A solution for the registration of multiple 3D point sets using unit quaternions
- 407 Downloads
Registering 3D point sets is a common problem in computer vision. The case of two point sets has been analytically well solved by several authors. In this paper we present an analytic solution for solving the problem of a simultaneous registration of M point sets, M>2, by rigid motions. The solution is based on the use of unit quaternions for the representation of the rotations.
We show that the rotation optimization can be decoupled from the translation one. The optimal translations are given by the resolution of a linear equation system which depends on the rotated centroid of the overlaps. The unit quaternions representing the best rotations are optimized by applying an iterative process on symmetric 4×4 matrices. The matrices correspond to the mutual overlaps between the point sets.
We have applied this method to the registration of several overlapping 3D surfaces sampled on an object. Our results on simulated and real data show that the algorithm works efficiently.
- 1.R. Benjemaa and F. Schmitt. Recalage rapide de surfaces 3D aprs projection dans des multi-zbuffers. 5th European Conferences on Rapid Prototyping — Paris, 11 pages, October 1996.Google Scholar
- 2.R. Benjemaa and F. Schmitt. Recalage global de plusieurs surfaces par une approche algbrique (in frensh). RFIA'98, 11me Congrs AFCET de Reconnaissance des Formes et Intelligence Artificielle, Clermont-Ferrand, France, January 1997, “accepted”.Google Scholar
- 3.R. Benjemaa and F. Schmitt. Fast global registration of 3D sampled surfaces using a multi-z-buffer technique. Proceedings of the IEEE International Conference on Recent Advances in 3D Digital Imaging and Modeling, Ottawa-Canada, pages 113–120, May 1997, Extended version to be published in the Journal Image and Vision Computing.Google Scholar
- 4.R. Bergevin, M. Soucy, H. Gagnon, and D. Laurendeau. Towards a general multiview registration technique. IEEE Trans. on PAMI, 18(5):540–547, May 1996.Google Scholar
- 5.P. J. Besl and N. D. McKay. A method for registration of 3-D shapes. IEEE Trans. on PAMI, 14(2):239–256, February 1992.Google Scholar
- 6.O. D. Faugeras and M. Hebert. A 3D recognition and positioning algorithm using geometrical matching between primitive surfaces. Int. Joint. Conf. Artificial Intelligence, Karlsruhe, Germany, pages 996–1002, 1983.Google Scholar
- 7.O. D. Faugeras and M. Hebert. The representation and recognition and locating of 3-D objects. Int. Jour. Robotic Research, vol. 5(3):27–52, 1986.Google Scholar
- 9.T. D. Howell and J-C Lafon. The complexity of the quaternion product. Technical Report TR 75-245, Departement of Computer Science, Cornell University, Ithaca, N. Y., June 1975. ftp://ftp.netcom.com/pub/hb/hbaker/quaternion/cornellcstr75-245.ps.gz.Google Scholar
- 10.B. Kaingar-Parsi, J. L. Jones, and A. Rosenfeld. Registration of multiple overlapping range images: Scenes without distinctive features. IEEE Trans. on PAMI, 13(9):857–871, September 1991.Google Scholar
- 11.Kenichi Kanatani. Analysis of 3D rotation fitting. IEEE Trans. on PAMI, 16(5):543–549, May 1994.Google Scholar
- 12.A. Lorusso, D. W. Eggert, and R. B. Fisher. A comparison of four algorithms for estimating 3D rigid transformations. British Machine Vision Conference, Birmingham, England, pages 237–246, 1995.Google Scholar
- 13.L. Reyes-Avila. Quaternions: une reprsentation paramtrique systmatique des rotations finies. Technical Report 1303, INRIA-Rocquencourt, October 1990.Google Scholar
- 14.E. Salamin. Application of quaternions to computation with rotations. Technical report, Stanford AI Lab, 1979. ftp://ftp.netcom.com/pub/hb/hbaker/quaternion/stanfordaiwp79-salamin.ps.gz.
- 15.A. J. Stoddart and A. Hilton. Registration of multiple point sets. ICPR '96, Vienna, Austria, August 1996.Google Scholar