Normal vector estimation method for rock mass point clouds with sharp feature preservation via local geometric adjustment

Normal vector estimation method for rock mass point clouds with sharp feature preservation via local geometric adjustment

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Mingming Ren^a^,^b, Manchao He^a, Jie Hu^a^,^*, Hongru Li^c, Yuxiang Ding^a^,^b, Xinhao Miao^a^,^b, Hongyi Zhang^a^,^b

Journal of Rock Mechanics and Geotechnical Engineering | 2026, 18(5) : 3722 - 3741

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Journal of Rock Mechanics and Geotechnical Engineering | 2026, 18(5): 3722-3741

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Normal vector estimation method for rock mass point clouds with sharp feature preservation via local geometric adjustment

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Mingming Ren^a^,^b, Manchao He^a, Jie Hu^a^,^*, Hongru Li^c, Yuxiang Ding^a^,^b, Xinhao Miao^a^,^b, Hongyi Zhang^a^,^b

Affiliations

^aState Key Laboratory for Tunnel Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China

^bSchool of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China

^cChina Academy of Safety Science and Technology, Beijing, 100012, China

Mingming Ren received his BSc degree in Software Engineering in 2018 and his MSc degree in Computer Technology in 2023 from North University of China. He is currently a PhD student in Civil Engineering at China University of Mining and Technology (Beijing). His research interests include rock mass stability analysis based on computer vision, geological hazard identification using artificial intelligence algorithms, and decision support systems based on multi-source data.

Published: 2026-05-25 doi: 10.1016/j.jrmge.2026.01.002

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Abstract

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Accurate extraction of rock mass discontinuity parameters is crucial for stability assessment and engineering safety. High-resolution remote sensing facilitates automated extraction, but its effectiveness relies heavily on precise normal estimation to ensure geometric reliability. Conventional methods struggle to preserve sharp features such as edges and corners, thereby reducing accuracy. To address this, we propose a normal estimation method based on local geometric adjustment that enhances feature extraction while maintaining sharp geometries. The approach consists of four steps: (1) classifying points, (2) applying normal and axial projections, (3) fitting segmentation lines via least squares, and (4) refining normals by optimizing local neighborhoods. The proposed method was evaluated on computer-aided design (CAD) models, real objects, and rock mass point clouds, and benchmarked against eight representative algorithms, including principal component analysis (PCA), 2-Jet PCA, Voronoi-based PCA, PCPNet, neural gradient function (NeuralGF), low rank representation (LRR), normal estimation via shifted neighborhood (NSN) and pair consistency voting (PCV). Experimental results demonstrate that our method achieves superior accuracy and efficiency, significantly improving structural plane extraction and ensuring better preservation of sharp geometric features.

Key words

Rock mass point cloud / Normal vector estimation / Sharp feature / Rock engineering

Cite this Article

Mingming Ren, Manchao He, Jie Hu, Hongru Li, Yuxiang Ding, Xinhao Miao, Hongyi Zhang. Normal vector estimation method for rock mass point clouds with sharp feature preservation via local geometric adjustment[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2026 , 18 (5) : 3722 -3741 . DOI: 10.1016/j.jrmge.2026.01.002

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Funding

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National Natural Science Foundation of China(42507210)
Fundamental Research Funds for the Central Universities(2025XJSB01)

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Year 2026 volume 18 Issue 5

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Article Info

doi: 10.1016/j.jrmge.2026.01.002

Receive Date：2025-07-17
Online Date：2026-06-17
Published：2026-05-25

Article Data

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History

Received：2025-07-17
Revised：2025-12-28
Accepted：2026-01-05

Funding

National Natural Science Foundation of China(42507210)

Fundamental Research Funds for the Central Universities(2025XJSB01)

Affiliations

^aState Key Laboratory for Tunnel Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China

^bSchool of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing, 100083, China

^cChina Academy of Safety Science and Technology, Beijing, 100012, China

Corresponding:

^* Corresponding author. E-mail address: hujie@cumtb.edu.cn (J. Hu).

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表12种不同金属材料的力学参数

科 Family	属数 Number of genus	种数 Number of species	占总种数比例 Percentage of total species (%)	属 Genus	种数 Number of species	占总种数比例 Percentage of total species (%)
鹅膏菌科Amanitaceae	2	11	5.26	鹅膏菌属 Amanita	10	4.78
小菇科 Mycenaceae	2	12	5.74	丝盖伞属 Inocybe	5	2.39
多孔菌科 Polyporaceae	8	14	6.70	蜡蘑属 Laccaria	5	2.39
红菇科 Russulaceae	3	23	11.00	小皮伞属 Marasmius	6	2.87
				小菇属 Mycena	11	5.26
				光柄菇属 Pluteus	5	2.39
				红菇属 Russula	17	8.13
				栓菌属 Trametes	5	2.39

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