Uniformization and Density Adaptation for Point Cloud Data Via Graph Laplacian

Uniformization and Density Adaptation for Point Cloud Data Via Graph Laplacian Point cloud data is one of the most common types of input for geometric processing applications. In this paper, we study the point cloud density adaptation problem that underlies many pre‐processing tasks of points data. Specifically, given a (sparse) set of points Q sampling an unknown surface and a target density function, the goal is to adapt Q to match the target distribution. We propose a simple and robust framework that is effective at achieving both local uniformity and precise global density distribution control. Our approach relies on the Gaussian‐weighted graph Laplacian and works purely in the points setting. While it is well known that graph Laplacian is related to mean‐curvature flow and thus has denoising ability, our algorithm uses certain information encoded in the graph Laplacian that is orthogonal to the mean‐curvature flow. Furthermore, by leveraging the natural scale parameter contained in the Gaussian kernel and combining it with a simulated annealing idea, our algorithm moves points in a multi‐scale manner. The resulting algorithm relies much less on the input points to have a good initial distribution (neither uniform nor close to the target density distribution) than many previous refinement‐based methods. We demonstrate the simplicity and effectiveness of our algorithm with point clouds sampled from different underlying surfaces with various geometric and topological properties. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computer Graphics Forum Wiley

Uniformization and Density Adaptation for Point Cloud Data Via Graph Laplacian

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
© 2018 The Eurographics Association and John Wiley & Sons Ltd.
ISSN
0167-7055
eISSN
1467-8659
D.O.I.
10.1111/cgf.13293
Publisher site
See Article on Publisher Site

Abstract

Point cloud data is one of the most common types of input for geometric processing applications. In this paper, we study the point cloud density adaptation problem that underlies many pre‐processing tasks of points data. Specifically, given a (sparse) set of points Q sampling an unknown surface and a target density function, the goal is to adapt Q to match the target distribution. We propose a simple and robust framework that is effective at achieving both local uniformity and precise global density distribution control. Our approach relies on the Gaussian‐weighted graph Laplacian and works purely in the points setting. While it is well known that graph Laplacian is related to mean‐curvature flow and thus has denoising ability, our algorithm uses certain information encoded in the graph Laplacian that is orthogonal to the mean‐curvature flow. Furthermore, by leveraging the natural scale parameter contained in the Gaussian kernel and combining it with a simulated annealing idea, our algorithm moves points in a multi‐scale manner. The resulting algorithm relies much less on the input points to have a good initial distribution (neither uniform nor close to the target density distribution) than many previous refinement‐based methods. We demonstrate the simplicity and effectiveness of our algorithm with point clouds sampled from different underlying surfaces with various geometric and topological properties.

Journal

Computer Graphics ForumWiley

Published: Jan 1, 2018

Keywords: ; ; ;

References

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