Related papers: Efficient Computation of Voronoi Diagrams Using Po…
Cell nuclei segmentation is one of the most important tasks in the analysis of biomedical images. With ever-growing sizes and amounts of three-dimensional images to be processed, there is a need for better and faster segmentation methods.…
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…
In this paper we study the most-demanding predicate for computing the Euclidean Voronoi diagram of axes-aligned line segments, namely the Incircle predicate. Our contribution is two-fold: firstly, we describe, in algorithmic terms, how to…
This paper presents a new approach for precisely estimating the renal vascular dominant region using a Voronoi diagram. To provide computer-assisted diagnostics for the pre-surgical simulation of partial nephrectomy surgery, we must obtain…
Late-interaction models such as ColBERT offer competitive performance across various retrieval tasks but require storing a dense embedding for each document token, leading to a substantial index storage overhead. Past works address this by…
Let $P$ be a simple polygon with $n$ vertices. For any two points in $P$, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in $P$. Given a set $S$ of $m$ sites being a subset…
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…
Cells of Voronoi diagrams in two dimensions are usually considered as having edges of zero width. However, this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large. In this…
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 use of numerical simulations in science is ever increasing and with it the computational size. In many cases single processors are no longer adequate and simulations are run on multiple core machines or supercomputers. One of the key…
We consider the Voronoi diagram of lines in $\mathbb{R}^3$ under the Euclidean metric, and give a full classification of its structure in the base case of four lines in general position. We first show that the number of vertices in the…
Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata --- finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting,…
This paper introduces a new open-source software program called VoroTop, which uses Voronoi topology to analyze local structure in atomic systems. Strengths of this approach include its abilities to analyze high-temperature systems and to…
Image segmentation plays an essential role in nuclei image analysis. Recently, the segment anything model has made a significant breakthrough in such tasks. However, the current model exists two major issues for cell segmentation: (1) the…
An optimal data partitioning in parallel & distributed implementation of clustering algorithms is a necessary computation as it ensures independent task completion, fair distribution, less number of affected points and better & faster…
Given a tesselation of the plane, defined by a planar straight-line graph $G$, we want to find a minimal set $S$ of points in the plane, such that the Voronoi diagram associated with $S$ "fits" \ $G$. This is the Generalized Inverse Voronoi…
Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…
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…
Deep learning has been used as a powerful tool for various tasks in computer vision, such as image segmentation, object recognition and data generation. A key part of end-to-end training is designing the appropriate encoder to extract…
In distributed mobile sensing applications, networks of agents that are heterogeneous respecting both actuation as well as body and sensory footprint are often modelled by recourse to power diagrams --- generalized Voronoi diagrams with…