There are plenty of different algorithms for aligning pairs of 2D-shapes and point-sets. They mainly concern the establishment of correspon-dences and the detection of outliers. All of them assume that the aligned shapes are quite similar and belonging to the same class of shapes. But special problems arise if we have to align shapes that are very different, for example aligning concave shapes to convex ones. In such cases it is indispensable to take into account the order of the point-sets and to enforce legal sets of correspondences; otherwise the calculated distances are incorrect. We present our novel shape alignment algorithm which can handle such cases also. The algorithm establishes legal one-to-one point correspondences between arbitrary shapes, represented as ordered sets of 2D-points and returns a distance measure which runs between 0 and 1.


Shape Alignment Correspondence Problem Aligning Convex to Concave Shapes and vise-versa 


  1. 1.
    Kendall, D.G.: A Survey of the Statistical Theory of Shape. Statistical Science 4(2), 87–120 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bookstein, F.L.: Size and Shape Spaces for Landmark Data in Two Dimensions. Statistical Science 1(2), 181–242 (1986)zbMATHCrossRefGoogle Scholar
  3. 3.
    Belongie, S., Malik, J., Puzicha, J.: Shape Matching and Object Recognition Using Shape Contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(24), 509–522 (2002)CrossRefGoogle Scholar
  4. 4.
    Ueda, N., Suzuki, S.: Learning Visual Models from Shape Contours Using Multiscale Convex/Concave Structure Matching. IEEE Trans. on Pattern Analysis and Machine Learning 15(4), 307–352 (1993)Google Scholar
  5. 5.
    Perner, P., Jänichen, S.: Learning of Form Models from Exemplars. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds.) SSPR&SPR 2004. LNCS, vol. 3138, pp. 153–161. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Rangarajan, A., Chui, H., Bookstein, F.L.: The Softassign Procrustes Matching Algorithm. In: Duncan, J.S., Gindi, G. (eds.) IPMI 1997. LNCS, vol. 1230, pp. 29–42. Springer, Heidelberg (1997)Google Scholar
  7. 7.
    Sclaroff, S., Pentland, A.: Modal Matching for Correspondence and Recognition. IEEE Trans. Pattern Analysis and Machine Intelligence 17(6), 545–561 (1995)CrossRefGoogle Scholar
  8. 8.
    Feldmar, J., Ayache, N.: Rigid, Affine and Locally Affine Registration of Free-Form Surfaces. The International Journal of Computer Vision 18(3), 99–119 (1996)CrossRefGoogle Scholar
  9. 9.
    Hill, A., Taylor, C.J., Brett, A.D.: A Framework for Automatic Landmark Identification Using a New Method of Nonrigid Correspondence. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(3), 241–251 (2000)CrossRefGoogle Scholar
  10. 10.
    Veltkamp, R.C.: Shape Matching: Similarity Measures and Algorithms. Shape Modelling International, pp. 188–197 (2001)Google Scholar
  11. 11.
    Lele, S.R., Richtsmeier, J.T.: An Invariant Approach to Statistical Analysis of Shapes. Chapman & Hall/CRC (2001)Google Scholar
  12. 12.
    Besl, P., McKay, N.: A Method for Registration of 3-D Shapes. IEEE Trans. Pattern Analysis and Machine Intelligence 14(2), 239–256 (1992)CrossRefGoogle Scholar
  13. 13.
    Marte, O.-C., Marais, P.: Model-Based Segmentation of CT Images. South African Computer Journal 28, 54–59 (2002)Google Scholar
  14. 14.
    Fitzgibbon, A.W.: Robust Registration of 2D and 3D Point Sets. In: Proc. British Machine Vision Conference, Manchester, UK, vol. II, pp. 411–420 (2001)Google Scholar
  15. 15.
    Belongie, S., Malik, J., Puzicha, J.: Shape Matching and Object Recognition Using Shape Contexts. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(24), 509–522 (2002)CrossRefGoogle Scholar
  16. 16.
    Perner, P., Jähnichen, S.: Case Acquisition and Case Mining for Case-Based Object Recognition. In: Funk, P., González Calero, P.A. (eds.) ECCBR 2004. LNCS (LNAI), vol. 3155, pp. 616–629. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Silke Jänichen
    • 1
  • Petra Perner
    • 1
  1. 1.Institute of Computer Vision and applied Computer SciencesIBaILeipzig

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