High-Precision Plane Fitting Model Based on Point Cloud Data and Accuracy Evaluation

Zhigang Li; Xinya Niu; Haodong Huang; Ying Guo

doi:10.3788/LOP242266

Laser & Optoelectronics Progress, Volume. 62, Issue 14, 1428005(2025)

High-Precision Plane Fitting Model Based on Point Cloud Data and Accuracy Evaluation

Zhigang Li¹, Xinya Niu^1,2、*, Haodong Huang², and Ying Guo²

Author Affiliations

¹Shandong Zhengyuan Aerial Remote Sensing Technology Co.,Ltd., Jinan 250101, Shandong , China

²College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao 266590, Shandong , China

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Figures & Tables(8)

Fig. 1. Schematic diagram of geometric deviation and shortest distance from measurement points

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Fig. 2. Schematic diagram of deviation from measurement points to fitted plane

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Fig. 3. Schematic diagrams of the plane fitted by two error estimation methods. (a) Plane Σ1; (b) plane Σ2

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Fig. 4. Schematic diagrams of experimental data-collection elevation position and fitting. (a) Vehicle mobile measurement system; (b) experimental selection of facade drawings; (c) fitting plane position diagram

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Table 1. Fitting results and error-free data of plane Σ1

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Table 1. Fitting results and error-free data of plane Σ1

Equation parameter	Error-free plane	Geometric error fitting plane	z-axis error fitting plane Σ1
m	0.3535	0.1407/-0.2128	0.2039/-0.1496
n	0.3535	0.2533/-0.1002	0.4287/0.0752
j	-0.8660	-0.9571/-0.0911	-0.8801/-0.0141
k /cm	-40.0	-43.4930/-3.4930	-40.8506/-0.8506
Error	$δ_{d}$ /mm	3.1309	2.1399
Error	$δ_{p}$	0.1456	0.0971

Table 2. Fitting results and error-free data of plane Σ2

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Table 2. Fitting results and error-free data of plane Σ2

Equation parameter	Error-free plane	Geometric error fitting plane	z-axis error fitting plane
m	0.3535	0.4958/0.1423	0.4132/0.0597
n	0.6124	0.5202/0.0922	0.5953/-0.0171
j	0.7071	0.6323/-0.0648	0.7474/0.0403
k /mm	60.0	60.1813/-0.8187	63.8941/-3.8941
Error	$δ_{d}$ /mm	2.8959	1.7472
Error	$δ_{p}$	0.0976	0.0608

Table 3. Equipment and precision indicators for experimental data collection

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Table 3. Equipment and precision indicators for experimental data collection

Equipment

Model

Precision indicator

Scanner

Riegl

Measuring accuracy：

\pm

3 mm

POS pose system

Novatel optical fiber integrated navigation system

Plane positioning accuracy： 1 cm

Elevation accuracy： 2 cm

Attitude： roll 0.003°， pitch 0.003°， course 0.004°

Point cloud

Coordinate accuracy （x，y，z）： 3 cm

Table 4. Parameters and error indicators of point cloud fitting planes

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Table 4. Parameters and error indicators of point cloud fitting planes

Plane

Coefficient of plane equation

(m, n, j, k)

Median error

σ_{l 0}

/mm

Attitude error

$(σ_{m}, σ_{n}, σ_{j})$

Positioning error

σ_{k}

/mm

0.450394446

-0.399482695

0.798472545

-5.104970995

3.853435

0.0037×10^-6

0.0117×10^-6

0.0035×10^-6

8.95×10^-4

0.073956521

0.036594787

0.996588989

8.650173349

5.446437

0.7780×10^-6

0.1270×10^-6

0.0070×10^-6

4.63×10^-4

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Zhigang Li, Xinya Niu, Haodong Huang, Ying Guo. High-Precision Plane Fitting Model Based on Point Cloud Data and Accuracy Evaluation[J]. Laser & Optoelectronics Progress, 2025, 62(14): 1428005

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Paper Information

Category: Remote Sensing and Sensors

Received: Nov. 15, 2024

Accepted: Feb. 4, 2025

Published Online: Jul. 2, 2025

The Author Email: Xinya Niu (1816606669@qq.com)

DOI:10.3788/LOP242266

CSTR:32186.14.LOP242266

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology