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Issue No.04 - July/August (2009 vol.15)
pp: 572-582
Hao Wang , University of Utah, Salt Lake City
Carlos E. Scheidegger , University of Utah, Salt Lake City
Cláudio T. Silva , University of Utah, Salt Lake City
We investigate the influence of bandwidth selection in the reconstruction quality of point-based surfaces. While the problem has received relatively little attention in the literature, we show that appropriate selection plays a significant role in the quality of reconstructed surfaces. We show how to compute optimal bandwidths for one class of moving least-squares surfaces by formulating the polynomial fitting step as a kernel regression problem for both noiseless and noisy data. In the context of Levin's projection, we also discuss the implications of the two-step projection for bandwidth selection. We show experimental comparisons of our method, which outperforms heuristically chosen functions and weights previously proposed. We also show the influence of bandwidth on the reconstruction quality of different formulations of point-based surfaces. We provide, to the best of our knowledge, the first quantitative comparisons between different MLS surface formulations and their optimal bandwidths. Using these experiments, we investigate the choice of effective bandwidths for these alternative formulations. We conclude with a discussion of how to effectively compare the different MLS formulations in the literature.
Bandwidth selection, MLS surfaces, surface reconstruction.
Hao Wang, Carlos E. Scheidegger, Cláudio T. Silva, "Bandwidth Selection and Reconstruction Quality in Point-Based Surfaces", IEEE Transactions on Visualization & Computer Graphics, vol.15, no. 4, pp. 572-582, July/August 2009, doi:10.1109/TVCG.2009.13
[1] The Digital Michelangelo Project, /, 2009.
[2] D. Levin, “Mesh-Independent Surface Interpolation,” Proc. Geometric Modelling for Scientific Visualization, 2003.
[3] M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C. Silva, “Computing and Rendering Point Set Surfaces,” IEEE Trans. Visualization and Computer Graphics, vol. 9, no. 1, pp. 3-15, Jan./Feb. 2003.
[4] T. Dey and J. Sun, “An Adaptive MLS Surface for Reconstruction with Guarantees,” Proc. Symp. Geometry Processing, pp. 43-52, 2005.
[5] R. Kolluri, “Provably Good Moving Least Squares,” ACM Trans. Algorithms, vol. 4, no. 2, pp.1-25, 2008.
[6] H. Wang, C. Scheidegger, and C. Silva, “Optimal Bandwidth Selection for MLS Surfaces,” Proc. Int'l Shape Modeling Conf., 2008.
[7] N. Amenta and Y.J. Kil, “Defining Point-Set Surfaces,” ACM Trans. Graphics, vol. 23, no. 3, pp. 264-270, 2004.
[8] M. Alexa and A. Adamson, “On Normals and Projection Operators for Surfaces Defined by Point Sets,” Proc. Eurographics Symp. Point-Based Graphics, pp. 149-156, 2004.
[9] G. Guennebaud and M. Gross, “Algebraic Point Set Surfaces,” Proc. ACM SIGGRAPH '07, p. 23, 2007.
[10] S. Fleishman, D. Cohen-Or, and C. Silva, “Robust Moving Least-Squares Fitting with Sharp Features,” ACM Trans. Graphics, vol. 24, no. 3, 2005.
[11] M. Zwicker, M. Pauly, O. Knoll, and M. Gross, “Pointshop 3D: An Interactive System for Point-Based Surface Editing,” ACM Trans. Graphics, vol. 21, no. 3, pp. 322-329, 2002.
[12] C. Shen, J.F. O'Brien, and J.R. Shewchuk, “Interpolating and Approximating Implicit Surfaces from Polygon Soup,” Proc. ACM SIGGRAPH '04, pp. 896-904, Aug. 2004.
[13] A. Adamson and M. Alexa, “Anisotropic Point Set Surfaces,” Proc. Fourth Int'l Conf. Computer Graphics, Virtual Reality, Visualization and Interaction in Africa (Afrigaph '06), pp. 7-13, 2006.
[14] Y. Lipman, D. Chohen-Or, and D. Levin, “Error Bounds and Optimal Neighborhoods for MLS Approximation,” Proc. Eurographics Symp. Geometry Processing, pp. 71-80, 2006.
[15] Z.-Q. Cheng, Y.-Z. Wang, B. Li, K. Xu, G. Dang, and S.Y. -Jin, “A Survey of Methods for Moving Least Squares Surfaces,” Proc. IEEE/EG Symp. Volume and Point-Based Graphics, 2008.
[16] M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and C.T. Silva, “Point Set Surfaces,” Proc. Visualization Conf. '01, pp.21-28, 2001.
[17] D. Cline, “Admissibile Kernel Estimators of a Multivariate Density,” The Annals of Statistics, vol. 16, no. 4, pp. 1421-1427, 1988.
[18] M. Wand and M. Jones, Kernel Smoothing, series on monographs on statistics and applied probability, vol. 60, Chapman & Hall, 1995.
[19] D. Ruppert, S. Sheather, and M. Wand, “An Effective Bandwidth Selector for Local Least Squares Regression,” J. Am. Statistical Assoc., vol. 90, no. 432, pp. 1257-1270, Dec. 1995.
[20] S. Sheather, “The Performance of Six Popular Bandwidth Selection Methods on Some Real Data Sets,” Computational Statistics, pp.225-250, 1992.
[21] W. Schucany, “Adaptive Bandwidth Choice for Kernel Regression,” J. Am. Statistical Assoc., vol. 90, no. 430, 1995.
[22] W. Hardle and J. Marron, “Fast and Simple Scatterplot Smoothing,” Computational Statistics and Data Analysis, vol. 20, no. 1, pp.1-17, 1995.
[23] C. Mallows, “Some Comments on $c_p$ ,” Technometrics, vol. 15, pp.661-675, 1973.
[24] D. Ruppert and M. Wand, “Multivariate Locally Weighted Least Squares Regression,” The Annals of Statistics, vol. 22, no. 3, pp.1346-1370, Sept. 1994.
[25] M. Wand and M. Jones, “Comparison of Smoothing Parameterizations in Bivariate Kernel Density Estimation,” J. Am. Statistical Assoc., pp. 520-528, 1993.
[26] N. Amenta and Y. Kil, “The Domain of a Point Set Surface,” Proc. Eurographics Symp. Point-Based Graphics, pp. 139-147, 2004.
[27] T. Ochotta, C. Scheidegger, J. Schreiner, Y. Lima, R.M. Kirby, and C. Silva, “A Unified Projection Operator for MLS Surfaces,” Technical Report UUSCI-2007-007, Scientific Computing and Imaging Inst., Univ. of Utah, 2007.
[28] P.-T. Bremer and J. Hart, “A Sampling Theorem for MLS Surfaces,” Proc. Symp. Point-Based Graphics, pp. 47-54, 2005.
[29] J. Schreiner, C. Scheidegger, and C. Silva, Afront, http:/, 2009.
[30] M. Pauly, N. Mitra, and L. Guibas, “Uncertainty and Variability in Point Cloud Surface Data,” Proc. Eurographics Symp. Point-Based Graphics, 2004.
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