Robust Normalization of Shapes

  • Javier Cortadellas
  • Josep Amat
  • Manel Frigola
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)


The normalization of a binary shape is a necessary step in many image processing tasks based on image domain operations. When one must deal with deformable shapes (due to the projection of non-rigid objects onto the image plane or small changes in the position of the view point), the traditional approaches doesn’t perform well. This paper presents a new method for shape normalization based on robust statistics techniques, which allows to keep the location and orientation of shapes constant independent of the possible deformations they can suffer. A numerical comparison of the sensitivity of both methods is used as a measure to validate the proposed technique, together with a ratio of areas between the non-overlapping regions and the overlapping regions of the normalized shapes. The results presented, involving synthetic and real shapes, show that the new normalization approach is much more reliable and robust that the traditional one.


  1. [1]
    M. J. Black and P. Anandan. “The robust estimation of multiple motions: parametric and piecewise-smooth flow-fields”. Computer Vision Image Understanding, Vol. 63, No. 1, pp. 75–104, 1996.CrossRefGoogle Scholar
  2. [2]
    J. C. Russ. The Image Processing handbook, 2nd. edition. CRC Press, 1995.Google Scholar
  3. [3]
    A. Rosenfeld, A. C. Kak. Digital Picture Processing, Vols. 1 & 2. Academic Press, 1982.Google Scholar
  4. [4]
    A. K. Jain, Fundamentals of Digital Image Processing. Prentice Hall, 1989.Google Scholar
  5. [5]
    R. M. Haralick, L. G. Shapiro. Computer and Robot Vision, Vols. I&II. Addison-Wesley, 1993.Google Scholar
  6. [6]
    F. de la Torre, M. Black. “A Framework for Robust Subspace Learning”. Accepted for Int. Journal of Computer Vision, 2002.Google Scholar
  7. [7]
    F. Hampel, E. Ronchetti, P. Rousseeuw, W. Stahel. Robust Statistics: The Approach based on Influence Functions. Wiley, 1986.Google Scholar
  8. [8]
    P. J. Huber. Robust Statistics. Wiley, 1981Google Scholar
  9. [9]
    S. Geman, D. McClure. “Statistical methods for tomo-graphic image reconstruction”. Bulletin of the Inter-national Statistical Institute. Vol. LII, pp. 4–5, 1987.Google Scholar
  10. [10]
    D. Mintz, P. Meer. “Robust Estimators in Computer Vision: an Introduction to Least Median of Squares Regression”. Artificial Intelligence and Computer vision, Y.A. Feldman, A. Bruckstein (Eds.). Elsevier, 1991.Google Scholar
  11. [11]
    G. Borgefors. “Distance transformations in arbitrary dimensions”. CVGIP, Vol.27, pp.321–345, 1984Google Scholar
  12. [12]
    P.L. Rosin. “Measuring Shape: Ellipticity, Rectangu-larity, and Triangularity”. 15th Int. Conf. Pattern Recognition, Barcelona, Spain, vol. 1, pp. 952–955, 2000.Google Scholar
  13. [13]
    J. Cortadellas, J. Amat, “Image Associative Memory”. 15th Int. Conf. Pattern Recognition, Barcelona, Spain, vol. 3, pp. 638–641, 2000.Google Scholar
  14. [14]
    V. Bruce, P.R. Green, M.A. Georgeson. Visual Perception. Physiology, Psychology and Ecology. 3rd. Ed., Psychology Press, 1996.Google Scholar
  15. [15]
    L. Xu, A. Yuille, “Robust Principal Component Analysis by Self-Organizing Rules Based on Statistical Physics Approach”, IEEE Trans. on Neural Networks, Vol. 6, N° 1, January 1995Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Javier Cortadellas
    • 1
  • Josep Amat
    • 2
  • Manel Frigola
    • 3
  1. 1.Departament d’Electrònica, Enginyeria La SalleUniversitat Ramon LlullBarcelonaSpain
  2. 2.IRI - Institut de Robòtica e InformàticaUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Departament d’Enginyeria de Sistemes, Automàtica i Informàtica IndustrialUniversitat Politècnica de CatalunyaBarcelonaSpain

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