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CLC number: TP391.4

On-line Access: 2011-03-09

Received: 2010-03-19

Revision Accepted: 2010-07-16

Crosschecked: 2011-01-31

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Journal of Zhejiang University SCIENCE C 2011 Vol.12 No.3 P.184-194


Curvature-aware simplification for point-sampled geometry

Author(s):  Zhi-xun Su, Zhi-yang Li, Yuan-di Zhao, Jun-jie Cao

Affiliation(s):  School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

Corresponding email(s):   zxsu@hotmail.com, lizy0205@gmail.com

Key Words:  Point-sampled geometry, Particle simulation, Locally optimal projection, Simplification

Zhi-xun Su, Zhi-yang Li, Yuan-di Zhao, Jun-jie Cao. Curvature-aware simplification for point-sampled geometry[J]. Journal of Zhejiang University Science C, 2011, 12(3): 184-194.

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%A Zhi-xun Su
%A Zhi-yang Li
%A Yuan-di Zhao
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T1 - Curvature-aware simplification for point-sampled geometry
A1 - Zhi-xun Su
A1 - Zhi-yang Li
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A1 - Jun-jie Cao
J0 - Journal of Zhejiang University Science C
VL - 12
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EP - 194
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Y1 - 2011
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.C1000068

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Adams, B., 2007. Surfel Viewer. Available from www. cs.kuleuven.be/$ hicksim$barta/sview/sview.html [Accessed on Oct. 18, 2009].

[2]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.

[3]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.

[4]Boubekeur, T., Alexa, M., 2009. Mesh simplification by stochastic sampling and topological clustering. Comput. Graph., 33(3):241-249.

[5]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.

[6]Dey, T.K., Giesen, J., Hudson, J., 2001. Decimating Samples for Mesh Simplification. Proc. 13th Canadian Conf. on Computational Geometry, p.85-88.

[7]Guennebaud, G., Gross, M., 2007. Algebraic point set surfaces. ACM Trans. Graph., 26(3):23.

[8]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.

[9]Huang, H., Li, D., Zhang, H., Ascher, U., Cohen-Or, D., 2009. Consolidation of Unorganized Point Clouds for Surface Reconstruction. SIGGRAPH, p.1-7.

[10]Kalaiah, A., Varshney, A., 2003. Statistical Point Geometry. Proc. Eurographics Symp. on Geometry Processing, p.107-115.

[11]Kobbelt, L., Botsch, M., 2004. A survey of point-based techniques in computer graphics. Comput. Graph., 28(6):801-814.

[12]Linsen, L., 2001. Point Cloud Representation. Technical Report, Faculty of Computer Science, University of Karlsruhe, Karlsruhe.

[13]Lipman, Y., Cohen-Or, D., Levin, D., Tal-Ezer, H., 2007. Parameterization-free projection for geometry reconstruction. ACM Trans. Graph., 26(3):22.

[14]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.

[15]Miao, Y., Pajarola, R., Feng, J., 2009a. Curvature-aware adaptive re-sampling for point-sampled geometry. Comput.-Aided Des., 41(6):395-403.

[16]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.

[17]Pauly, M., Gross, M., Kobbelt, L.P., 2002. Efficient Simplification of Point-Sampled Surfaces. Proc. Conf. on Visualization, p.163-170.

[18]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.

[19]Proenca, J., Jorge, J., Sousa, M.C., 2007. Sampling Point-Set Implicits. Proc. Eurographics Symp. on Point-Based Graphics, p.11-8.

[20]Saleem, W., Schall, O., Patane, G., Belyaev, A., Seidel, H.P., 2007. On stochastic methods for surface reconstruction. Vis. Comput., 23(6):381-395.

[21]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.

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