Registration of a curve on a surface using differential properties
This article presents a new method to find the best rigid registration between a curve and a surface. It is possible to write a compatibility equation between a curve point and a surface point, which constrains completely the 6 parameters of the sought rigid displacement. This requires the local computation of third order differential quantities and leads to an algebraic equation of degree 16.
A second approach consists in considering pairs of curve and surface points. Then only first order differential are necessary to compute locally the parameters of the rigid displacement. Although computationally more expensive, the second approach is more robust, and can be accelerated with a preprocessing of the surface data.
To our knowledge, it is the first method which takes full advantage of local differential computations to register a curve on a surface.
KeywordsSurface Point Curve Point Rigid Transformation Differential Property Scene Point
- 1.P.J. Besl. The Free-Form Surface Matching Problem (Machine Vision for 3-D Scenes). H. Freeman, Ed., 1990.Google Scholar
- 2.W.E.L Grimson, T. Lozano-Pérez, N. Noble, and S.J. White. An automatic tube inspection system that finds cylinders in range data. In Proceedings CVPR '93, New York City, NY. IEEE, June 1993.Google Scholar
- 3.O. Monga, S. Benayoun, and O.D. Faugeras. Using partial derivatives of 3d images to extract typical surface features. In Proceedings CVPR '92, Urbana Champaign, Illinois. IEEE, July 1992.Google Scholar
- 4.Jean-Philippe Thirion and Alexis Gourdon. The 3D marching lines algorithm and its application to crest lines extraction. Technical Report 1672, INRIA, May 1992.Google Scholar
- 5.B.H. Romeny, L. Florack, A. Salden, and M. Viergever. Higher order differential structure of images. In H.H. Barrett and A.F. Gmitro, editors, IPMI, pages 77–93, Flagstaff, Arizona (USA), June 1993. Springer-Verlag.Google Scholar
- 6.M.P. Do Carmo. Differential geometry of curves and surfaces. Prentice Hall, 1976.Google Scholar
- 7.William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling. Numerical Recipes in C, The Art of Scientific Computing. Cambridge University Press, 1990.Google Scholar
- 8.Stéphane Lavallée, Richard Szeliski, and Lionel Brunie. Matching 3-d smooth surfaces with their 2-d projections using 3-d distance maps. In SPIE, Geometric Methods in Computer Vision, San Diego, Ca, July 1991.Google Scholar
- 9.P.J. Besl and N.D. McKay. A method for registration of 3-D shapes. IEEE Transactions on PAMI, 14(2), February 1992.Google Scholar