Signed Euclidean Distance Transform Applied to Shape Analysis

  • Qin-Zhong Ye
Part of the International Centre for Mechanical Sciences book series (CISM, volume 307)


The signed Euclidean distance transform is a modified version of Danielsson’s Euclidean distance transform [1]. This distance transform produces a distance map in which each pixel is a vector of two integer components. If a distance map is created inside the objects, the two integer values of a pixel in the distance map represent the displacements of the pixel from the nearest background point in x and y directions, respectively. The unique feature of this distance transform that a vector in the distance map is always pointing to the nearest background point is exploited in several applications, such as the detection of dominant points in digital curves, curve smoothing, computing Dirichlet tessellations and finding convex hulls.


Convex Hull Binary Image Label Image Original Curve Distance Transform 


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  1. [1]
    Danielsson, P.E.: “Euclidean Distance Mapping”, Computer Graphics and Image Processing 14, 1980, pp. 227–248.CrossRefGoogle Scholar
  2. [2]
    Borgefors, G.: “Distance Transformations in Arbitrary Dimensions”, Computer Vision, Graphics and Image Processing 27, 1984, pp. 321–345.Google Scholar
  3. [3]
    Borgefors, G.: “Distance Transformations in Digital Images”, Computer Vision, Graphics and Image Processing 34, No.3, 1986, pp. 344–371.Google Scholar
  4. [4]
    Rosenfeld, A. and J.S. Weszka: “An Improved Method of Angle Detection on Digital Curves”, IEEE Trans. Comput., Vol. C-24, 1975, pp. 940–941.CrossRefGoogle Scholar
  5. [5]
    Sankar, P.V. and C.V. Sharma: “A Parallel Procedure for the Detection of Dominant Points on a Digital Curve”, Computer Graphics and Image Processing 7, 1978, pp. 403–412.CrossRefGoogle Scholar
  6. [6]
    Wall, K. and P.E. Danielsson: “A Fast Sequential Method for Polygonal Approximation of Digitized Curves”, Computer Graphics and Image Processing 28, 1984, pp. 220–227.CrossRefGoogle Scholar
  7. [7]
    Ahuja, N. and B.J. Schachter: Pattern Models, John Wiley & Sons, New York, 1983.Google Scholar
  8. [8]
    Borgefors, G.: “Distance Transformations in Digital Images”, FOA report, C 30401-E1, August 1985.Google Scholar
  9. [9]
    Rosenfeld, A. and A.C. Kak: Digital Picture Processing, Academic Press, Ice, New York, 1982.Google Scholar
  10. [10]
    Duda, R.O. and P.E. Hart: Pattern Classification and Scene Analysis, John Wiley, New York, 1973.MATHGoogle Scholar
  11. [11]
    Sklansky, J.: “Measuring Concavity on a rectangular mosaic”, IEEE Trans. Computers, Vol. C-21, December 1972, pp. 1355–1364.Google Scholar
  12. [12]
    Ye, Q.Z.: “A Convex Hull Algorithm Using the Signed Euclidean Distance Transform”, Internal Report, LiTH-ISY-I-0919, Dept. of EE, Linöping University, April 1988.Google Scholar
  13. [13]
    Yamada, H.: “Complete Euclidean Distance Transformation by Parallel Operation”, Proc. of 7th Int. Conf. on Pattern Recognition, Montreal, Canada, July 1984, pp. 69–71.Google Scholar

Copyright information

© Springer-Verlag Wien 1989

Authors and Affiliations

  • Qin-Zhong Ye
    • 1
  1. 1.Linköping UniversityLinköpingSweden

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