and surface reconstruction, and also find significant use in materials science, molecular biology, and crystallography. Apollonius diagrams…

Consider a Voronoi tiling of the Euclidean space based on a realization of a inhomogeneous Poisson random set. A Voronoi polyomino is a finite and connected union of Voronoi tiles. In this paper we provide tail bounds for the number of…

This paper considers several approximate operators used in a particle method based on a Voronoi diagram. We introduce and study our approximate operators on gradient and Laplace operators. We derive error estimates for these approximate…

The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively…

Calculations on atomistic scale are necessary for understanding of physical phenomena occurring during advanced processing of liquids, slurries, and nano-ceramics composite materials. This paper describes some new ideas for using the…

Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…

We present an extension of Voronoi diagrams where when considering which site a client is going to use, in addition to the site distances, other site attributes are also considered (for example, prices or weights). A cell in this diagram is…

The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic…

Classical objects in computational geometry are defined by explicit relations. Several years ago the pioneering works of T. Asano, J. Matousek and T. Tokuyama introduced "implicit computational geometry", in which the geometric objects are…

We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes.…

For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi…

The round-trip distance function on a geographic network (such as a road network, flight network, or utility distribution grid) defines the "distance" from a single vertex to a pair of vertices as the minimum length tour visiting all three…