Advertisement

Chordal Axis on Weighted Distance Transforms

  • Jérôme Hulin
  • Edouard Thiel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4245)

Abstract

Chordal Axis (CA) is a new representation of planar shapes introduced by Prasad in [1], useful for skeleton computation, shape analysis, characterization and recognition. The CA is a subset of chord and center of discs tangent to the contour of a shape, derivated from Medial Axis (MA). Originally presented in a computational geometry approach, the CA was extracted on a constrained Delaunay triangulation of a discretely sampled contour of a shape. Since discrete distance transformations allow to efficiently compute the center of distance balls and detect discrete MA, we propose in this paper to redefine the CA in the discrete space, to extract on distance transforms in the case of chamfer norms, for which the geometry of balls is well-known, and to compare with MA.

Keywords

image analysis shape description chordal axis medial axis discrete geometry chamfer or weighted distances 

References

  1. 1.
    Prasad, L.: Morphological analysis of shapes. CNLS Newsletter 139 (1997)Google Scholar
  2. 2.
    Blum, H.: A transformation for extracting new descriptors of shape. In: Wathen-Dunn, W. (ed.) Models for the Perception of Speech and Visual Form, pp. 362–380. MIT Press, Cambridge (1967)Google Scholar
  3. 3.
    Pfaltz, J., Rosenfeld, A.: Computer representation of planar regions by their skeletons. Comm. of ACM 10, 119–125 (1967)CrossRefGoogle Scholar
  4. 4.
    Montanari, U.: Continuous skeletons from digitized images. Journal of the ACM 16(4), 534–549 (1969)zbMATHCrossRefGoogle Scholar
  5. 5.
    Attali, D., Montanvert, A.: Semicontinuous skeletons of 2d and 3d shapes. In: Aspects of Visual Form Processing, pp. 32–41. World Scientific, Singapore (1994)Google Scholar
  6. 6.
    Prasad, L.: Rectification of the chordal axis transform and a new criterion for shape decomposition. In: 11th DGCI, Poitiers (2005)Google Scholar
  7. 7.
    Remy, E., Thiel, E.: Medial Axis for Chamfer Distances: computing LUT and Neighbourhoods in 2D or 3D. Pattern Recognition Letters 23(6), 649–661 (2002)zbMATHCrossRefGoogle Scholar
  8. 8.
    Remy, E., Thiel, E.: Exact Medial Axis with Euclidean Distance. Image and Vision Computing 23(2), 167–175 (2005)CrossRefGoogle Scholar
  9. 9.
    Borgefors, G.: Distance transformations in arbitrary dimensions. Computer Vision, Graphics and Image Processing 27, 321–345 (1984)CrossRefGoogle Scholar
  10. 10.
    Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. Journal of ACM 13(4), 471–494 (1966)zbMATHCrossRefGoogle Scholar
  11. 11.
    Borgefors, G.: Distance transformations in digital images. Computer Vision, Graphics and Image Processing 34, 344–371 (1986)CrossRefGoogle Scholar
  12. 12.
    Thiel, E.: Géométrie des distances de chanfrein. HDR, Univ. de la Méditerranée, Aix-Marseille 2 (2001), http://www.lif-sud.univ-mrs.fr/~thiel/hdr
  13. 13.
    Attali, D., Sanniti di Baja, G., Thiel, E.: Skeleton simplification through non significant branch removal. Image Processing and Communications 3(3-4), 63–72 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jérôme Hulin
    • 1
  • Edouard Thiel
    • 1
  1. 1.Laboratoire d’Informatique Fondamentale de Marseille (LIF, UMR 6166)France

Personalised recommendations