Systematized Calculation of Optimal Coefficients of 3-D Chamfer Norms

  • Céline Fouard
  • Grégoire Malandain
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2886)

Abstract

Chamfer distances are widely used in image analysis, and many ways have been investigated to compute optimal chamfer mask coefficients. Unfortunately, these methods are not systematized: they have to be conducted manually for every mask size or image anisotropy. Since image acquisition (e.g. medical imaging) can lead to anisotropic discrete grids with unpredictable anisotropy value, automated calculation of chamfer mask coefficients becomes mandatory for efficient distance map computation. This article presents a systematized calculation of these coefficients based on the automatic construction of chamfer masks of any size associated with a triangulation that allows to derive analytically the relative error with respect to the Euclidean distance, in any 3-D anisotropic lattice.

Keywords

chamfer distance anisotropic lattice 

References

  1. 1.
    Pudney, C.J.: Distance-ordered homotopic thinning: A skeletonization algorithm for 3d digital images. CVIU 72(3), 404–413 (1998)Google Scholar
  2. 2.
    Herman, G.T., Zheng, J., Bucholtz, C.A.: Shape-based interpolation. IEEE Computer Graphics & Applications, 69–79 (1992)Google Scholar
  3. 3.
    Shih, F.Y., Mitchell, O.R.: A mathematical morphology approach to euclidean distance transformation. IEEE Trans. on Image Processing 1(2), 197–204 (1992)CrossRefGoogle Scholar
  4. 4.
    Huang, C.T., Mitchel, O.R.: A euclidean distance transform using grayscale morphology decomposition. IEEE Trans. on PAMI 16(4), 443–448 (1994)Google Scholar
  5. 5.
    Saito, T., Toriwaki, J.I.: New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications. Pattern Recognition 27(11), 1551–1565 (1994)CrossRefGoogle Scholar
  6. 6.
    Hirata, T.: A unified linear-time algorithm for computing distance maps. Information Processing Letters 58, 129–133 (1996)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Danielsson, P.E.: Euclidean distance mapping. CGIP 14, 227–248 (1980)Google Scholar
  8. 8.
    Ragnemalm, I.: The euclidean distance transform in arbitrary dimensions. PRL 14(11), 883–888 (1993)MATHGoogle Scholar
  9. 9.
    Borgefors, G.: Distance transformations in digital images. CVGIP 34(3), 344–371 (1986)Google Scholar
  10. 10.
    Borgefors, G.: Distance transformations in arbitrary dimensions. CVGIP 27, 321–345 (1984)Google Scholar
  11. 11.
    Verwer, B.J.H.: Local distances for distance transformations in two and three dimensions. PRL 12, 671–682 (1991)Google Scholar
  12. 12.
    Borgefors, G.: On digital distance transforms in three dimensions. CVIU 64(3), 368–376 (1996)Google Scholar
  13. 13.
    Coquin, D., Bolon, P.: Discrete distance operator on rectangular grids. PRL 16, 911–923 (1995)Google Scholar
  14. 14.
    Mangin, J.F., Bloch, I., López-Krahe, J., Frouin, V.: Chamfer distances in anisotropic 3D images. In: VII European Signal Processing Conference, Edimburgh, UK (1994)Google Scholar
  15. 15.
    Sintorn, I.M., Borgefors, G.: Weighted distance transfoms for images using elongated voxel grids. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 244–254. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Remy, E.: Optimizing 3d chamfer masks with norm constraints. In: IWCIA, pp. 39–56 (July 2000)Google Scholar
  17. 17.
    Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. JACM 13(4), 471–494 (1966)MATHCrossRefGoogle Scholar
  18. 18.
    Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers. Oxford University Press, Oxford (1978)Google Scholar
  19. 19.
    Thiel, E.: Les distances de chanfrein en analyse d’images: fondements et applications. PhD thesis, Université Joseph Fourier (1994)Google Scholar
  20. 20.
    Remy, E.: Normes de chanfrein et axe médian dans le volume discret. PhD thesis, Université de la Méditerranée, Marseille, France (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Céline Fouard
    • 1
    • 2
    • 3
  • Grégoire Malandain
    • 1
  1. 1.Epidaure Research ProjectINRIA Sophia AntipolisFrance
  2. 2.TGS Europe SAMerignac Cedex
  3. 3.INSERM U455 Toulouse 

Personalised recommendations