Abstract
We introduce a distance field guided \(L_1\)-median method to extract topologically clean 1D curve skeleton from the point cloud model. We first voxelize the input point cloud, and compute the distance field for the point cloud. Then with the distance field, we extract the initial skeleton of the model using a multi-scale parameter controlled thinning method. Finally, we incorporate the initial skeleton into the \(L_1\)-median optimization, and develop a distance field guided \(L_1\)-median to effectively extract the complete skeleton from the point cloud. Our method exhibits the advantages of both the distance field based skeleton extraction methods and the \(L_1\)-median skeleton extraction methods. Our skeleton extraction system is robust and effective, and can be applied to the raw scanned point cloud data.











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Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T.: Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. Graph. 9(1), 3–15 (2003)
Au, O.K.C., Tai, C.L., Chu, H.K., Cohen-Or, D., Lee, T.Y.: Skeleton extraction by mesh contraction. ACM Trans. Graph. (TOG) 27(3), 44 (2008)
Avron, H., Sharf, A., Greif, C., Cohen-Or, D.: \(\ell \)1-sparse reconstruction of sharp point set surfaces. ACM Trans. Graph. (TOG) 29(5), 135 (2010)
Bitter, I., Kaufman, A.E., Sato, M.: Penalized-distance volumetric skeleton algorithm. IEEE Trans. Vis. Comput. Graph. 7(3), 195–206 (2001)
Bouix, S., Siddiqi, K.: Divergence-based medial surfaces. In: Computer Vision-ECCV, Springer, pp. 603–618 (2000)
Bucksch, A., Lindenbergh, R., Menenti, M.: Skeltre. Vis. Comput. 26(10), 1283–1300 (2010)
Cao, J., Tagliasacchi, A., Olson, M., Zhang, H., Su, Z.: Point cloud skeletons via laplacian based contraction. In: Shape Modeling International Conference (SMI), pp. 187–197. IEEE (2010)
Chuang, J.H., Ahuja, N., Lin, C.C., Tsai, C.H., Chen, C.H.: A potential-based generalized cylinder representation. Comput. Graph. 28(6), 907–918 (2004)
Chuang, M., Kazhdan, M.: Fast mean-curvature flow via finite-elements tracking. In: Computer Graphics Forum, vol. 30, pp. 1750–1760. Wiley Online Library (2011)
Cornea, N.D., Silver, D., Min, P.: Curve-skeleton properties, applications, and algorithms. IEEE Trans. Vis. Comput. Graph. 13(3), 530–548 (2007)
Dey, T.K., Sun, J.: Defining and computing curve-skeletons with medial geodesic function. In: Symposium on Geometry Processing, pp. 143–152 (2006)
Gagvani, N., Silver, D.: Parameter-controlled volume thinning. Graph. Models Image Process. 61(3), 149–164 (1999)
Hassouna, M.S., Farag, A.A.: Robust centerline extraction framework using level sets. In: Computer Vision and Pattern Recognition, CVPR. IEEE Computer Society Conference on, vol. 1, pp. 458–465. IEEE (2005)
Huang, H., Li, D., Zhang, H., Ascher, U., Cohen-Or, D.: Consolidation of unorganized point clouds for surface reconstruction. ACM Trans. Graph. (TOG) 28(5), 176 (2009)
Huang, H., Wu, S., Cohen-Or, D., Gong, M., Zhang, H., Li, G., Chen, B.: L1-medial skeleton of point cloud. ACM Trans. Graph. 32(4), 65 (2013)
Jalba, A.C., Sobiecki, A., Telea, A.C.: An unified multiscale framework for planar, surface, and curve skeletonization. IEEE Trans. Pattern Anal. Mach Intell 38(1), 30–45 (2016)
Jiang, W., Xu, K., Cheng, Z.Q., Martin, R.R., Dang, G.: Curve skeleton extraction by coupled graph contraction and surface clustering. Graph. Models 75(3), 137–148 (2013)
Katz, S., Tal, A.: Hierarchical mesh decomposition using fuzzy clustering and cuts, vol. 22. ACM (2003)
Kustra, J., Jalba, A., Telea, A.: Computing refined skeletal features from medial point clouds. Pattern Recognit. Lett. 76, 13–21 (2016)
Li, G., Liu, L., Zheng, H., Mitra, N.J.: Analysis, reconstruction and manipulation using arterial snakes. ACM Trans. Graph. TOG 29(6), 152 (2010)
Li, X., Woon, T.W., Tan, T.S., Huang, Z.: Decomposing polygon meshes for interactive applications. In: Proceedings of the 2001 symposium on Interactive 3D graphics, pp. 35–42. ACM (2001)
Liao, B., Xiao, C., Jin, L., Fu, H.: Efficient feature-preserving local projection operator for geometry reconstruction. Comput. Aided Des. 45(5), 861–874 (2013)
Lipman, Y., Cohen-Or, D., Levin, D., Tal-Ezer, H.: Parameterization-free projection for geometry reconstruction. ACM Trans. Graph. (TOG) 26(3), 22 (2007)
Livny, Y., Yan, F., Olson, M., Chen, B., Zhang, H., El-Sana, J.: Automatic reconstruction of tree skeletal structures from point clouds. ACM Trans. Graph. (TOG) 29(6), 151 (2010)
Malandain, G., Fernández-Vidal, S.: Euclidean skeletons. Image and vision computing 16(5), 317–327 (1998)
Natali, M., Biasotti, S., Patanè, G., Falcidieno, B.: Graph-based representations of point clouds. Graph. Models 73(5), 151–164 (2011)
Pang, Z., Zhao, Y., Xiao, C.: Effective skeletons extraction for animated surfaces based on geometry propagation. Comput. Anim. Virtual Worlds 26(3–4), 301–309 (2015)
Preiner, R., Mattausch, O., Arikan, M., Pajarola, R., Wimmer, M.: Continuous projection for fast l1 reconstruction. ACM Transactions on Graphics (Proc. of ACM SIGGRAPH) 33(4), 47:1–47:13 (2014)
Sethian, J.A.: Fast marching methods. SIAM Rev. 41(2), 199–235 (1999)
Sharf, A., Lewiner, T., Shamir, A., Kobbelt, L.: On-the-fly curve-skeleton computation for 3d shapes. Comput. Graph. Forum 26(3), 323–328 (2007)
Siddiqi, K., Pizer, S.: Medial representations: mathematics, algorithms and applications, 1st edn. Springer Publishing Company Incorporated, New York (2008)
Small, C.G.: A survey of multidimensional medians. International Statistical Review/Revue Internationale de Statistique pp. 263–277 (1990)
Tagliasacchi, A., Alhashim, I., Olson, M., Zhang, H.: Mean curvature skeletons. Comput. Graph. Forum 31(5), 1735–1744 (2012)
Tagliasacchi, A., Zhang, H., Cohen-Or, D.: Curve skeleton extraction from incomplete point cloud. ACM Trans. Graph. (TOG) 28(3), 71 (2009)
Verroust, A., Lazarus, F.: Extracting skeletal curves from 3d scattered data. In: Shape Modeling and Applications, 1999. Proceedings. Shape Modeling International ’99, pp. 194–201 (1999). doi:10.1109/SMA.1999.749340
Zheng, Q., Hao, Z., Huang, H., Xu, K., Zhang, H., Cohen-Or, D., Chen, B.: Skeleton-intrinsic symmetrization of shapes. In: Computer Graphics Forum, Wiley Online Library, vol. 34, pp. 275–286 (2015)
Zhou, Y., Toga, A.: Efficient skeletonization of volumetric objects. IEEE Trans. Vis. Comput. Graph. 5(3), 196–209 (1999). doi:10.1109/2945.795212
Acknowledgments
This work was partly supported by NSFC (No.61472288, No. 61672390, No. 41201404, No. U1536204), NCET (NCET-13-0441) and the Key Grant Project of State Key Lab of Software Engineering (SKLSE-2015-A-05).
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Song, C., Pang, Z., Jing, X. et al. Distance field guided \(L_1\)-median skeleton extraction. Vis Comput 34, 243–255 (2018). https://doi.org/10.1007/s00371-016-1331-z
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DOI: https://doi.org/10.1007/s00371-016-1331-z