Related papers: Edge Detecting New Physics the Voronoi Way
Gersho's conjecture in 3D asserts the asymptotic periodicity and structure of the optimal centroidal Voronoi tessellation. This relatively simple crystallization problem remains to date open. We prove bounds on the geometric complexity of…
Convexification techniques have gained increasing interest over the past decades. In this work, we apply a recently developed convexification technique for fractional programs by He, Liu and Tawarmalani (2024) to the problem of determining…
We present a novel approach to the detection and characterization of edges, ridges, and blobs in two-dimensional images which exploits the symmetry properties of directionally sensitive analyzing functions in multiscale systems that are…
We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric…
We present careful numerical convergence studies, using parameterized curves to reach very high resolutions in two dimensions, of a level set method for multiphase curvature motion known as the Voronoi implicit interface method. Our tests…
Edge detection is a fundamental technique in various computer vision tasks. Edges are indeed effectively delineated by pixel discontinuity and can offer reliable structural information even in textureless areas. State-of-the-art heavily…
Detecting anomalous edges and nodes in dynamic networks is critical in various areas, such as social media, computer networks, and so on. Recent approaches leverage network embedding technique to learn how to generate node representations…
We introduce an algorithm to estimate the redshift distribution of a sample of galaxies selected photometrically given a subsample with measured spectroscopic redshifts. The approach uses a non-parametric Voronoi tessellation density…
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…
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…
This work leverages laser vibrometry and the weak form of the sparse identification of nonlinear dynamics (WSINDy) for partial differential equations to learn macroscale governing equations from full-field experimental data. In the…
This work introduces the Hookean-Voronoi energy, a minimal model for the packing of soft, deformable balls. This is motivated by recent studies of quasi-periodic equilibria arising from dense packings of diblock and star polymers.…
Navigating topological transitions in cellular mechanical systems is a significant challenge for existing simulation methods. While abstract models lack predictive capabilities at the cellular level, explicit network representations…
The Hilbert metric is a distance function defined for points lying within a convex body. It generalizes the Cayley-Klein model of hyperbolic geometry to any convex set, and it has numerous applications in the analysis and processing of…
A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…
Many Standard Model extensions predict metastable massive particles that can be detected by looking for displaced decay vertices in the inner detector volume. Current approaches to search for these events in high-energy particle collisions…
I present a concise review of advances realized over the past three years on planar Poisson-Voronoi tessellations. These encompass new analytic results, a new Monte Carlo method, and application to experimental data.
We propose a new strategy to systematically search for new physics processes in particle collisions at the energy frontier. An examination of all possible topologies which give identifiable resonant features in a specific final state leads…
We use the energy method to study the well-posedness of initial-boundary value problems approximated by overset mesh methods in one and two space dimensions for linear constant-coefficient hyperbolic systems. We show that in one space…
In this paper, a novel learning paradigm is presented to automatically identify groups of informative and correlated features from very high dimensions. Specifically, we explicitly incorporate correlation measures as constraints and then…