Abstract
In this paper, we propose a new framework to perform nonrigid surface registration. It is based on various extensions of an iterative algorithm recently presented by several researchers (Besl and McKay, 1992; Champleboux et al., 1992; Chen and Medioni, 1992; Menq and Lai, 1992; Zhang, 1994) to rigidly register surfaces represented by a set of 3D points, when a prior estimate of the displacement is available. Our framework consists of three stages:
•First, we search for the best rigid displacement to superpose the two surfaces. We show how to efficiently use curvatures to superpose principal frames at possible corresponding points in order to find a prior rough estimate of the displacement and initialize the iterative algorithm.
•Second, we search for the best affine transformation. We introduce differential information in points coordinates: this allows us to match locally similar points. Then, we show how principal frames and curvatures are transformed by an affine transformation. Finally, we introduce this differential information in a global criterion minimized by extended Kalman filtering in order to ensure the convergence of the algorithm.
•Third, we locally deform the surface. Instead of computing a global affine transformation, we attach to each point a local affine transformation varying smoothly along the surface. We call this deformation a locally affine deformation.
All these stages are illustrated with experiments on various real biomedical surfaces (teeth, faces, skulls, brains and hearts), which demonstrate the validity of the approach.
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Ayache, N. 1991. Artificial Vision for Mobile Robots-Stereo-Vision and Multisensory Perception. MIT Press.
Ayache, N. 1993. Analysis of three-dimensional medical images-results and challenges. Technical Report 2050, INRIA.
BajcsyR. and KovacicS. 1989. Multiresolution elastic matching. CVGIP, 46:1–21.
Bardinet, E., Cohen, L., and Ayache, N. 1994. Fitting 3-d data using superquadrics and free-form deformations. In Proceedings of the IEEE International Conference on Pattern Recognition, Jerusalem, Israel. Also in Proceedings of the IEEE Workshop on Biomedical Images Analysis (WBIA'94), Seattle, Washington.
BeslP. and McKayN. 1992. A method for registration of 3-D shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(2):239–256.
BrownL.G. 1992. A survey of image registration techniques. ACM Computing Surveys, 24(4):325–375.
Champleboux, G., Lavallée, S., Szeliski, R., and Brunie, L. 1992. From accurate range imaging sensor calibration to accurate modelbased 3-D object localization. In Proceedings of the IEEE Conference on Vision and Pattern Recognition, Urbana Champaign.
ChenY. and MedioniG. 1992. Object modeling by registration of multiple range images. Image and Vision Computing, 10(3):145–155.
Cohen, I., Ayache, N., and Sulger, P. 1992. Tracking points on deformable objects using curvature information. In Proceedings of the Second European Conference on Computer Vision 1992, Santa Margherita Ligure, Italy.
Cohen, L. 1994. Use of auxiliary variables in computer vision problems. Cahiers de mathematiques de la décision, (9409).
DanielssonP.E., 1980. Euclidean distance mapping. Computer Graphics and Image Processing, 14:227–248.
Delingette, H. 1994. Simplex meshes: A general representation for 3d shape reconstruction. In IEEE Conference on Vision and Pattern Recognition, Seattle.
deCarmoM.P. 1976. Differential Geometry of Curves and Surfaces. Prentice-Hall: Englewood Cliffs.
Duncan, J.S., Owen, R.L., Staib, L.H., and Anandan, P. 1991. Measurement of non-rigid motion using contour shape descriptor. In CVPR'91, Hawaii.
FaugerasO. and HébertM. 1986. The representation, recognition and locating of 3d objects. Int. J. Robotics Res., 5(3):27–52.
Gourdon, A. and Ayache, N. 1994. Matching a curve on a surface using differential properties. In Proceedings of the Third European Conference on Computer Vision 1994, Stockholm, Sweden.
Grimson, W. 1990. Object Recognition by Computer: The role of geometric constraints. MIT Press.
Guéziec, A. and Ayache, N. 1994. Smoothing and matching of 3-D-space curves. Int. Journal of Computer Vision, 12(1).
Guéziec, A. 1993. Large deformable splines, crest lines and matching. In Proceedings of the Fourth International Conference on Computer Vision (ICCV'93), Berlin.
HosakaM. 1992. Modeling of Curves and Surfaces in CAD/CAM. Springer Verlag: Berlin.
Malandain, G. and Rocchisani, J.M. 1992. Registration of 3-D medical images using a mechanical based method. In Proceedings of the Fourteenth Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBS 92), Satellite Symposium on 3-D Advanced Image Processing in Medicine, Rennes, France.
McInerney, D. and Terzopoulos, T. 1993. A finite element model for 3d shape reconstruction and non rigid motion tracking. In Proceedings of the Fourth International Conference on Computer Vision (ICCV'93), Berlin.
Menq YauH.-T.C.-H. and LaiG.-Y., 1992. Automated precision measurement of surface profile in cad-directed inspection. IEEE Trans. RA, 8(2):268–278.
Metaxas, D. and Terzopoulos, D. 1991. Constrained deformable superquadrics and nonrigid motion tracking. In IEEE Proceedings of Computer Vision and Pattern Recognition, pp. 337–343. IEEE Computer Society Conference. Lahaina, Maui, Hawaii.
Nastar, C. and Ayache, N. 1993. Fast segmentation, tracking, and analysis of deformable objects. In Proceedings of the Fourth International Conference on Computer Vision (ICCV'93), Berlin.
PentlandA. and SclaroffS. 1991. Closed-form solutions for physically based shape modelling and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-13(7):715–729.
Preparata, F.P. and Shamos, M.I. 1985. Computational Geometry, an Introduction. Springer Verlag.
Szeliski, R. and Lavallée, S. 1994. Matching 3-d anatomical surfaces with non-rigid volumetric deformations. In Proceedings of the IEEE Workshop on Biomedical Images Analysis (WBIA'94), Seattle, Washington. Also in AAAI 1994 Spring Symposium Series. Application of Computer Vision in Medical Image Processing, Stanford University.
Thirion, J.P. 1994. New feature points based on geometric invariants for 3D image registration. In IEEE Conference on Vision and Pattern Recognition, Seattle,
Thirion, J.P. and Gourdon, A. 1992. The 3-D marching lines algorithm and its application to crest lines extraction. Technical Report 1672, INRIA.
ZhangZ. 1994. Iterative point matching for registration of free-form curves and surfaces. The International Journal of Computer Vision, 13(2):119–152. Also Research Report No. 1658, INRIA Sophia-Antipolis.
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Feldmar, J., Ayache, N. Rigid, affine and locally affine registration of free-form surfaces. Int J Comput Vision 18, 99–119 (1996). https://doi.org/10.1007/BF00054998
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DOI: https://doi.org/10.1007/BF00054998