Related papers: Delaunay Bifiltrations of Functions on Point Cloud…

Point cloud processing is a challenging task due to its sparsity and irregularity. Prior works introduce delicate designs on either local feature aggregator or global geometric architecture, but few combine both advantages. We propose…

The reconstruction of real-world surfaces is on high demand in various applications. Most existing reconstruction approaches apply 3D scanners for creating point clouds which are generally sparse and of low density. These points clouds will…

We consider offsets of a union of convex objects. We aim for a filtration, a sequence of nested cell complexes, that captures the topological evolution of the offsets for increasing radii. We describe methods to compute a filtration based…

Point clouds acquired from 3D sensors are usually sparse and noisy. Point cloud upsampling is an approach to increase the density of the point cloud so that detailed geometric information can be restored. In this paper, we propose a Dual…

Point cloud is point sets defined in 3D metric space. Point cloud has become one of the most significant data format for 3D representation. Its gaining increased popularity as a result of increased availability of acquisition devices, such…

We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties…

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…

Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…

We consider the point cloud registration problem, the task of finding a transformation between two point clouds that represent the same object but are expressed in different coordinate systems. Our approach is not based on a point-to-point…

We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…

IIn computational geometry, the construction of essential primitives like convex hulls, Voronoi diagrams and Delaunay triangulations require the evaluation of the signs of determinants, which are sums of products. The same signs are needed…

Point cloud is often regarded as a discrete sampling of Riemannian manifold and plays a pivotal role in the 3D image interpretation. Particularly, rotation perturbation, an unexpected small change in rotation caused by various factors (like…

The goal of this paper is to address the problem of global point cloud registration (PCR) i.e., finding the optimal alignment between point clouds irrespective of the initial poses of the scans. This problem is notoriously challenging for…

Point cloud denoising aims to restore clean point clouds from raw observations corrupted by noise and outliers while preserving the fine-grained details. We present a novel deep learning-based denoising model, that incorporates normalizing…

Via circle pattern techniques, random planar triangulations (with angle variables) are mapped onto Delaunay triangulations in the complex plane. The uniform measure on triangulations is mapped onto a conformally invariant spatial point…

We propose DeepMapping, a novel registration framework using deep neural networks (DNNs) as auxiliary functions to align multiple point clouds from scratch to a globally consistent frame. We use DNNs to model the highly non-convex mapping…

Formulating boundary value problems for multidimensional partial derivative equations in terms of invariant operators of vector (tensor) analysis is convenient. Computational algorithms for approximate solutions are based on constructing…

Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functions, which assert to what extent a given object exhibits some…

In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…

Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex…