Related papers: Edge Detecting New Physics the Voronoi Way
Magnetic fields play an important role in astrophysics on a wide variety of scales, ranging from the Sun and compact objects to galaxies and galaxy clusters. Here we discuss a novel implementation of ideal magnetohydrodynamics (MHD) in the…
We study the Voronoi and void statistics of super-homogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Super-homogeneous or hyperuniform point patterns arise in one-component plasmas,…
The Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and…
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to…
In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we consider a variational functional that penalizes oscillations…
Power line detection is a critical inspection task for electricity companies and is also useful in avoiding drone obstacles. Accurately separating power lines from the surrounding area in the aerial image is still challenging due to the…
Line segment detection plays a cornerstone role in computer vision tasks. Among numerous detection methods that have been recently proposed, the ones based on edge drawing attract increasing attention owing to their excellent detection…
In this paper we develop a numerical method for solving a class of optimization problems known as optimal location or quantization problems. The target energy can be written either in terms of atomic measures and the Wasserstein distance or…
Objective: Modelling the associations from high-throughput experimental molecular data has provided unprecedented insights into biological pathways and signalling mechanisms. Graphical models and networks have especially proven to be useful…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
We prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson random sets in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. The result relies on…
We develop a new edge detection algorithm that tackles two important issues in this long-standing vision problem: (1) holistic image training and prediction; and (2) multi-scale and multi-level feature learning. Our proposed method,…
For pedestrians moving without spatial constraints, extensive research has been devoted to develop methods of density estimation. In this paper we present a new approach based on Voronoi cells, offering a means to estimate density for…
We present a paralell approach to discrete geometry: the first one introduces Voronoi cell complexes from statistical tessellations in order to know the mean scalar curvature in term of the mean number of edges of a cell. The second one…
We consider the Voronoi tessellation associated to a stationary simple point process on $\mathbb{R}^d$ with finite and positive intensity. We introduce the Delaunay triangulation as its dual graph, i.e.~the graph with vertex set given by…
Consider a homogeneous Poisson point process of the Euclidean plane and its Voronoi tessellation. The present note discusses the properties of two stationary point processes associated with the latter and depending on a parameter $\theta$.…
Edges of an image are considered a crucial type of information. These can be extracted by applying edge detectors with different methodology. Edge detection is a vital step in computer vision tasks, because it is an essential issue for…
We present an edge labeling of order-$k$ Voronoi diagrams, $V_k(S)$, of point sets $S$ in the plane, and study properties of the regions defined by them. Among them, we show that $V_k(S)$ has a small orientable cycle and path double cover,…
Edge detection in images is the foundation of many complex tasks in computer graphics. Due to the feature loss caused by multi-layer convolution and pooling architectures, learning-based edge detection models often produce thick edges and…
I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm…