Related papers: Geodesic Centroidal Voronoi Tessellations: Theorie…
Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set…
Convolutional Neural Networks (Convnets) have achieved good results in a range of computer vision tasks the recent years. Though given a lot of attention, visualizing the learned representations to interpret Convnets, still remains a…
Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…
In this paper, we develop a novel method for fast geodesic distance queries. The key idea is to embed the mesh into a high-dimensional space, such that the Euclidean distance in the high-dimensional space can induce the geodesic distance in…
3D meshes are fundamental data representations for capturing complex geometric shapes in computer vision and graphics applications. While Convolutional Neural Networks (CNNs) have excelled in structured data like images, extending them to…
Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…
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…
Though the underlying fields associated with vector-valued environmental data are continuous, observations themselves are discrete. For example, climate models typically output grid-based representations of wind fields or ocean currents,…
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…
Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
Intrinsic Delaunay triangulation (IDT) is a fundamental data structure in computational geometry and computer graphics. However, except for some theoretical results, such as existence and uniqueness, little progress has been made towards…
Mimicking natural tessellation patterns is a fascinating multi-disciplinary problem. Geometric methods aiming at reproducing such partitions on surface meshes are commonly based on the Voronoi model and its variants, and are often faced…
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…
Video depth estimation extends monocular prediction into the temporal domain to ensure coherence. However, existing methods often suffer from spatial blurring in fine-detail regions and temporal inconsistencies. We argue that current…
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…
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…
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…
There exists a correlation between geospatial activity temporal patterns and type of land use. A novel self-supervised approach is proposed to stratify landscape based on mobility activity time series. First, the time series signal is…
This draft summarizes some basics about geometric computer vision needed to implement efficient computer vision algorithms for applications that use measurements from at least one digital camera mounted on a moving platform with a special…