Abstract
We propose a novel curvature-aware simplification technique for point-sampled geometry based on the locally optimal projection (LOP) operator. Our algorithm includes two new developments. First, a weight term related to surface variation at each point is introduced to the classic LOP operator. It produces output points with a spatially adaptive distribution. Second, for speeding up the convergence of our method, an initialization process is proposed based on geometry-aware stochastic sampling. Owing to the initialization, the relaxation process achieves a faster convergence rate than those initialized by uniform sampling. Our simplification method possesses a number of distinguishing features. In particular, it provides resilience to noise and outliers, and an intuitively controllable distribution of simplification. Finally, we show the results of our approach with publicly available point cloud data, and compare the results with those obtained using previous methods. Our method outperforms these methods on raw scanned data.
Similar content being viewed by others
References
Adams, B., 2007. Surfel Viewer. Available from www.cs.kuleuven.be/~barta/sview/sview.html [Accessed on Oct. 18, 2009].
Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., Silva, C.T., 2001. Point Set Surfaces. Proc. Conf. on Visualization, p.21–28. [doi:10.1109/VISUAL.2001.964489]
Alexa, M., Rusinkiewicz, S., Nehab, D., Shilane, P., 2004. Stratified Point Sampling of 3D Models. Proc. Eurographics Symp. on Point-Based Graphics, p.49–56.
Boubekeur, T., Alexa, M., 2009. Mesh simplification by stochastic sampling and topological clustering. Comput. Graph., 33(3):241–249. [doi:10.1016/j.cag.2009.03.025]
de Figueiredo, L.H., Gomes, J.D.M., Terzopoulos, D., Velho, L., 1992. Physically-Based Methods for Polygonization of Implicit Surfaces. Proc. Conf. on Graphics Interface, p.250–257.
Dey, T.K., Giesen, J., Hudson, J., 2001. Decimating Samples for Mesh Simplification. Proc. 13th Canadian Conf. on Computational Geometry, p.85–88.
Guennebaud, G., Gross, M., 2007. Algebraic point set surfaces. ACM Trans. Graph., 26(3):23. [doi:10.1145/1276377.1276406]
Hart, J.C., Bachta, E., Jarosz, W., Fleury, T., 2005. Using Particles to Sample and Control More Complex Implicit Surfaces. ACM SIGGRAPH Courses, p.269–276. [doi:10.1145/1198555.1198657]
Huang, H., Li, D., Zhang, H., Ascher, U., Cohen-Or, D., 2009. Consolidation of Unorganized Point Clouds for Surface Reconstruction. SIGGRAPH, p.1–7. [doi:10.1145/1661412.1618522]
Kalaiah, A., Varshney, A., 2003. Statistical Point Geometry. Proc. Eurographics Symp. on Geometry Processing, p.107–115.
Kobbelt, L., Botsch, M., 2004. A survey of point-based techniques in computer graphics. Comput. Graph., 28(6):801–814. [doi:10.1016/j.cag.2004.08.009]
Linsen, L., 2001. Point Cloud Representation. Technical Report, Faculty of Computer Science, University of Karlsruhe, Karlsruhe.
Lipman, Y., Cohen-Or, D., Levin, D., Tal-Ezer, H., 2007. Parameterization-free projection for geometry reconstruction. ACM Trans. Graph., 26(3):22. [doi:10.1145/1276377.1276405]
Meyer, M.D., Georgel, P., Whitaker, R.T., 2005. Robust Particle Systems for Curvature Dependent Sampling of Implicit Surfaces. Proc. Int. Conf. on Shape Modeling and Applications, p.124–133. [doi:10.1109/SMI.2005.41]
Miao, Y., Pajarola, R., Feng, J., 2009a. Curvatureaware adaptive re-sampling for point-sampled geometry. Comput.-Aided Des., 41(6):395–403. [doi:10.1016/j. cad.2009.01.006]
Miao, Y., Diaz-Gutierrez, P., Pajarola, R., Gopi, M., Feng, J., 2009b. Shape Isophotic Error Metric Controllable Resampling for Point-Sampled Surfaces. IEEE Int. Conf. on Shape Modeling and Applications, p.28–35. [doi:10.1109/SMI.2009.5170160]
Pauly, M., Gross, M., Kobbelt, L.P., 2002. Efficient Simplification of Point-Sampled Surfaces. Proc. Conf. on Visualization, p.163–170. [doi:10.1109/VISUAL.2002.1183771]
Pauly, M., Mitra, N.J., Guibas, L.J., 2004. Uncertainty and Variability in Point Cloud Surface Data. Proc. Eurographics Symp. on Point-Based Graphics, p.77–84.
Proenca, J., Jorge, J., Sousa, M.C., 2007. Sampling Point-Set Implicits. Proc. Eurographics Symp. on Point-Based Graphics, p.11–18.
Saleem, W., Schall, O., Patane, G., Belyaev, A., Seidel, H.P., 2007. On stochastic methods for surface reconstruction. Vis. Comput., 23(6):381–395. [doi:10.1007/s00371-006-0094-3]
Witkin, A.P., Heckbert, P.S., 1994. Using Particles to Sample and Control Implicit Surfaces. Proc. 21st Annual Conf. on Computer Graphics and Interactive Techniques, p.269–277. [doi:10.1145/192161.192227]
Author information
Authors and Affiliations
Corresponding author
Additional information
Project (Nos. 60673006 and U0935004) supported by the National Natural Science Foundation of China and an INBRE grant from NIH, USA (No. 5P20RR01647206)
Rights and permissions
About this article
Cite this article
Su, Zx., Li, Zy., Zhao, Yd. et al. Curvature-aware simplification for point-sampled geometry. J. Zhejiang Univ. - Sci. C 12, 184–194 (2011). https://doi.org/10.1631/jzus.C1000068
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.C1000068