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Affine Invariant Mathematical Morphology Applied to A Generic Shape Recognition Algorithm

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Mathematical Morphology and its Applications to Image and Signal Processing

Part of the book series: Computational Imaging and Vision ((CIVI,volume 18))

Abstract

We design a generic contrast and affine invariant planar shape recognition algorithm. By generic, we mean an algorithm which delivers a list of all shapes two digital images have in common, up to any affine transform or contrast change. We define as“shape elements” all pieces of level lines of the image. Their number can be drastically reduced by using affine and contrast invariant smoothing Matheron operators, which we describe as alternate affine erosions-dilations. We then discuss an efficient local encoding of the shape elements. We finally show experiments. Applications aimed at include image registration, image indexing, optical flow.

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References

  1. L. Alvarez, F. Guichard, P.L. Lions, J.M. Morel, Axioms and Fundamental Equations on Image Processing, Technical Report 9231, CEREMADE, 1992 and Arch. for Rat. Mech. Anal. 16(9), 200–257, 1993.

    MathSciNet  Google Scholar 

  2. H. Asada and M. Brady. The curvature primal sketch. IEEE PAMI, 8(1), 2–14, 1986.

    Google Scholar 

  3. K. Astrom. Affine and projective normalization of planar curves and regions, ECCV 94, pp. B:439–448, 1994.

    Google Scholar 

  4. S.K. Bose, K.K. Biswas and S.K. Gupta. Model-based object recognition: the role of affine invariants. AIEng, 10(3): 227–234, 1996.

    Google Scholar 

  5. V. Caselles, B. Coll, and J.M. Morel. A Kanisza programme. Progress in Nonlinear Differential Equations and their Applications, 25, 1996.

    Google Scholar 

  6. V. Caselles and B. Coll and J.M. Morel, Topographic maps, preprint CEREMADE, 1997. To appear in I.J.C.V.

    Google Scholar 

  7. V. Caselles and J.L. Lisani and G. Sapiro and J.M. Morel, Shape preserving histogram modification, IEEE Trans. on Image Processing, February 1999.

    Google Scholar 

  8. Cohignac, T. and Lopez, C. and Morel, J.M., Integral and Local Affine Invariant Parameter and Application to Shape Recognition, ICPR pp. A:164–168, 1994.

    Google Scholar 

  9. G. Dudek and J.K. Tsotsos. Shape representation and recognition from multiscale curvature, CVIU, 68(2), pp. 170–189, 1997.

    Google Scholar 

  10. O. Faugeras and R. Keriven, Some recent results on the projective evolution of 2D curves. In Proc. IEEE ICIP, vol. 3, pp. 13–16, Washington, October 1995.

    Google Scholar 

  11. F. Guichard and J.M. Morel, Image iterative filtering and PDE’s, Preprint, 1999. Book in preparation.

    Google Scholar 

  12. R.A. Hummel, H.J. Wolfson. Affine invariant matching. DARPA88, pp. 351–364, 1988.

    Google Scholar 

  13. P. Kempenaers, L. Van Gool, and A. Oosterlinck. Shape recognition under affine distortions. VF91, pp. 323–332, 1991.

    Google Scholar 

  14. A. Mackworth and F. Mokhtarian, A theory of multiscale, curvature-based shape representation for planar curves, IEEE PAMI, 14: 789–805, 1992.

    Google Scholar 

  15. G. Koepfler, L. Moisan, Geometric Multiscale Representation of Numerical Images, Proc. of the Second Int. Conf. on Scale-Space Theories in Computer Vision, in Springer Lecture Notes in Computer Science, vol. 1682, pp. 339–350, 1999.

    Google Scholar 

  16. G. Matheron, Random Sets and Integral Geometry, John Wiley, N.Y., 1975.

    Google Scholar 

  17. L. Moisan, Traitement numérique d’images et de films: équations aux dérivées partielles préservant forme et relief, PhD dissertation, Université Paris-Dauphine, France, 1997.

    Google Scholar 

  18. L. Moisan, Affine Plane Curve Evolution: a Fully Consistent Scheme, IEEE Transactions On Image Processing, vol. 7:3, pp. 411–420, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  19. P. Monasse, Contrast Invariant Image Registration, Proc. of I. V. Conf. on Acoustics, Speech and Signal Processing, Phoenix, Arizona, vol 6, 1999, pp. 3221–3224.

    Google Scholar 

  20. P. Monasse and F. Guichard, Fast Computation of a Contrast-Invariant Image Representation, to appear in IEEE Transactions on Image Processing, 1998, preprint CMLA 9815, available at http://www.cmla.ens-cachan.fr

  21. P. Monasse and F. Guichard, Scale-Space from a Level Lines Tree, Proc. of 2nd Int. Conf. on Scale-Space Theories in Computer Vision, Corfu, Greece, 1999, pp. 175–186.

    Google Scholar 

  22. G. Sapiro and A. Tannenbaum, Affine Invariant Scale Space, IJCV, 11(1), 25–44, 1993.

    Article  Google Scholar 

  23. J. Serra, Image Analysis and Mathematical Morphology, Academic Press, 1982.

    Google Scholar 

  24. A.P. Witkin, Scale space filtering, Proc. IJCAI, 1019–1023, 1983.

    Google Scholar 

  25. L. Younes Computable elastic distances between shapes, SIAM J. of Ap. Maths., 1998.

    Google Scholar 

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© 2002 Kluwer Academic/Plenum Publishers

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Lisani, J.L., Moisan, L., Monasse, P., Morel, J.M. (2002). Affine Invariant Mathematical Morphology Applied to A Generic Shape Recognition Algorithm. In: Goutsias, J., Vincent, L., Bloomberg, D.S. (eds) Mathematical Morphology and its Applications to Image and Signal Processing. Computational Imaging and Vision, vol 18. Springer, Boston, MA. https://doi.org/10.1007/0-306-47025-X_11

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  • DOI: https://doi.org/10.1007/0-306-47025-X_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-7862-4

  • Online ISBN: 978-0-306-47025-7

  • eBook Packages: Springer Book Archive

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