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Diffeomorphisms Groups and Pattern Matching in Image Analysis

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Abstract

In a previous paper, it was proposed to see the deformations of a common pattern as the action of an infinite dimensional group. We show in this paper that this approac h can be applied numerically for pattern matching in image analysis of digital images. Using Lie group ideas, we construct a distance between deformations defined through a metric given the cost of infinitesimal deformations. Then we propose a numerical scheme to solve a variational problem involving this distance and leading to a sub-optimal gradient pattern matching. Its links with fluid models are established.

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References

  • Amit, Y., Grenander, U., and Piccioni, M. 1991. Structural image restoration through deformable templates. Jour. Amer. Stat. Ass., 86:376-387.

    Google Scholar 

  • Azencott, R. 1994. Random and deterministic deformations applied to shape recognition. Cortona workshop, 10th-16th, Italy.

  • Besl, J.P. 1989. The free-form surface matching problem. In Machine Vision for Three-Dimensional Scenes (Workshop on Machine Vision-Acquirind and Interpreting the 3D Scene), H. Freeman (Ed.), New Brunswick, NJ, Academic Press, pp. 25-71.

    Google Scholar 

  • Bookstein, F.L. and Green W.D.K. 1993. A feature space for derivatives of deformations. In Information Processing in Medical Imaging (IPMI’93), H.H. Barett and A.F Gmitro (Eds.), Flagstaff, Arizona, vol. 687 of Lecture Notes in Computer Science, Springer-Verlag, pp. 1-16.

  • Chow, Y., Grenander, U., and Keenan, D.M. 1991. HANDS, A pattern Theoretical Study of Biological Shapes. Springer-Verlag.

  • Christensen, G., Rabbit, R.D., and Miller, M.I. 1996. Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing, 5(10):1437-1447.

    Article  Google Scholar 

  • Lanitis, A., Taylor, C.J., and Cootes, T.F. 1995.Aunified approach to coding and interpreting face images. In Proc. 5th ICCV, pp. 368-373.

  • Miller, M.I., Christensen, G.E., Amit, Y., and Grenander, U. 1993. Mathematical textbook of deformable neuroanatomies. In Proc. of the National Academy of Science, vol. 90, pp. 11944-11948.

    Google Scholar 

  • Piccioni, M., Scarlatti, S., and Trouvé, A. A variational problem arising from speech recognition. Siam. J. Appl. Math., to appear.

  • Ruprecht, D. and Müller, H. 1992. Image warping with scattered data interpolation methods. Research Report 443, Dortmunt University.

  • Szeliski, R. and Coughlan, J. 1994. Hierarchical spline-based image registration. In IEEE Conf. on Computer Vision and Pattern Recognition (CVPR’94), Seattle, Washington, pp. 194-201.

  • Trouvé, A. 1995a. An approach of pattern recognition through infi-nite dimensional group actions. Rapport de recherche du LMENS.

  • Trouvé, A. 1995b. An infinite dimensional group approach for physics based models in pattern recognition. Preprint.

  • Younes, L. Computable elastic distance between shapes. Siam. J. Appl. Math., to appear.

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Trouvé, A. Diffeomorphisms Groups and Pattern Matching in Image Analysis. International Journal of Computer Vision 28, 213–221 (1998). https://doi.org/10.1023/A:1008001603737

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  • DOI: https://doi.org/10.1023/A:1008001603737

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