Abstract
Terrestrial laser scanners capture 3D geometry of real world objects as a point cloud. This paper reports on a new algorithm developed for the skeletonization of a laser scanner point cloud. The skeletonization algorithm proposed in this paper consists of three steps: (i) extraction of a graph from an octree organization, (ii) reduction of the graph to a skeleton, and (iii) embedding of the skeleton into the point cloud. For these three steps, only one input parameter is required. The results are validated on laser scanner point clouds representing 2 classes of objects; first on botanic trees as a special application and secondly on popular arbitrary objects. The presented skeleton found its first application in obtaining botanic tree parameters like length and diameter of branches and is presented here in a new, generalized version. Its definition as Reeb Graph, proofs the usefulness of the skeleton for applications like shape analysis. In this paper we show that the resulting skeleton contains the Reeb Graph and investigate the practically relevant parameters: centeredness and topological correctness. The robustness of this skeletonization method against undersampling, varying point density and systematic errors of the point cloud is demonstrated on real data examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amenta, N., Choi, S., Kolluri, R.: The power crust, unions of balls and the medial axis transform. Comput. Geom., Theory Appl. 19(2–3), 127–153 (2001)
Arthur, D., Vassilvitskii, S.: On the worst case complexity of the k-means method. Technical Report, Stanford 698 (2005)
Blum, H.: A transformation for extracting new descriptors of shape. In: Proceedings Models for Perception of Speech and Visual Form, pp. 362–380 (1967)
Bucksch, A., Lindenbergh, R.: Campino—a skeletonization method for point cloud processing. ISPRS J. Photogramm. Remote Sens. 63, 115–127 (2008)
Bucksch, A., Lindenbergh, R., Menenti, M.: Skeltre—Fast skeletonization of imperfect point clouds of botanic trees. In: Proceedings 3D Object Retrieval Workshop 2009 (3DOR), pp. 13–20 (2009)
Chen, H.H., Huang, T.S.: A survey of construction and manipulation of octrees. Comput. Vis. Graph. Image Process. Arch. 43(3), 409–431 (1988)
Cole-McLaughlin, K., Edelsbrunner, H., Harer, J., Natarajan, V., Pascucci, V.: Loops in Reeb graphs of 2-manifolds. Discrete Comput. Geom. 32(2), 231–244 (2004)
Cornea, N.D., Min, P.: Curve-skeleton properties, applications, and algorithms. IEEE Trans. Vis. Comput. Graph. 13(3), 530–548 (2007)
Côtè, J.F., Widlowski, J.L., Fournier, R.A., Verstraete, M.M.: The structural and radiative consistency of three-dimensional tree reconstructions from terrestrial lidar. Remote Sens. Environ. 113(5), 1067–1081 (2009)
Dey, T.K., Sun, J.: Defining and computing curve-skeletons with medial geodesic function. In: Proceedings 4th Eurographics Symposium on Geometry Processing, pp. 143–152 (2006)
Foreman, R.: Morse theory for cell complexes. Adv. Math. 134, 90–145 (1998)
Gorte, B.: Skeletonization of laser-scanned trees in the 3d raster domain. In: Proceedings 3DGeoInfo 2006 (2006)
Gorte, B., Pfeifer, N.: Structuring laser-scanned trees using 3D mathematical morphology. Int. Arch. Photogramm. Remote Sens. XXXV(B5), 929–933 (2004)
Milnor, J.: Morse Theory. Princeton University Press, Princeton (1963)
Musser, D., Saini, A.: Stl Tutorial and Reference Guide: C++ Programming with the Standard Template Library. Addison-Wesley Professional Computing Series. Addison-Wesley, Reading (1996)
Palagyi, K., Sorantin, E., Balogh, E., Kuba, A., Halmai, C., Erdohelyi, B., Hausegger, K.: A sequential 3D thinning algorithm and its medical applications. In: Proceedings 17th International Conference Information Processing in Medical Imaging, pp. 409–415 (2001)
Pascucci, V., Scorzelli, G., Bremer, P.T., Mascarenhas, A.: Robust on-line computation of Reeb graphs: simplicity and speed. ACM Trans. Graph. 26(3), 58 (2007)
Pemmaraju, S., Skiena, S.: Computational Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Cambridge University Press, Cambridge (2003)
Reeb, G.: Sur les points singuliers d’une forme de Pfaff complèment intégrable ou d’une fonction numérique. C. R. Acad. Sci. 222, 847–849 (1946)
Saito, T., Toriwaki, J.: New algorithms for Euclidean distance transformation of an n-dimensional digitized picture with applications. Pattern Recogn. 27, 1551–1565 (1994)
Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1982)
Shan, J., Todd, C. (eds.): Topographic Laser Ranging and Scanning. CRC Press, Boca Raton (2008)
Shinagawa, Y., Kunii, T.L.: Surface coding based on Morse theory. IEEE Comput. Graph. Appl. 11, 66–78 (1991)
Verroust, A., Lazarus, F.: Extracting skeletal curves from 3d scattered data. Vis. Comput. 16, 15–25 (2000)
Xu, H., Gossett, N., Chen, B.: Knowledge and heuristic-based modeling of laser-scanned trees. ACM Trans. Graph. 26(4), 19 (2007)
Yan, D.M., Wintz, J., Mourrain, B., Wang, W., Boudon, F., Godin, C.: Efficient and robust branch model reconstruction from laser scanned points. In: Proceedings 11th IEEE International Conference on Computer-Aided Design and Computer Graphics (2009)
Zhou, Y., Kaufman, A., Toga, A.W.: Three-dimensional skeleton and centerline generation based on an approximate minimum distance field. Vis. Comput. 14(7), 303–314 (1998)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bucksch, A., Lindenbergh, R. & Menenti, M. SkelTre. Vis Comput 26, 1283–1300 (2010). https://doi.org/10.1007/s00371-010-0520-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00371-010-0520-4