Advertisement

Two-Dimensional Discrete Morphing

  • Isameddine Boukhriss
  • Serge Miguet
  • Laure Tougne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)

Abstract

In this article we present an algorithm for discrete object deformation. This algorithm is a first step for computing an average shape between two discrete objects and may be used for building a statistical atlas of shapes. The method we develop is based on discrete operators and works only on digital data. We do not compute continuous approximations of objects so that we have neither approximations nor interpolation errors. The first step of our method performs a rigid transformation that aligns the shapes as best as possible and decreases geometrical differences between them. The next step consists in searching the progressive transformations of one object toward the other one, that iteratively adds or suppresses pixels. These operations are based on geodesic distance transformation and lead to an optimal (linear) algorithm.

Keywords

Distance Information Average Shape Rigid Transformation Inertia Moment Rigid Registration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ber96]
    Bertrand, G.: A Boolean Characterization of Three-dimensional Simple Points. Pattern Recognition Letters 17, 115–124 (1996)CrossRefGoogle Scholar
  2. [Blu67]
    Blum: A Transformation for Extracting new Descriptors of Shape. In models for perception of speech and visual form, 362–380 (1967)Google Scholar
  3. [Bor88]
    Borgefors, G.: Hierarchical Chamfer Matching: a Parametric Edge Matching Algorithm. IEEE transactions on pattern analysis and machine intelligence (1988)Google Scholar
  4. [BTSG00]
    Blanding, R., Turkiyyah, G., Storti, D., Ganter, M.: Skeleton-based Three Dimensional Geometric Morphing. Computational Geometry 15, 129–148 (2000)CrossRefGoogle Scholar
  5. [CLRS01]
    Cormen, T.H., Leiserson, C.H., Rivest, R.L., Stein, C.: Inroduction à l’Algorithmique. xDunod, Paris (2001)Google Scholar
  6. [CMT04]
    Coeurjolly, D., Miguet, S., Tougne, L.: 2D and 3D Visibility in Discrete Geometry: An Application to Discrete Geodesic Paths. Pattern Recognition Letters 25, 561–570 (2004)CrossRefGoogle Scholar
  7. [FLD02]
    Fleute, M., Lavallé, S., Desbat, L.: Integrated approach for matching statistical shape models with intra-operative 2D and 3D data. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002, Part II. LNCS, vol. 2489, pp. 364–372. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. [Iwa02]
    Iwanowski, M.: Image Morphing Based on Morphological Interpolation Combined with Linear Filtering (2002), Available at http://wscg.zcu.cz/wscg2002/Papers_2002/A23.pdf
  9. [LB98]
    Liu, A., Bullitt, E.: 3D/2D Registration via Skeletal near Projective Invariance in Tubular Objectives. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 952–963. Springer, Heidelberg (1998)Google Scholar
  10. [MMF98]
    Maurer, C.R., Maciunas, R.J., Fitzpatrick, J.M.: Registration of Head CT Images to Physical Space Using Multiple Geometrical Features. In: Proc. SPIE Medical Imaging 1998, San diego, CA, February 1998, vol. 3338, pp. 72–80 (1998)Google Scholar
  11. [RMP+̂98]
    Roche, A., Malandain, G., Pennec, X., Cathier, P., Ayache, N.: Multimodal Image Registration by Maximisation of the Correlation Ratio. Technical Report 3378, INRIA (1998), Available at http://www.inria.fr/rrrt/rr-3378.html
  12. [RP68]
    Rosenfeld, A., Pfaltz, J.L.: Distance functions on digital pictures. Pattern Recognition 1, 33–61 (1968)CrossRefMathSciNetGoogle Scholar
  13. [Wol90]
    Wolberg, G.: Digital Image Warping. IEEE Computer Society Press, Los Alamitos (1990)Google Scholar
  14. [WV96]
    Wells, A., Viola, P.: Multimodal Volume Registration by Maximization of Mutual Information. Medical Image Analysis 1, 32–52 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Isameddine Boukhriss
    • 1
  • Serge Miguet
    • 1
  • Laure Tougne
    • 1
  1. 1.Laboratoire LIRISUniversité Lyon 2Bron CedexFrance

Personalised recommendations