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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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.
H. Asada and M. Brady. The curvature primal sketch. IEEE PAMI, 8(1), 2–14, 1986.
K. Astrom. Affine and projective normalization of planar curves and regions, ECCV 94, pp. B:439–448, 1994.
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.
V. Caselles, B. Coll, and J.M. Morel. A Kanisza programme. Progress in Nonlinear Differential Equations and their Applications, 25, 1996.
V. Caselles and B. Coll and J.M. Morel, Topographic maps, preprint CEREMADE, 1997. To appear in I.J.C.V.
V. Caselles and J.L. Lisani and G. Sapiro and J.M. Morel, Shape preserving histogram modification, IEEE Trans. on Image Processing, February 1999.
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.
G. Dudek and J.K. Tsotsos. Shape representation and recognition from multiscale curvature, CVIU, 68(2), pp. 170–189, 1997.
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.
F. Guichard and J.M. Morel, Image iterative filtering and PDE’s, Preprint, 1999. Book in preparation.
R.A. Hummel, H.J. Wolfson. Affine invariant matching. DARPA88, pp. 351–364, 1988.
P. Kempenaers, L. Van Gool, and A. Oosterlinck. Shape recognition under affine distortions. VF91, pp. 323–332, 1991.
A. Mackworth and F. Mokhtarian, A theory of multiscale, curvature-based shape representation for planar curves, IEEE PAMI, 14: 789–805, 1992.
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.
G. Matheron, Random Sets and Integral Geometry, John Wiley, N.Y., 1975.
L. Moisan, Traitement numérique d’images et de films: équations aux dérivées partielles préservant forme et relief, PhD dissertation, Université Paris-Dauphine, France, 1997.
L. Moisan, Affine Plane Curve Evolution: a Fully Consistent Scheme, IEEE Transactions On Image Processing, vol. 7:3, pp. 411–420, 1998.
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.
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
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.
G. Sapiro and A. Tannenbaum, Affine Invariant Scale Space, IJCV, 11(1), 25–44, 1993.
J. Serra, Image Analysis and Mathematical Morphology, Academic Press, 1982.
A.P. Witkin, Scale space filtering, Proc. IJCAI, 1019–1023, 1983.
L. Younes Computable elastic distances between shapes, SIAM J. of Ap. Maths., 1998.
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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
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