# A Fast Voxel-Based Method for Outlier Removal in Laser Measurement

• Hao Chen
• Yu Chen
• Xu Zhang
• Baiyuan Li
• Xiaoqiang Liu
• Xuefei Shi
• Jie Shen
Regular Paper

## Abstract

Discrete data points are noncontinuous without structural information. In this paper, we propose a new fast outlier removal method via voxel-based surface propagation. The main technical components of our approach include (a) an efficient and simple spatial partitioning scheme and (b) a specially-designed surface propagation method. Numerical analyses indicate that our method is about 10 times faster than an existing method and significantly better than other two methods in terms of denoising accuracy. This provides an efficient solution to handling noisy laser-scanning data.

## Keywords

Surface propagation Laser scanning Data outlier Discrete data point

## List of Symbols

$$\left( {\lambda_{1} \ge \lambda_{2} \ge \lambda_{3} } \right)$$

Three eigenvalues

$$\varvec{\lambda}_{{\varvec{max}}}$$

Maximum eigenvalue

$$\varvec{\lambda}_{{\varvec{min}}}$$

Minimum eigenvalue

$$\theta$$

Angle between two vectors

i, j, k

The index in directions x, y, z, respectively

$$n_{x} ,\; n_{y} ,\;n_{z}$$

The number voxels in directions x, y, z, respectively

$$\varvec{n}_{\varvec{v}}$$

Total number of voxels in each problem

$$\left( {{\mathbf{v}}_{1} ,{\mathbf{v}}_{2} ,{\mathbf{v}}_{3} } \right)$$

Three eigenvectors

$$Voxel_{i}$$

The set of data points in the current voxel, i, i = 1,$$\varvec{n}_{\varvec{v}}$$

## Notes

### Acknowledgements

This work was in part supported by U.S. National Science Foundation DMI-0514900, CMMI-0721625, ECCS-1039563, and IIP-1445355.

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© Korean Society for Precision Engineering 2019

## Authors and Affiliations

• Hao Chen
• 1
• Yu Chen
• 2
• Xu Zhang
• 3
• Baiyuan Li
• 4
• Xiaoqiang Liu
• 4
• Xuefei Shi
• 5
• Jie Shen
• 6
Email author
1. 1.College of Automotive EngineeringShanghai University of Engineering ScienceShongjiang, ShanghaiChina
2. 2.Department of Computer ScienceRensselaer Polytechnic InstituteTroyUSA
3. 3.College of Mechanical EngineeringShanghai University of Engineering ScienceShongjiang, ShanghaiChina
4. 4.College of Computer and Information ScienceDonghua UniversityShanghaiChina
5. 5.School of Automation and Electrical EngineeringBeijing Science and Technology UniversityBeijingChina
6. 6.Department of Computer ScienceUniversity of Michigan-DearbornDearbornUSA