Related papers: Voronoi Diagram: The Generator Recognition Problem
We propose a text-guided variational image generation method to address the challenge of getting clean data for anomaly detection in industrial manufacturing. Our method utilizes text information about the target object, learned from…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
We present an efficient algorithm for a problem in the interface between clustering and graph embeddings. An embedding $\varphi:G\rightarrow M$ of a graph $G$ into a 2-manifold $M$ maps the vertices in $V(G)$ to distinct points and the…
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…
The traditional approach to mobile phone positioning is based on the assumption that the geographical location of a cell tower recorded in a call details record (CDR) is a proxy for a device's location. A Voronoi tessellation is then…
Recent work on distinct multicellular organisms has revealed a hitherto unknown type of biological noise; rather than a regular arrangement, cellular neighborhood volumes, obtained by Voronoi tessellations of the cell locations, are broadly…
We use Lie sphere geometry to describe two large categories of generalized Voronoi diagrams that can be encoded in terms of the Lie quadric, the Lie inner product, and polyhedra. The first class consists of diagrams defined in terms of…
We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based…
Mathematical morphology (MM) helps to describe and analyze shapes using set theory. MM can be effectively applied to binary images which are treated as sets. Basic morphological operators defined can be used as an effective tool in image…
The novel approach was developed for multilevel signal detection in channels with impulsive non-Gaussian noise. This approach consists of using morphological nonlinear image filtration principles for two dimensional signals. It is a new…
Starting from three-dimensional volume data of a granular packing, as e.g. obtained by X-ray Computed Tomography, we discuss methods to first detect the individual particles in the sample and then analyze their properties. This analysis…
Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier…
Neural Radiance Fields (NeRFs) learn to represent a 3D scene from just a set of registered images. Increasing sizes of a scene demands more complex functions, typically represented by neural networks, to capture all details. Training and…
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…
Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…
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…
votess is a library for computing parallel 3D Voronoi tessellations on heterogeneous platforms, from CPUs and GPUs, to future accelerator architectures. To do so, it leverages the SYCL abstraction layer to achieve portability and…
Higher-order Voronoi diagrams and Delaunay mosaics in polygonal metrics have only recently been studied, yet no tools exist for visualizing them. We introduce a tool that fills this gap, providing dynamic interactive software for…
Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic…