Yaron Lipman
ABSTRACT
We introduce a Locally Optimal Projection operator (LOP) for surface approximation from point-set data. The operator is parameterization free, in the sense that it does not rely on estimating a local normal, fitting a local plane, or using any other local parametric representation. Therefore, it can deal with noisy data which clutters the orientation of the points. The method performs well in cases of ambiguous orientation, e.g., if two folds of a surface lie near each other, and other cases of complex geometry in which methods based upon local plane fitting may fail. Although defined by a global minimization problem, the method is effectively local, and it provides a second order approximation to smooth surfaces. Hence allowing good surface approximation without using any explicit or implicit approximation space. Furthermore, we show that LOP is highly robust to noise and outliers and demonstrate its effectiveness by applying it to raw scanned data of complex shapes.
Supplemental Material
- Alexa, M., Behr, J., Cohen-Or, D., Fleishman, S., Levin, D., and Silva, C. T. 2001. Point set surfaces. In VIS '01: Proceedings of the conference on Visualization '01, 21--28. Google Scholar
Digital Library
- Amenta, N., and Kil, Y. J. 2004. Defining point-set surfaces. ACM Trans. Graph. 23, 3, 264--270. Google ScholarDigital Library
- Amenta, N., Bern, M., and Kamvysselis, M. 1998. A new voronoi-based surface reconstruction algorithm. ACM Press, New York, NY, USA, 415--421.Google Scholar
- Brown, B. M. 1983. Statistical uses of the spatial median. J. R. Stat. Soc. 45, 1, 25--30.Google Scholar
- Carr, J. C., Beatson, R. K., Cherrie, J. B., Mitchell, T. J., Fright, W. R., McCallum, B. C., and Evans, T. R. 2001. Reconstruction and representation of 3d objects with radial basis functions. In SIGGRAPH '01, 67--76. Google ScholarDigital Library
- Hoppe, H., DeRose, T., Duchamp T., McDonald, J., and Stuetzle, W. 1992. Surface reconstruction from unorganized points. Computer Graphics 26, 2, 71--78. Google ScholarDigital Library
- Kazhdan, M., Bolitho, M., and Hoppe, H. 2006. Poisson surface reconstruction. In Symposium on Geometry Processing, 61--70. Google ScholarDigital Library
- Kuhn, H. W. 1973. Math. Program. 4, 98--107.Google ScholarCross Ref
- Levin, D. 2003. Mesh-independent surface interpolation. Geometric Modeling for Scientific Visualization, 37--49.Google Scholar
- Levoy, M., Pulli, K., Curless, B., Rusinkiewicz, S., Koller, D., Pereira, L., Ginzton, M., Anderson, S., Davis, J., Ginsberg, J., Shade, J., and Fulk, D. 2000. The digital michelangelo project: 3d scanning of large statues. In SIGGRAPH '00, 131--144. Google ScholarDigital Library
- Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., and Seidel, H.-P. 2003. Multi-level partition of unity implicits. ACM Trans. Graph. 22, 3, 463--470. Google ScholarDigital Library
- Small, C. G. 1990. A survey of multidimensional medians. Int. Stat. rev. 58, 3, 263--277.Google ScholarCross Ref
- Weber, A. 1909. {translated by Carl J. Friedrich from Weber's 1909 book}. Theory of the Location of Industries. Chicago: The University of Chicago Press, 1929.Google Scholar
- Weiszfeld, E. 1937. Sur le point pour lequel la somme des distances de points dennes est minimum. Tohoko Math. J. 43, 355--386.Google Scholar
- Zwicker, M., Pauly, M., Knoll, O., and Gross, M. 2002. Pointshop 3d: an interactive system for point-based surface editing. ACM Trans. Graph. 21, 3, 322--329. Google ScholarDigital Library
Index Terms
- Parameterization-free projection for geometry reconstruction
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