Related papers: VoronoiNet: General Functional Approximators with …

We introduce VoroFields, a hierarchical neural-field framework for approximating generalized Voronoi diagrams of finite geometric site sets in low-dimensional domains under arbitrary evaluable point-to-site distances. Instead of…

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…

We investigate the problem of image retrieval based on visual queries when the latter comprise arbitrary regions-of-interest (ROI) rather than entire images. Our proposal is a compact image descriptor that combines the state-of-the-art in…

Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly…

Representing a scanned map of the real environment as a topological structure is an important research topic in robotics. Since topological representations of maps save a huge amount of map storage space and online computing time, they are…

Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define…

Patterns stored within pre-trained deep neural networks compose large and powerful descriptive languages that can be used for many different purposes. Typically, deep network representations are implemented within vector embedding spaces,…

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…

We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional…

Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…

Recently, implicit neural representations have gained popularity for learning-based 3D reconstruction. While demonstrating promising results, most implicit approaches are limited to comparably simple geometry of single objects and do not…

In stark contrast to the case of images, finding a concise, learnable discrete representation of 3D surfaces remains a challenge. In particular, while polygon meshes are arguably the most common surface representation used in geometry…

Voronoi treemaps are used to depict nodes and their hierarchical relationships simultaneously. However, in addition to the hierarchical structure, data attributes, such as co-occurring features or similarities, frequently exist. Examples…

Voronoi diagrams, and their more general weighted counterpart, power diagrams, are fundamental geometric constructs with wide-ranging applications. Recently, they have gained renewed attention in mesh-based neural rendering. Despite being…

The rapid progress in image classification has been largely driven by the adoption of Graph Convolutional Networks (GCNs), which offer a robust framework for handling complex data structures. This study introduces a novel approach that…

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…

With the advent of deep neural networks, learning-based approaches for 3D reconstruction have gained popularity. However, unlike for images, in 3D there is no canonical representation which is both computationally and memory efficient yet…

For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi…

In this article, we investigate vacuum leakage detection problems in composite manufacturing. Our approach uses Voronoi diagrams, a well-known structure in discrete geometry. The Voronoi diagram of the vacuum connection positions partitions…