Related papers: Efficient Computation of Voronoi Diagrams Using Po…
Cellular structures found in nature exhibit remarkable properties such as high strength, high energy absorption, excellent thermal/acoustic insulation, and fluid transfusion. Many of these structures are Voronoi-like; therefore researchers…
In view of the recent paradigm shift in deep AI based image processing methods, medical image processing has advanced considerably. In this study, we propose a novel deep neural network (DNN), entitled InceptNet, in the scope of medical…
Identifying Blaschke-Santal\'o diagrams is an important topic that essentially consists in determining the image $Y=F(X)$ of a map $F:X\to{\mathbb{R}}^d$, where the dimension of the source space $X$ is much larger than the one of the target…
Let $S$ be a set of $n$ points in general position in $\mathbb{R}^d$. The order-$k$ Voronoi diagram of $S$, $V_k(S)$, is a subdivision of $\mathbb{R}^d$ into cells whose points have the same $k$ nearest points of $S$. Sibson, in his seminal…
The size distributions of 2D and 3D Voronoi cells and of cells of $V_p(2,3)$,--2D cut of 3D Voronoi diagram--are explored, with the single-parameter (re-scaled) gamma distribution playing a central role in the analytical fitting.…
Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…
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…
Point-to-mesh distance queries are fundamental in computer graphics and geometric modeling. While the state-of-the-art P2M method achieves high-speed queries via Voronoi-based localization, it suffers from prohibitive precomputation costs.…
Vertex connectivity and edge connectivity are fundamental concepts in graph theory that have been widely studied from both structural and algorithmic perspectives. The focus of this paper is on computing these two parameters for graphs…
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…
In Computer Vision, edge detection is one of the favored approaches for feature and object detection in images since it provides information about their objects boundaries. Other region-based approaches use probabilistic analysis such as…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…
A novel algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is tested. Neighbouring tracer particles are naturally identified through…
Improving on the Voronoi cell based techniques of Micciancio and Voulgaris (SIAM J. Comp. 13), and Sommer, Feder and Shalvi (SIAM J. Disc. Math. 09), we give a Las Vegas $\tilde{O}(2^n)$ expected time and space algorithm for CVPP (the…
Geodesic models are known as an efficient tool for solving various image segmentation problems. Most of existing approaches only exploit local pointwise image features to track geodesic paths for delineating the objective boundaries.…
In cellular networks, users are grouped into different cells and served by different access points (base stations) that provide wireless access to services and applications. In general, the service demand is very heterogeneous,…
We introduce a dynamical system based on the vertices of Voronoi tessellations. This dynamical system acts on finite or discrete point sets in the plane, taking a point set to the vertex set of its Voronoi tessellation. We explore the…
Anomaly detection aims to identify data instances that deviate significantly from majority of data, which has been widely used in fraud detection, network security, and industrial quality control. Existing methods struggle with datasets…
We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the…
We introduce two new methods to obtain reliable velocity field statistics from N-body simulations, or indeed from any general density and velocity fluctuation field sampled by discrete points. These methods, the {\it Voronoi tessellation…