Advertisement

Some Weighted Distance Transforms in Four Dimensions

  • Gunilla Borgefor
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

Abstract

In a digital distance transform,each picture element in the shape (background)has a va ue measuring the distance to the background (shape).In a weighted distance transform,the distance between two points is de .ned by path consisting of a number of steps between neighbouring picture e ements,where each type of possible step is given a ength-va ue,or a weight.In 4D,using 3 ×3 ×3 ×3 neighbourhoods,there are four di .erent weights.In this paper,optimal real and integer weights are computed for one type of 4D weighted distance transforms.The most useful integer transform is probably (3 , 4 , 5 , 6) , but there are a number of other ones listed.Two integer distance transform are illustrated by their associated balls.

References

  1. 1.
    G. Borgefors, Distance transformations in arbitrary dimensions, Computer Vision, Graphics, and Image Processing 27 1984, pp.321–345.325,326,328,333CrossRefGoogle Scholar
  2. 2.
    G. Borgefors, Distance transformations in digital images Computer Vision, Graph-ics, and Image Processing 34 1986, pp.344–371.326CrossRefGoogle Scholar
  3. 3.
    G. Borgefors, On digita distance transforms in three dimensions,Computer Vision and Image Understanding, Vo.64 No.3, (1996), pp.368–376. 326,327,332,333CrossRefGoogle Scholar
  4. 4.
    H. S. M. Coxeter, Regular polytopes, Dover Publications, Inc., New York, 1973. 332Google Scholar
  5. 5.
    G. Borgefors, H. Guo, Weighted distance transform hyperspheres in four dimensions, Proc. SSAB Symposium on Image Analysis 1997, Stockholm, Sweden, March 1997, pp.71–76. 332Google Scholar
  6. 6.
    M. Fidrich: Iso-surface extraction in 4D with applications related to scale space, In Miguet, Montanvert, Ubéda, Eds., Discrete Geometry for Computer Imagery, Springer 1996 (LNCS 1176), pp.257–268. 325Google Scholar
  7. 7.
    P. P. Jonker and O. Vermeij, On skeletonization in 4D images,In Perner, Wang, Rosenfeld, Eds., Advances in Structura and Syntactica Pattern Recognition, Springer 1996 (LNCS 1121), pp.79–89. 325Google Scholar
  8. 8.
    C.O. Kiselman, Regularity properties of distance transformations in image analysis, Computer Vision and Image Understanding, Vol. 64 No.3, (1996), pp. 390–398. 325,326,327CrossRefGoogle Scholar
  9. 9.
    T.Y. Kong, Topology-preserving deletion of 1’ s from 2-, 3-, and 4-dimensional binary images,In Ahronovitz and Fiorio, Eds., Discrete Geometry for Computer Imagery,Springer 1997 (LNCS 1347), pp. 3–18. 325Google Scholar
  10. 10.
    A. Rosenfeld and J. Pfaltz, Sequentia operations in digita picture processing, Journal of the ACM 13 (4), 1966, pp.471–494. 325zbMATHCrossRefGoogle Scholar
  11. 11.
    M. Yamashita and T. Ibaraki: Distance defined by neighborhood sequences, Pattern Recognition 19 1986, pp.237–246.326zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Gunilla Borgefor
    • 1
  1. 1.Centre for Image AnalysisSwedish University of Agricultural SciencesUppsalaSweden

Personalised recommendations