Related papers: Delaunay Bifiltrations of Functions on Point Cloud…
In this paper we present a scalable approach for robustly computing a 3D surface mesh from multi-scale multi-view stereo point clouds that can handle extreme jumps of point density (in our experiments three orders of magnitude). The…
Given a smooth submanifold of the Euclidean space, a finite point cloud and a scale parameter, we introduce a construction which we call the flat Delaunay complex (FDC). This is a variant of the tangential Delaunay complex (TDC) introduced…
This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A…
In this paper a new connection between the discrete conformal geometry problem of disk pattern construction and the continuous conformal geometry problem of metric uniformization is presented. In a nutshell, we discuss how to construct disk…
Point clouds produced by 3D scanning are often sparse, non-uniform, and noisy. Recent upsampling approaches aim to generate a dense point set, while achieving both distribution uniformity and proximity-to-surface, and possibly amending…
Distribution-to-distribution (D2D) point cloud registration techniques such as the Normal Distributions Transform (NDT) can align point clouds sampled from unstructured scenes and provide accurate bounds of their own solution error…
Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…
Advanced representation learning techniques require reliable and general evaluation methods. Recently, several algorithms based on the common idea of geometric and topological analysis of a manifold approximated from the learned data…
We show how to efficiently solve a clustering problem that arises in a method to evaluate functions of matrices. The problem requires finding the connected components of a graph whose vertices are eigenvalues of a real or complex matrix and…
The mixing properties of vapor content, temperature and particle fields are of paramount importance in cloud turbulence as they pertain to essential processes, such as cloud water droplet evaporation and entrainment. Our study examines the…
In this paper, a novel learning-based network, named DeepDT, is proposed to reconstruct the surface from Delaunay triangulation of point cloud. DeepDT learns to predict inside/outside labels of Delaunay tetrahedrons directly from a point…
As incremental Structure from Motion algorithms become effective, a good sparse point cloud representing the map of the scene becomes available frame-by-frame. From the 3D Delaunay triangulation of these points, state-of-the-art algorithms…
We present Bayesian Diffusion Models (BDM), a prediction algorithm that performs effective Bayesian inference by tightly coupling the top-down (prior) information with the bottom-up (data-driven) procedure via joint diffusion processes. We…
Reconstructing building wireframe from airborne LiDAR point clouds yields a compact, topology-centric representation that enables structural understanding beyond dense meshes. Yet a key limitation persists: conventional methods have failed…
Point cloud analysis is challenging due to the irregularity of the point cloud data structure. Existing works typically employ the ad-hoc sampling-grouping operation of PointNet++, followed by sophisticated local and/or global feature…
In contrast to the literature where local patterns in 3D point clouds are captured by customized convolutional operators, in this paper we study the problem of how to effectively and efficiently project such point clouds into a 2D image…
In recent years, the performance of point cloud models has been rapidly improved. However, due to the limited amount of relevant explainability studies, the unreliability and opacity of these black-box models may lead to potential risks in…
We propose the first GPU algorithm for the 3D triangulation refinement problem. For an input of a piecewise linear complex $\mathcal{G}$ and a constant $B$, it produces, by adding Steiner points, a constrained Delaunay triangulation…
The Hilbert metric is a distance function defined for points lying within the interior of a convex body. It arises in the analysis and processing of convex bodies, machine learning, and quantum information theory. In this paper, we show how…
High-quality point cloud data is a critical foundation for tasks such as autonomous driving and 3D reconstruction. However, LiDAR-based point cloud acquisition is often affected by various disturbances, resulting in a large number of noise…