On Constructing NURBS Surface Model from Scattered and Unorganized 3-D Range Data

정렬되지 않은 3차원 거리 데이터로부터의 NURBS 곡면 모델 생성 기법

  • Park, In-Kyu (School of Electrical Engineering, Seoul National Univ) ;
  • Yun, Il-Dong (Dept. of Control and Instrumentation Eng., Hankuk Univ. of F.S.) ;
  • Lee, Sang-Uk (School of Electrical Engineering, Seoul National Univ)
  • 박인규 (서울대학교 전기공학부) ;
  • 윤일동 (한국외국어대학교 제어계측공학과) ;
  • 이상욱 (서울대학교 전기공학부)
  • Published : 2000.05.25

Abstract

In this paper, we propose an efficient algorithm to produce 3-D surface model from a set of range data, based on NURBS (Non-Uniform Rational B-Splines) surface fitting technique. It is assumed that the range data is initially unorganized and scattered 3-D points, while their connectivity is also unknown. The proposed algorithm consists of three steps: initial model approximation, hierarchical representation, and construction of the NURBS patch network. The mitral model is approximated by polyhedral and triangular model using K-means clustering technique Then, the initial model is represented by hierarchically decomposed tree structure. Based on this, $G^1$ continuous NURBS patch network is constructed efficiently. The computational complexity as well as the modeling error is much reduced by means of hierarchical decomposition and precise approximation of the NURBS control mesh Experimental results show that the initial model as well as the NURBS patch network are constructed automatically, while the modeling error is observed to be negligible.

Keywords

References

  1. M Soucy and D. Laurendeau, 'A general surface approach to the integration of a set of range views,' IEEE Trans on Pattern Analysis and Machine Intelligence, vol. 17, no 4, pp.344-358, April 1995 https://doi.org/10.1109/34.385982
  2. G. Turk and M. Levoy, 'Zippered polygon meshes from range images,' Proc of SIGGRAPH '94, pp. 311-318, July 1994 https://doi.org/10.1145/192161.192241
  3. Curless and M. Levoy, 'A volumetric method for building complex models from range Images,' Proc of SIGGRAPH '96, pp 303-312, Aug. 1996 https://doi.org/10.1145/237170.237269
  4. M. Eck and H. Hoppe, 'Automatic reconstruction of B-spline surfaces of arbitrary topological type,' Proc of SIGGRAPH '96, pp. 325-334 Aug. 1996 https://doi.org/10.1145/237170.237271
  5. V. Krishnamurthy and M Levoy, 'Fitting smooth surfaces to dense polygon meshes,' Proc. of SIGGRAPH '96, pp. 313-324, Aug 1996 https://doi.org/10.1145/237170.237270
  6. D. R. Forsey and R H. Bartels, 'Surface fitting with hierarchical splines,' ACM Trans. on Graphics, vol. 14, no. 2, pp. 134-161, April 1995 https://doi.org/10.1145/221659.221665
  7. M Soucy and D. Laurendeau, 'Multiresolution surface modeling based on hierarchical triangulation,' Computer Vision and Image Understanding, vol. 63, no. 1, pp. 1-14, January 1996 https://doi.org/10.1006/cviu.1996.0002
  8. H. Hoppe, T. DeRose, T. Duchamp, J. Mc-Donald, and W. Stuetzle, 'Surface reconstruction from unorganized points,' Proc. of SIGGRAPH '92, pp. 71-78, July 1992 https://doi.org/10.1145/133994.134011
  9. H Hoppe, T DeRose, T. Duchamp, J McDonald, and W. Stuetzle, 'Mesh optimization,' Proc of SIGGRAPH '93, pp. 19-26, August 1993 https://doi.org/10.1145/166117.166119
  10. Y. Chen and G Mediom, 'Description of complex objects from multiple range Images using an inflating balloon model,' Computer Vision and Image Understanding, vol. 61, no 3, pp. 325-334, May 1995 https://doi.org/10.1006/cviu.1995.1026
  11. M. J Milroy, C Bradley, G. W. Vickers, and D J Weir, 'G1 continuity of b-spline surface patches m reverse engineering,' Computer-Aided Design, vol. 27, pp. 471-478, 1995 https://doi.org/10.1016/0010-4485(95)00020-R
  12. W Ma and J P Kruth, 'Parameterization of randomly measured points for least square fitting of b-spline curves and surfaces,' Computer-Aided Design, vol. 27, no. 9, pp. 663-675, 1995 https://doi.org/10.1016/0010-4485(94)00018-9
  13. A Gersho and R M Gray, Vector quantization and signal compression, Kluwer Academic Publishers, 1992
  14. J L Marroqum and F. Girosi, 'Some extensions of the K-means algorithm for image segmentation and pattern recognition,' AI Memo 1930, MIT Artificial Intelligence Laboratory, January 1993
  15. D H Chung, I. D Yun, and S U Lee, 'Registration of multiple range views using the reverse calibration technique,' Pattern Recognition, vol 31, no 4, April 1998 https://doi.org/10.1016/S0031-3203(97)00063-0
  16. I. K. Park and S. U Lee, 'Geometric modeling from scattered 3-D range data,' Proc of IEEE International Conference on Image Processing, vol 2, pp 712-715, October 1997 https://doi.org/10.1109/ICIP.1997.638595
  17. I K Park, I. D. Yun, and S U Lee, 'Constructing NURBS surface model from scattered and unorganized range data,' Proc. of Second International Conference on 3-D Digital Imaging and Modeling, pp 312-321, October 1999 https://doi.org/10.1109/IM.1999.805361
  18. 박인규, 이경무, '정렬되지 않은 3차원 거리 데이터로부터의 다중 해상도 삼각형 메쉬 모델의 생성 기법,' 한국통신학회 논문지, Vol. 23, no. 10, pp. 2799-2810, 1998년 10월
  19. G Farin, Curves and surfaces for computer aided geometric design, Academic Press, 1990
  20. L Piegl and W Tiller, The NURBS book, Springer-Verlag, 1995