Laplace-Beltrami Operator on Point Clouds Based on Anisotropic Voronoi Diagram

2017 ◽  
Vol 37 (6) ◽  
pp. 106-117 ◽  
Author(s):  
Hongxing Qin ◽  
Yi Chen ◽  
Yunhai Wang ◽  
Xiaoyang Hong ◽  
Kangkang Yin ◽  
...  
Keyword(s):  
Voronoi Diagram ◽  
Point Clouds ◽  
Beltrami Operator

scholarly journals Point Integral Method for Solving Poisson-Type Equations on Manifolds from Point Clouds with Convergence Guarantees

2017 ◽  
Vol 22 (1) ◽  
pp. 228-258 ◽  
Author(s):  
Zhen Li ◽  
Zuoqiang Shi ◽  
Jian Sun
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Integral Method ◽  
Numerical Experiments ◽  
Point Cloud ◽  
Geometrical Structure ◽  
Point Clouds ◽  
Beltrami Operator ◽  
Applied Fields ◽  
Poisson Type

AbstractPartial differential equations (PDE) on manifolds arise in many areas, including mathematics and many applied fields. Due to the complicated geometrical structure of the manifold, it is difficult to get efficient numerical method to solve PDE on manifold. In the paper, we propose a method called point integral method (PIM) to solve the Poisson-type equations from point clouds. Among different kinds of PDEs, the Poisson-type equations including the standard Poisson equation and the related eigenproblem of the Laplace-Beltrami operator are one of the most important. In PIM, the key idea is to derive the integral equations which approximates the Poisson-type equations and contains no derivatives but only the values of the unknown function. This feature makes the integral equation easy to be discretized from point cloud. In the paper, we explain the derivation of the integral equations, describe the point integral method and its implementation, and present the numerical experiments to demonstrate the convergence of PIM.

Registration and Fusion of UAV LiDAR System Sequence Images and Laser Point Clouds

2020 ◽  
Author(s):  
Jiayong Yu ◽  
Longchen Ma ◽  
Maoyi Tian, ◽  
Xiushan Lu
Keyword(s):  
Point Cloud ◽  
Image Data ◽  
Point Clouds ◽  
Optical Image ◽  
Point Cloud Data ◽  
Feature Points ◽  
Lidar System ◽  
Registration Accuracy ◽  
Cloud Data ◽  
Intensity Image

The unmanned aerial vehicle (UAV)-mounted mobile LiDAR system (ULS) is widely used for geomatics owing to its efficient data acquisition and convenient operation. However, due to limited carrying capacity of a UAV, sensors integrated in the ULS should be small and lightweight, which results in decrease in the density of the collected scanning points. This affects registration between image data and point cloud data. To address this issue, the authors propose a method for registering and fusing ULS sequence images and laser point clouds, wherein they convert the problem of registering point cloud data and image data into a problem of matching feature points between the two images. First, a point cloud is selected to produce an intensity image. Subsequently, the corresponding feature points of the intensity image and the optical image are matched, and exterior orientation parameters are solved using a collinear equation based on image position and orientation. Finally, the sequence images are fused with the laser point cloud, based on the Global Navigation Satellite System (GNSS) time index of the optical image, to generate a true color point cloud. The experimental results show the higher registration accuracy and fusion speed of the proposed method, thereby demonstrating its accuracy and effectiveness.

Model and algorithm for searching for victims in emergency situations and fires using the Voronoi diagram

2019 ◽  
Vol 86 ◽  
pp. 53-61
Author(s):  
N. G. Topolskiy ◽  
◽  
A. V. Mokshantsev ◽  
To Hoang Thanh ◽  
◽  
...  
Keyword(s):  
Voronoi Diagram ◽  
Emergency Situations

Topological feature recognition and blend feature protection for non-duality point clouds

2020 ◽  
Vol 28 (10) ◽  
pp. 2301-2310
Author(s):  
Chun-kang ZHANG ◽  
◽  
Hong-mei LI ◽  
Xia ZHANG
Keyword(s):  
Feature Recognition ◽  
Point Clouds ◽  
Topological Feature
Sign in / Sign up

Export Citation Format

Share Document