Fast Resampling of 3D Point Clouds via Graphs

To reduce the cost of storing, processing and visualizing a large-scale point cloud, we propose a randomized resampling strategy that selects a representative subset of points while preserving application-dependent features. The strategy is based on graphs, which can represent underlying surfaces and lend themselves well to efficient computation. We use a general feature-extraction operator to represent application-dependent features and propose a general reconstruction error to evaluate the quality of resampling; by minimizing the error, we obtain a general form of optimal resampling distribution. The proposed resampling distribution is guaranteed to be shift-, rotationand scale-invariant in the 3D space. We then specify the featureextraction operator to be a graph filter and study specific resampling strategies based on allpass, lowpass, highpass graph filtering and graph filter banks. We validate the proposed methods on three applications: large-scale visualization, accurate registration and robust shape modeling demonstrating the effectiveness and efficiency of the proposed resampling methods. IEEE Transactions on Signal Processing This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2017 201 Broadway, Cambridge, Massachusetts 02139