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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…
Point cloud completion is the task of predicting complete geometry from partial observations using a point set representation for a 3D shape. Previous approaches propose neural networks to directly estimate the whole point cloud through…
Since the Voronoi diagram appears in many applications, the topic of improving its computational efficiency remains attractive. We propose a novel yet efficient method to compute Voronoi diagrams bounded by a given domain, i.e., the clipped…
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…
Learning and selecting important points on a point cloud is crucial for point cloud understanding in various applications. Most of early methods selected the important points on 3D shapes by analyzing the intrinsic geometric properties of…
Learning new representations of 3D point clouds is an active research area in 3D vision, as the order-invariant point cloud structure still presents challenges to the design of neural network architectures. Recent works explored learning…
Two-dimensional Delaunay triangulation is a fundamental aspect of computational geometry. This paper presents a novel algorithm that is specifically designed to ensure the correctness of 2D Delaunay triangulation, namely the Polygonal…
Technology to recognize the type of component represented by a point cloud is required in the reconstruction process of an as-built model of a process plant based on laser scanning. The reconstruction process of a process plant through…
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…
In this paper, we propose a method to segment regions in three-dimensional point clouds. We assume that (i) the shape and the number of regions in the point cloud are not known and (ii) the point cloud may be noisy. The method consists of…
Urban reconstruction from a video captured by a surveying vehicle constitutes a core module of automated mapping. When computational power represents a limited resource and, a detailed map is not the primary goal, the reconstruction can be…
Although 3D point cloud data has received widespread attentions as a general form of 3D signal expression, applying point clouds to the task of dense correspondence estimation between 3D shapes has not been investigated widely. Furthermore,…
The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi…
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…
3D object recognition has attracted wide research attention in the field of multimedia and computer vision. With the recent proliferation of deep learning, various deep models with different representations have achieved the…
We present a method that detects boundaries of parts in 3D shapes represented as point clouds. Our method is based on a graph convolutional network architecture that outputs a probability for a point to lie in an area that separates two or…
A laser scanner can easily acquire the geometric data of physical environments in the form of a point cloud. Recognizing objects from a point cloud is often required for industrial 3D reconstruction, which should include not only geometry…
In recent years, point cloud representation has become one of the research hotspots in the field of computer vision, and has been widely used in many fields, such as autonomous driving, virtual reality, robotics, etc. Although deep learning…
Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve…
Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a…