Orthogonal least squares in partition of unity surface reconstruction with radial basis function

Geometric Modeling and Imaging New Trends, 2006

Volumn 2006, Issue , 2006, Pages 28-33

  Xia, Qi ^a   Wang, Michael Yu ^a   Wu, Xiaojun ^b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

OCTREE CELLS; ORTHOGONAL LEAST SQUARES (OLS); PARTITION OF UNITY (POU) METHODS;

ITERATIVE METHODS; LEARNING ALGORITHMS; LEAST SQUARES APPROXIMATIONS; RADIAL BASIS FUNCTION NETWORKS; ROBUSTNESS (CONTROL SYSTEMS);

SURFACE RECONSTRUCTION;

EID: 33947613636     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/GMAI.2006.40     Document Type: Conference Paper

References (23)

1. I. Babuska and J. Melenk. The partition of unity finite element method: Basic theory and applications. Comput. Methods Appl. Mech. Engrg., 139:289-314, 1996.
2. I. Babuska and J. Melenk. The partition of unity method. Internat. J. Numer. Methods Engrg., 40:727-758, 1997.
3. R. Beatson and W. Light. Fast evaluation of radial basis functions: Methods for two-dimensional polyharmonic splines. IMA Journal of Numerical Analysis, 17:343-372, 1997.
4. R. Beatson, W. Light, and S. Billings. Fast solution of the radial basis function interpolation equations: Domain decomposition methods. SIAM J. Sci. Comput., 22:1717-1740, 2000.
5. R. Beatson and G. Newsam. Fast evaluation of radial basis functions: 1. Computational Mathematics and Applications, 24(12):7-19, 1992.
6. M. Botsch and L. Kobbelt. Real-time shape editing using radial basis functions. In Eurographics 2005, pages 611-621, 2005.
7. M. D. Buhmann. Radial Basis Functions: Theory and Implementations, volume 12 of Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, New York, NY, 2004.
8. J. Carr, R. Beatson, J. Cherrie, T. Mitchell, W. Fright, B. McCallum, and T. Evans. Reconstruction and representation of 3d objects with radial basis functions. In SIGGRAPH 2001, pages 67-76, August 2001.
9. S. Chen, C. Cowan, and P. Grant. Orthogonal least squares learning algorithm for radial basis function networks. IEEE Transactions on neural networks, 2(2):302-309. March 1991.
10. C. Drioli and D. Rocchesso. Orthogonal least squares algorithm for the approximation of a map and its derivatives with a rbf network. Signal Processing, 83:283-296, 2003.
11. A. Iske. Multlresolution Methods In Scattered Data Modelling, volume 37 of Lecture Notes in Computational Science and Engineering. Springer-Verlag, Heidelberg, 2004.
12. N. Kojekine, I. Hagiwara, and V. Savchenko. Software tools using csrbf for processing scattered data. Computers and Graphics, 27(2):311-319, 2003.
13. T. Lewiner, H. Lopes, A. Vieira, and G. Tavares. Efficient implementation of Marching Cubes cases with topological guarantees. Journal of Graphics Tools, 8(2): 1-15, December 2003.
14. B. Morse, T. Yoo, P. Rheingans, D. Chen, and K. Subramanian. Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. In Proceedings of Shape Modeling International, 2001.
15. Y. Ohtake, A. Belyaev, M. Alexa, G. Turk, and H. Seidel. Multi-level partition of unity implicits. In SIGGRAPH 2003, pages 27-31, July 2003.
16. Y. Ohtake, A. Belyaev, and H. Seidel. A multi-scale approach to 3d scattered data interpolation with compactly supported basis functions. In Shape Modeling International 2003, May 2003.
17. I. Tobor, P. Reuter, and C. Schlick. Efficient reconstruction of large scattered geometric datasets using the partition of unity and radial basis functions. In WSCG 2004, 2004.
18. I. Tobor, P. Reuter, and C. Schlick. Multiresolution reconstruction of implicit surface with attributes from lagre unorganized point sets. In Shape Modeling International (SMI 2004), pages 19-30, 2004.
19. G. Turk and J. O'Brien. Shape transformation using variational implicit surfaces. In SIGGRAPH 99, pages 335-342, August 1999.
20. G. Turk and J. O'Brien. Modeling with implicit surfaces that interpolate. ACM Transaction on Graphics, 21(4):855-873, 2002.
21. H. Wendland. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Advances in Computational Mathematics, 4:389-396, 1995.
22. H. Wendland. Computational aspects of radial basis function approximation. Topics in Multivariate Approximation and Interpolation, pages 231-256, 2005.
23. H. Xie, K. McDonnell, and H. Qin. Surface reconstruction of noisy and defective data-sets. In IEEE Visualization, pages 259-266, Austin, Texas, 2004.