A feature-preserving framework for point cloud denoising

doi:10.1016/j.cad.2020.102857

Computer-Aided Design

Volume 127, October 2020, 102857

https://doi.org/10.1016/j.cad.2020.102857 Get rights and content

Highlights

•
An anisotropic second order regularization method is presented to restore the point normal field.
•
A bi-tensor voting scheme, combining the normal and point tensor voting, is proposed to detect features on the noisy input.
•
A simple yet effective RANSAC-based algorithm is introduced to estimate the multiple normals at each feature point.

Abstract

Point cloud denoising has been an attractive problem in geometry processing. The main challenge is to eliminate noise while preserving different levels of features and preventing unnatural effects (such as over-sharpened artifacts on smoothly curved faces and cross artifacts on sharp edges). In this paper, we propose a novel feature-preserving framework to achieve these goals. Firstly, we newly define some discrete operators on point clouds, which can be used to construct a second order regularization for restoring a point normal field. Then, based on the filtered normals, we perform a feature detection step by a bi-tensor voting scheme. As will be seen, it is robust against noise and can locate underlying geometric features accurately. Finally, we reposition points with a multi-normal strategy by using a simple yet effective RANSAC-based algorithm. Intensive experimental results show that the proposed method performs favorably compared to other state-of-the-art approaches.

Graphical abstract

Introduction

Point cloud data has attracted considerable attention due to the rapid development of scanning devices (e.g., Microsoft Kinect, Xtion Pro, Google Project Tango, and Intel RealSense). However, even with high-fidelity devices, the corruption of scanned data is usually inevitable from the degradation during its acquisition. Thus, recovering high quality point clouds from the noisy inputs is a typical inverse problem in geometry processing. The main challenge is to distinguish sharp features and noise as they are of high frequency information, and at the same time prevent unnatural effects during the denoising process.

Over the years, state-of-the-art methods have been proposed for recovering noise-free point clouds. In [1], Öztireli et al. proposed a method combining moving least square and local kernel regression to preserve geometric features. However, when the noise level increases, it is unlikely to perform well with satisfactory results. Especially, this limitation is more severe for point clouds containing sharp features. By using robust principal component analysis, [2] exploits sparse characteristics of subspaces to preserve sharp features, which is also robust against outliers. Unfortunately, [2] usually over-sharpens curved features because it depends on sparse and low-rank modeling. In [3], Huang et al. developed an edge-aware upsampling technique to recover the point cloud with well-preserved sharp features. Nevertheless, it sometimes flattens fine details, since it chooses large neighborhood size to pull points away from sharp features for upsampling. Moreover, this method may be sensitive to high density noise, because of its unfaithful upsampling around sharp features without explicitly estimating the point normal field. Sun et al. [4] extended $ℓ_{0}$ minimization to point clouds for preserving sharp features. Although their method achieves impressive results for data with piecewise constant priors, it tends to flatten smoothly curved regions and produce pseudo edges in these regions due to its high requirement of sparsity.

As we have seen, the aforementioned state-of-the-art methods are either less able to preserve sharp features well, or may produce unnatural artifacts in denoised results. To overcome these limitations, we propose a novel feature-preserving framework to recover point normals as well as positions. It consists of three cascaded stages: normal filtering; feature detection; and multi-normal point updating, as illustrated in Fig. 1. In the first stage, we present an anisotropic second order variational method to restore the normal field from the noisy input; see Fig. 1, Fig. 1. Based on the filtered normals, we define normal and point voting tensors, and then introduce a bi-tensor voting scheme to detect features; see Fig. 1(c). The scheme utilizes the best properties of the normal and point tensor voting and overcomes the weakness of both. In the following multi-normal point updating stage, we estimate the multiple normals per feature point using a RANSAC-based algorithm; see Fig. 1(d). Then, we update point positions according to the restored normals (the normals at non-feature points are produced by our second order normal filtering, and those at feature points are estimated by the RANSAC-based algorithm); see Fig. 1(e). The main contributions of the paper are summarized as follows:

•
An anisotropic second order regularization method is presented to restore the point normal field. It is able to preserve sharp features well and simultaneously prevent unnatural effects in denoised results.
•
A bi-tensor voting scheme, which combines the normal and point tensor voting, is proposed to detect features on the noisy input. The combined technique is not only robust against noise but also can accurately locate features.
•
A simple yet effective RANSAC-based algorithm is introduced to estimate the multiple normals at each feature point. It can significantly reduce cross artifacts during the point reconstruction process.

Section snippets

Related work

Point cloud denoising is a fundamental problem in digital geometry processing, which has been studied extensively. It is beyond our scope to review numerous existing methods, and we only review noticeable ones closely related to this work. Generally, we classify point cloud denoising methods into four main categories as following.

MLS-based methods. Moving least squares (MLS) has been originally designed for surface reconstruction by Alexa et al. [5]. Later, many extensions and modifications [6]

Normal filtering via second order regularization

The noisy point cloud $P$ can be considered as a set of unorganized points ${p_{i}}_{i = 1}^{M}$ sampled from a 2-dimensional manifold in $R^{3}$ , where $M$ is the number of sampled points. For the $i$ th point of $P$ , its index set of K-nearest neighborhood (KNN) is denoted as $N (i)$ , which consists of $K$ elements. We further arrange KNNs of the point in a counterclockwise order using local PCA.

Feature detection by bi-tensor voting

The tensor voting is a fundamental tool in geometry processing for accurately detecting features on high-quality meshes [25], [26]. Recently, it was extended to point clouds by analyzing the normal voting tensor [27], [28] or the point voting tensor [29], [30]. However, performing direct the normal or point tensor voting on noisy point clouds usually produces spurious effects. Specifically, the point tensor voting is sensitive to the noise, which tends to produce pseudo features in smooth

Multi-normal point updating

After obtaining filtered point normals, it is necessary to reposition points to match the filtered normals. Because the single normals at feature points are ambiguous and undefinable, it is necessary to adopt multi-normal point updating strategy as proposed in previous works [30], [31], [32]. This technique can overcome cross artifacts at sharp features and preserve sharp features better than the conventional single normal based approaches, especially when the point cloud is corrupted with high

Experimental results and comparisons

To testify the performance of our point cloud denoising method, we perform it on both synthetic and real data. The tested point clouds are contaminated by either synthetic or raw scanned noise. The synthetic noise is generated by a zero-mean Gaussian function with standard deviation proportional to the diagonal of the axis-aligned bounding box of the ground truth. We also provide visual and quantitative comparisons of our method to the state-of-the-art ones including RIMLS [1], MRPCA [2], EAR

Conclusion

In this paper, a feature-preserving framework has been proposed to recover a noisy-free point cloud. It first utilizes a second order regularization to restore the normal field. With the filtered normals, a well-designed bi-tensor voting scheme is introduced to detect features, which overcomes the weakness of the normal and point tensor voting. Finally, point positions are reconstructed by the multi-normal strategy to reduce cross artifacts. Experimental results show that our denoising method

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors would like to thank anonymous reviewers for their constructive suggestions for improving the manuscript. Zheng Liu’s research is supported by National Natural Science Foundation of China (No. 61702467). Weina Wang’s research is supported by Zhejiang Provincial Natural Science Foundation of China (No. LQ20A010007). Ling Zhang’s research is supported by China Postdoctoral Science Found (No. 2018M642933) and National Natural Science Foundation of China (No. 61902286). Zhong Xie’s

References (32)

SunY. et al.
Denoising point sets via $ℓ_{0}$ minimization
Comput Aided Geom Design
(2015)
LiuZ. et al.
A novel anisotropic second order regularization for mesh denoising
Comput Aided Geom Des
(2019)
KimH.S. et al.
Feature detection of triangular meshes based on tensor voting theory
Comput Aided Des
(2009)
ParkM.K. et al.
Multi-scale tensor voting for feature extraction from unstructured point clouds
Graph Models
(2012)
YadavS.K. et al.
Constraint-based point set denoising using normal voting tensor and restricted quadratic error metrics
Comput Graph
(2018)
ZhangJ. et al.
Point cloud normal estimation via low-rank subspace clustering
Comput Graph
(2013)
ZhengY. et al.
Rolling normal filtering for point clouds
Comput Aided Geom Design
(2018)
ÖztireliA.C. et al.
Feature preserving point set surfaces based on non-linear kernel regression
Comput Graph Forum
(2009)
MatteiE. et al.
Point cloud denoising via moving RPCA
Comput Graph Forum
(2017)
HuangH. et al.
Edge-aware point set resampling
ACM Trans Graph
(2013)

AlexaM. et al.

Computing and rendering point set surfaces

IEEE Trans Vis Comput Graphics

(2003)

FleishmanS. et al.

Robust moving least-squares fitting with sharp features

ACM Trans Graph

(2005)

AdamsonA. et al.

Point-sampled cell complexes

ACM Trans Graph

(2006)

GuennebaudG. et al.

Algebraic point set surfaces

ACM Trans Graph

(2007)

GuennebaudG. et al.

Dynamic sampling and rendering of algebraic point set surfaces

Comput Graph Forum

(2010)

LipmanY. et al.

Parameterization-free projection for geometry reconstruction

ACM Trans Graph

(2007)

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View full text

A feature-preserving framework for point cloud denoising

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Related work

Normal filtering via second order regularization

Feature detection by bi-tensor voting

Multi-normal point updating

Experimental results and comparisons

Conclusion

Declaration of Competing Interest

Acknowledgments

Comput Aided Geom Design

Comput Aided Geom Des

Comput Aided Des

Graph Models

Comput Graph

Comput Graph

Comput Aided Geom Design

Feature preserving point set surfaces based on non-linear kernel regression

Comput Graph Forum

Point cloud denoising via moving RPCA

Comput Graph Forum

Edge-aware point set resampling

ACM Trans Graph

Computing and rendering point set surfaces

IEEE Trans Vis Comput Graphics

Robust moving least-squares fitting with sharp features

ACM Trans Graph

Point-sampled cell complexes

ACM Trans Graph

Algebraic point set surfaces

ACM Trans Graph

Dynamic sampling and rendering of algebraic point set surfaces

Comput Graph Forum

Parameterization-free projection for geometry reconstruction

ACM Trans Graph