### Edge-Aware Point Set Resampling

ACM Transactions on Graphics 2013

Figure 1:Points (222K) acquired by a laser scan (b) are corrupted with noise and not intrinsically equipped with normals. Resampling the data without accounting for surface singularities may smear the sharp features after surface reconstruction (c). Our edge-aware resampling leads to a piecewise smooth reconstruction (d) while preserving the sharp edges. Point colors are the result of normal maps and the original object is shown in (a).

Abstract
Points acquired by laser scanners are not intrinsically equipped with normals, which are essential to surface reconstruction and point set rendering using surfels. Normal estimation is notoriously sensitive to noise. Near sharp features, the computation of noise-free normals becomes even more challenging due to the inherent under-sampling problem at edge singularities. As a result, common edge-aware consolidation techniques such as bilateral smoothing may still produce erroneous normals near the edges. We propose a resampling approach to process a noisy and possibly outlier-ridden point set in an edge-aware manner. Our key idea is to first resample away from the edges so that reliable normals can be computed at the samples, and then based on reliable data, we progressively resample the point set while approaching the edge singularities. We demonstrate that our edge-aware resampling (EAR) algorithm is capable of producing consolidated point sets with noise-free normals and clean preservation of sharp features. We also show that EAR leads to improved performance of edge-aware reconstruction methods and point set rendering techniques.

Reference

[To reference our ALGORITHM, API, CODE or DATA in any publication, please include the bibtex below and a link to this webpage.]

Video

Overview

Figure 2: Overview of EAR scheme. Given a noisy point scan (a) with 163K points, we first resample away from edges, leaving gaps near sharp features (b). Based on reliable normals associated with the point set thus obtained, we upsample while approaching the edges and filling the gaps (c). Point density can be further increased through upsampling to obtain a quality point set rendering (d).

Results

Figure 3: Power of edge-preserving upsampling in our EAR scheme. For a clean and oriented point set with a rather low density (a), APSS (b) and RIMLS (c) cannot provide a good surface definition without upsampling. MLS upsampling (d) improves the performances of APSS (e) and RIMLS (f), but smear sharp features. With EAR (g), APSS (h) and RIMLS (i) successfully preserve the sharp features.

Figure 4: Result comparison on a raw scan (a) using the edge-oblivious Poisson [Kazhdan et al. 2006] and edge-aware RIMLS surface reconstructions. (b) Poisson over oriented PCA normals. (c) Poisson over a filtered and upsampled point set using MLS. (d) Poisson over output of EAR. (e) RIMLS over the same oriented PCA normals used in (b). (f) RIMLS over an oriented point set $S$ after resampling away from edges with $\sigma_p = h$. (g) RIMLS over the same point set $S$ with a much larger $\sigma_p$. (h) RIMLS over the output of the complete EAR with the same $\sigma_p$ as in (f). The ability of EARto lead to piecewise smooth and feature preserving reconstructions in both scenarios is evident. }

Figure 5: EAR for surfel point set rendering, where each output surfel is displayed using a single pixel and colored by its normal direction. The input scan (a) of a shutter blind is noisy and unevenly distributed. MLS resampling (b) smears the edges whereas EAR (d) preserves them well. Comparing (c) and (e), dominating edges are enhanced on EAR point set surface using radiance scaling [Vergne et al. 2010].

Data & Code

Note that the DATA and CODE are free for Research and Education Use ONLY.

Please cite our paper (add the bibtex below) if you use any part of our ALGORITHM, CODE, DATA or RESULTS in any publication.

Acknowledgments

The authors would like to thank all the reviewers for their valuable comments. This work is supported in part by grants from NSFC (61103166), Guangdong Science and Technology Program (2011B050200007), National 863 Program (2011AA010503), Shenzhen Science and Innovation Program (CXB201104220029A), NSERC (293127, 84306 and 611370) and the Israel Science Foundation. The models in Figures 14 and 16 are courtesy of Andrei Sharf and the models in Figures 3, 13 and 15 are courtesy of AIM@SHAPE Shape Repository.

BibTex

@ARTICLE{EAR2013
title = {Edge-Aware Point Set Resampling},
author = {H. Huang and S. Wu and M. Gong and D. Cohen-Or and U. Ascher and H. Zhang},
journal = {ACM Transactions on Graphics},
volume = {32},
issue = {1},
pages = {9:1-9:12},
year = {2013},
}