research-article

L₁-medial skeleton of point cloud

Authors:

Daniel Cohen-Or,

Baoquan ChenAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 32, Issue 4

Article No.: 65, Pages 1 - 8

https://doi.org/10.1145/2461912.2461913

Published: 21 July 2013 Publication History

Abstract

We introduce L₁-medial skeleton as a curve skeleton representation for 3D point cloud data. The L₁-median is well-known as a robust global center of an arbitrary set of points. We make the key observation that adapting L₁-medians locally to a point set representing a 3D shape gives rise to a one-dimensional structure, which can be seen as a localized center of the shape. The primary advantage of our approach is that it does not place strong requirements on the quality of the input point cloud nor on the geometry or topology of the captured shape. We develop a L₁-medial skeleton construction algorithm, which can be directly applied to an unoriented raw point scan with significant noise, outliers, and large areas of missing data. We demonstrate L₁-medial skeletons extracted from raw scans of a variety of shapes, including those modeling high-genus 3D objects, plant-like structures, and curve networks.

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References

[1]

Au, O. K.-C., Tai, C.-L., Chu, H.-K., Cohen-Or, D., and Lee, T.-Y. 2008. Skeleton extraction by mesh contraction. ACM Trans. on Graph (Proc. of SIGGRAPH) 27, 3, 44:1--44:10.

Digital Library

[2]

Avron, H., Sharf, A., Greif, C., and Cohen-Or, D. 2010. l₁-sparse reconstruction of sharp point set surfaces. ACM Trans. on Graph 29, 5, 135:1--135:12.

Digital Library

[3]

Blum, H. 1967. A transformation for extracting new descriptors of shape. Models for the Perception of Speech and Visual Form, 362--380.

[4]

Bucksch, A., Lindenbergh, R., and Menenti, M. 2010. Skeltre: Robust skeleton extraction from imperfect point clouds. The Visual Computer 26, 10, 1283--1300.

Digital Library

[5]

Cao, J., Tagliasacchi, A., Olson, M., Zhang, H., and Su, Z. 2010. Point cloud skeletons via laplacian based contraction. Proc. IEEE Int. Conf. on Shape Modeling and Applications, 187--197.

Digital Library

[6]

Chuang, M., and Kazhdan, M. 2011. Fast mean-curvature flow via finite-elements tracking. Computer Graphics Forum (Proc. of Eurographics) 30, 6, 1750--1760.

[7]

Chung, J.-h., Tsai, C.-h., and Ko, M.-c. 2000. Skeletonization of three-dimensional object using generalized potential field. IEEE Trans. Pat. Ana. & Mach. Int. 22, 11, 1241--1251.

Digital Library

[8]

Cornea, N. D., Silver, D., and Min, P. 2007. Curve-skeleton properties, applications, and algorithms. IEEE Trans. Vis. & Comp. Graphics 13, 3, 530--548.

Digital Library

[9]

Daszykowski, M., Kaczmarek, K., Heyden, Y. V., and Walczak, B. 2007. Robust statistics in data analysis - a review: Basic concept. Chemometrics and Intelligent Lab. Sys. 85, 2, 203--219.

[10]

Dey, T. K., and Sun, J. 2006. Defining and computing curve-skeletons with medial geodesic function. Symp. on Geom. Proc., 143--152.

Digital Library

[11]

Fukunaga, K., and Hostetler, L. D. 1975. The estimation of the gradient of a density function with applications in pattern recognition. IEEE Trans. Info. Theo. 21, 32--40.

Digital Library

[12]

Gander, W., Golub, G. H., and Strebel, R. 1994. Least squares fitting of circles and ellipses. BIT Numerical Mathematics 34, 558--578.

[13]

Hassouna, M. S., and Farag, A. A. 2009. Variational curve skeletons using gradient vector flow. IEEE Trans. Pat. Ana. & Mach. Int. 31, 12, 2257--2274.

Digital Library

[14]

Hilaga, M., Shinagawa, Y., Kohmura, T., and Kunil, T. L. 2001. Topology matching for fully automatic similarity estimation of 3D shapes. Proc. of SIGGRAPH, 203--212.

Digital Library

[15]

Huang, H., Li, D., Zhang, H., Ascher, U., and Cohen-Or, D. 2009. Consolidation of unorganized point clouds for surface reconstruction. ACM Trans. on Graph (Proc. of SIGGRAPH Asia) 28, 5, 176:1--176:7.

Digital Library

[16]

Jiang, W., Xu, K., Cheng, Z., Martin, R. R., and Dang, G. 2013. Curve skeleton extraction by coupled graph contraction and surface clustering. Graphical Models 75, 3, 137--148.

Digital Library

[17]

Katz, S., and Tal, A. 2003. Hierarchical mesh decomposition using fuzzy clustering and cuts. ACM Trans. on Graph (Proc. of SIGGRAPH) 22, 3, 954--961.

Digital Library

[18]

Li, G., Liu, L., Zheng, H., and Mitra, N. J. 2010. Analysis, reconstruction and manipulation using arterial snakes. ACM Trans. on Graph (Proc. of SIGGRAPH Asia) 29, 5, 152:1--152:10.

Digital Library

[19]

Lipman, Y., Cohen-Or, D., Levin, D., and Tal-Ezer, H. 2007. Parameterization-free projection for geometry reconstruction. ACM Trans. on Graph (Proc. of SIGGRAPH) 26, 3, 22:1--22:6.

Digital Library

[20]

Livny, Y., Yan, F., Olson, M., Chen, B., Zhang, H., and El-sana, J. 2010. Automatic reconstruction of tree skeletal structures from point clouds. ACM Trans. on Graph (Proc. of SIGGRAPH Asia) 29, 6, 151:1--151:8.

Digital Library

[21]

Lu, L., Lévy, B., and Wang, W. 2012. Centroidal voronoi tessellations for line segments and graphs. Computer Graphics Forum (Proc. of Eurographics) 31, 2, 775--784.

Digital Library

[22]

Milasevic, P., and Ducharme, G. R. 1987. Uniqueness of the spatial median. Ann. Statist. 15, 1332--1333.

[23]

Mullen, P., de Goes, F., Desbrun, M., Cohen-Steiner, D., and Alliez, P. 2010. Signing the unsigned: Robust surface reconstruction from raw pointsets. Computer Graphics Forum 29, 1733--1741.

[24]

Natali, M., Biasotti, S., Patan, G., and BiancaFalcidieno. 2011. Graph-based representations of point clouds. Graphical Models 73, 151--164.

Digital Library

[25]

Sharf, A., Lewiner, T., Shamir, A., and Kobbelt, L. 2007. On-the-fly curve-skeleton computation for 3D shapes. Computer Graphics Forum 26, 323--328.

[26]

Siddiqi, K., and Pizer, S. 2009. Medial Representations: Mathematics, Algorithms and Applications. Springer.

[27]

Small, C. G. 1990. A survey of multidimensional medians. International Statistical Review 58, 3, 263--277.

[28]

Tagliasacchi, A., Zhang, H., and Cohen-Or, D. 2009. Curve skeleton extraction from incomplete point cloud. ACM Trans. on Graph (Proc. of SIGGRAPH) 28, 3, 71:1--71:9.

Digital Library

[29]

Tagliasacchi, A., Alhashim, I., Olson, M., and Zhang, H. 2012. Mean curvature skeletons. Computer Graphics Forum (Proc. of Symposium on Geometry Processing) 31, 5, 1735--1744.

Digital Library

[30]

Weber, A. 1909. Über den Standort der Industrie. Tübingen, J. C. B. Mohr (Paul Siebeck). English translation by C. J. Freidrich (1929): Alfred WebersTheory of the Location of Industries.

[31]

Willcocks, C. G., and Li, F. W. B. 2012. Feature-varying skeletonization - intuitive control over the target feature size and output skeleton topology. The Visual Computer 28, 6-8, 775--785.

Digital Library

Cited By

Chen SFan GLi JHao H(2025)Automatic complex concrete crack detection and quantification based on point clouds and deep learningEngineering Structures10.1016/j.engstruct.2025.119635327(119635)Online publication date: Mar-2025
https://doi.org/10.1016/j.engstruct.2025.119635
Song HWen WWu SGuo X(2025)Comprehensive review on 3D point cloud segmentation in plantsArtificial Intelligence in Agriculture10.1016/j.aiia.2025.01.006Online publication date: Jan-2025
https://doi.org/10.1016/j.aiia.2025.01.006
Chi H(2024)CCL16 is a pro-tumor chemokine that recruits monocytes and macrophages to promote hepatocellular carcinoma progressionAmerican Journal of Cancer Research10.62347/VCTW688914:7(3600-3613)Online publication date: 2024
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Index Terms

L₁-medial skeleton of point cloud
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 32, Issue 4

July 2013

1215 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2461912

Issue’s Table of Contents

Copyright © 2013 ACM.

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Association for Computing Machinery

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Publication History

Published: 21 July 2013

Published in TOG Volume 32, Issue 4

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Funding Sources

Guangdong Science and Technology Program
Natural Sciences and Engineering Research Council of Canada
National Natural Science Foundation of China
Shenzhen Nanshan Program
Shenzhen Innovation Program
Israel Science Foundation

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Cited By

Chen SFan GLi JHao H(2025)Automatic complex concrete crack detection and quantification based on point clouds and deep learningEngineering Structures10.1016/j.engstruct.2025.119635327(119635)Online publication date: Mar-2025
https://doi.org/10.1016/j.engstruct.2025.119635
Song HWen WWu SGuo X(2025)Comprehensive review on 3D point cloud segmentation in plantsArtificial Intelligence in Agriculture10.1016/j.aiia.2025.01.006Online publication date: Jan-2025
https://doi.org/10.1016/j.aiia.2025.01.006
Chi H(2024)CCL16 is a pro-tumor chemokine that recruits monocytes and macrophages to promote hepatocellular carcinoma progressionAmerican Journal of Cancer Research10.62347/VCTW688914:7(3600-3613)Online publication date: 2024
https://doi.org/10.62347/VCTW6889
Yang LLiu KOu RQian PWu YTian ZZhu CFeng SYang F(2024)Surface Defect-Extended BIM Generation Leveraging UAV Images and Deep LearningSensors10.3390/s2413415124:13(4151)Online publication date: 26-Jun-2024
https://doi.org/10.3390/s24134151
Xiong KZheng MXu QWen CShen SWang CWooldridge MDy JNatarajan S(2024)SPEALProceedings of the Thirty-Eighth AAAI Conference on Artificial Intelligence and Thirty-Sixth Conference on Innovative Applications of Artificial Intelligence and Fourteenth Symposium on Educational Advances in Artificial Intelligence10.1609/aaai.v38i6.28446(6279-6287)Online publication date: 20-Feb-2024
https://dl.acm.org/doi/10.1609/aaai.v38i6.28446
Guo MWang BMatusik W(2024)Medial Skeletal Diagram: A Generalized Medial Axis Approach for Compact 3D Shape RepresentationACM Transactions on Graphics10.1145/368796443:6(1-23)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687964
Jin LGu SWei DAdhinarta JKuang KZhang YPfister HNi BYang JLi M(2024)RibSeg v2: A Large-Scale Benchmark for Rib Labeling and Anatomical Centerline ExtractionIEEE Transactions on Medical Imaging10.1109/TMI.2023.331362743:1(570-581)Online publication date: Jan-2024
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Wang YLiu YZeng HZhu H(2024)Volume Estimation of Oil Tanks Based on 3-D Point Cloud CompletionIEEE Transactions on Instrumentation and Measurement10.1109/TIM.2024.347662073(1-10)Online publication date: 2024
https://doi.org/10.1109/TIM.2024.3476620
Wen QTafrishi SJi ZLai Y(2024)GLSkeleton: A Geometric Laplacian-Based Skeletonisation Framework for Object Point CloudsIEEE Robotics and Automation Letters10.1109/LRA.2024.33841289:5(4615-4622)Online publication date: May-2024
https://doi.org/10.1109/LRA.2024.3384128
Scott BSchofield SGreen R(2024)Detection of Pinus Radiata Cutpoints Using Neural Medial Axis Skeletonization2024 39th International Conference on Image and Vision Computing New Zealand (IVCNZ)10.1109/IVCNZ64857.2024.10794487(1-6)Online publication date: 4-Dec-2024
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