Related papers: Delaunay Bifiltrations of Functions on Point Cloud…

Large-scale datasets are usually required to train deep neural networks, but it increases the computational complexity hindering the practical applications. Recently, dataset distillation for images and texts has been attracting a lot of…

Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…

Following the tremendous success of transformer in natural language processing and image understanding tasks, in this paper, we present a novel point cloud representation learning architecture, named Dual Transformer Network (DTNet), which…

The $k$-cover of a point cloud $X$ in $\mathbb{R}^{d}$ at radius $r$ is the set of all points within distance $r$ of at least $k$ points of $X$. By varying $r$ and $k$ we obtain a two-parameter filtration known as the multicover…

In topological data analysis (TDA), a longstanding challenge is to recognize underlying geometric structures in noisy data. One motivating examples is the shape of a point cloud in Euclidean space given by image. Carlsson et al. proposed a…

We propose a new refinement algorithm to generate size-optimal quality-guaranteed Delaunay triangulations in the plane. The algorithm takes $O(n \log n + m)$ time, where $n$ is the input size and $m$ is the output size. This is the first…

An extension of the restricted Delaunay-refinement algorithm for surface mesh generation is described, where a new point-placement scheme is introduced to improve element quality in the presence of mesh size constraints. Specifically, it is…

Point clouds are crucial for capturing three-dimensional data but often suffer from incompleteness due to limitations such as resolution and occlusion. Traditional methods typically rely on point-based approaches within discriminative…

Reliable knowledge of road boundaries is critical for autonomous vehicle navigation. We propose a robust curb detection and filtering technique based on the fusion of camera semantics and dense lidar point clouds. The lidar point clouds are…

In this paper, we present a novel deep method to reconstruct a point cloud of an object from a single still image. Prior arts in the field struggle to reconstruct an accurate and scalable 3D model due to either the inefficient and expensive…

The alpha complex, a subset of the Delaunay triangulation, has been extensively used as the underlying representation for biomolecular structures. We propose a GPU-based parallel algorithm for the computation of the alpha complex, which…

With the development of 3D sensing technologies, point clouds have attracted increasing attention in a variety of applications for 3D object representation, such as autonomous driving, 3D immersive tele-presence and heritage reconstruction.…

In our physically inspired in-tree (IT) based clustering algorithm and the series after it, there is only one free parameter involved in computing the potential value of each point. In this work, based on the Delaunay Triangulation or its…

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing…

We introduce a novel learning-based, visibility-aware, surface reconstruction method for large-scale, defect-laden point clouds. Our approach can cope with the scale and variety of point cloud defects encountered in real-life Multi-View…

Point cloud is a collection of 3D coordinates that are discrete geometric samples of an object's 2D surfaces. Imperfection in the acquisition process means that point clouds are often corrupted with noise. Building on recent advances in…

Point cloud compression plays a crucial role in reducing the huge cost of data storage and transmission. However, distortions can be introduced into the decompressed point clouds due to quantization. In this paper, we propose a novel…

High quality upsampling of sparse 3D point clouds is critically useful for a wide range of geometric operations such as reconstruction, rendering, meshing, and analysis. In this paper, we propose a data-driven algorithm that enables an…

In this paper, we propose a novel gradient-based method to optimize curvilinear masks in optical lithography. The mask pattern is represented by periodic B-spline curves. We apply Delaunay triangulation to discretize the domains circled by…

This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…