Abstract
We introduce in this paper a new type of feature points of 3D surfaces, based on geometric invariants. We call this new type of feature points the extremal points of the 3D surfaces, and we show that the relative positions of those 3D points are invariant according to 3D rigid transforms (rotation and translation). We show also how to extract those points from 3D images, such as Magnetic Resonance images (MRI) or Cat-Scan images, and also how to use them to perform precise 3D registration. Previously, we described a method, called the Marching Lines algorithm, which allow us to extract the extremal lines, which are geometric invariant 3D curves, as the intersection of two implicit surfaces: the extremal points are the intersection of the extremal lines with a third implicit surface. We present an application of the extremal points extraction to the fully automatic registration of two 3D images of the same patient, taken in two different positions, to show the accuracy and robustness of the extracted extremal points.
Similar content being viewed by others
References
BeslP.J. and McKayN.D. 1989. A method for the registration of 3-d shapes. IEEE Trans. on Pattern Anal. and Machine Intell., 14(2):239–256.
Brunie, L., Lavallée, S., and Szeliski, R. 1992. Using force field derived from 3-d distance maps for infering the attitude of a 3d rigid object. Proc. 2nd ECCV, pp. 670–675.
Do Carmo, M.P. 1976. Differential Geometry of Curves and Surfaces. Prentice Hall.
Gauch. J.M. 1992. Multiresolution Image Shape Description. Springer-Verlag.
Giraudon, G. and Deriche, R. 1991. On corner and vertex detection. In Conference on Computer Vision and Pattern Recognition, Hawaii (USA).
Guéziec, A. and Ayache, N. 1992. Smoothing and matching of 3D-space curves. In Proceedings of the Second European Conference on Computer Vision 1992, Santa Margherita Ligure, Italy.
Jiang, H., Robb, R.A., and Holton, K.S. 1992. A new approach to 3d registration of multimodality medical images by surface matching. Proc. SPIE Visualization in Biomedical Computing, pp. 192–213.
KitchenL. and RosenfeldA. 1982. Gray-level corner detection. Pattern Recognition Letters, 1:95–102.
Koenderink, J.J. 1990. Solid shape. The MIT Press.
Malandain, G. and Rocchisani, J.M. 1992. Registration of 3d medical images using a mechanical based method. Proc. 14th Int. Conf. IEEE EMBS, Sat. Symp. on 3D Advanced Image Processing in Medicine, pp. 91–95.
Metcalf, D., Kikinis, R., Guttmann, C., Vaina, L., and Jolesz, F. 1992. 4d connected component labelling applied to quantitative analysis of ms lesion temporal development. IEEE EMBS.
Monga, O., Benayoun, S., and Faugeras, O.D. 1992. Using partial derivatives of 3d images to extract typical surface features. In Proceedings CVPR'92, Urbana Champaign, Illinois. IEEE, also an INRIA Research Report (1599).
NobleA.J. 1988. Finding corners. Image and Vision Computing, 6:121–128.
PelizzariC.A., ChenG.T.Y., SpelbringD.R., WeichselbaumR.R., and ChenC.T., 1989. Accurate three-dimensional registration of ct, pet, and/or mr images of the brain. J. Comp. Assist. Tomog., 13(1):20–26.
Thirion, J.-P., Ayache, N., Monga, O., and Gourdon, A. 1992. Dispositif de traitement d'informations d'images tri-dimensionnelles avec extraction de lignes remarquables. Brevet Français, numero 92 03900. Pattent.
Thirion, J.-P. and Gourdon, A. 1992. The 3d marching lines algorithm and its application to crest lines extraction. Technical Report 1672, INRIA.
Thirion, J.-P. and Gourdon, A. 1993. The 3d marching lines algorithm: New results and proofs. Technical Report 1881, INRIA.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Thirion, JP. New feature points based on geometric invariants for 3D image registration. Int J Comput Vision 18, 121–137 (1996). https://doi.org/10.1007/BF00054999
Issue Date:
DOI: https://doi.org/10.1007/BF00054999