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Approximating Euclidean Distance Using Distances Based on Neighbourhood Sequences in Non-standard Three-Dimensional Grids

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Combinatorial Image Analysis (IWCIA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4040))

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Abstract

In image processing, it is often of great importance to have small rotational dependency for distance functions. We present an optimization for distances based on neighbourhood sequences for the face-centered cubic (fcc) and body-centered cubic (bcc) grids. In the optimization, several error functions are used measuring different geometrical properties of the balls obtained when using these distances.

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References

  1. Rosenfeld, A., Pfaltz, J.L.: Sequential operations in digital picture processing. J. ACM 13(4), 471–494 (1966)

    Article  MATH  Google Scholar 

  2. Rosenfeld, A., Pfaltz, J.L.: Distance functions on digital pictures. Pattern Recognition 1, 33–61 (1968)

    Article  MathSciNet  Google Scholar 

  3. Aswatha, M., Chatterji, B.N., Mukherjee, J., Das, P.P.: Representation of 2D and 3D binary images using medial circles and spheres. International Journal of Pattern Recognition and Artificial Intelligence 10(4), 365–387 (1996)

    Article  Google Scholar 

  4. Borgefors, G.: Distance transformations in arbitrary dimensions. Computer Vision, Graphics, and Image Processing 27, 321–345 (1984)

    Article  Google Scholar 

  5. Borgefors, G.: Distance transformations in digital images. Computer Vision, Graphics, and Image Processing 34, 344–371 (1986)

    Article  Google Scholar 

  6. Verwer, B.J.H.: Local distances for distance transformations in two and three dimensions. Pattern Recognition Letters 12(11), 671–682 (1991)

    Article  Google Scholar 

  7. Borgefors, G.: Distance transformations on hexagonal grids. Pattern Recognition Letters 9, 97–105 (1989)

    Article  Google Scholar 

  8. Strand, R., Borgefors, G.: Distance transforms for three-dimensional grids with non-cubic voxels. Computer Vision and Image Understanding 100(3), 294–311 (2005)

    Article  Google Scholar 

  9. Borgefors, G., di Baja, G.S.: Skeletonizing the distance transform on the hexagonal grid. In: Proceedings of 9th International Conference on Pattern Recognition, Rome, Italy, pp. 504–507 (1988)

    Google Scholar 

  10. Strand, R.: Surface skeletons in grids with non-cubic voxels. In: Proceedings of 17th International Conference on Pattern Recognition (ICPR 2004), Cambridge, UK, vol. I, pp. 548–551 (2004)

    Google Scholar 

  11. Matej, S., Lewitt, R.M.: Efficient 3D grids for image reconstruction using spherically-symmetric volume elements. IEEE Transactions on Nuclear Science 42(4), 1361–1370 (1995)

    Article  Google Scholar 

  12. Yamashita, M., Honda, N.: Distance functions defined by variable neighbourhood sequences. Pattern Recognition 17(5), 509–513 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  13. Yamashita, M., Ibaraki, T.: Distances defined by neighbourhood sequences. Pattern Recognition 19(3), 237–246 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  14. Das, P.P., Chakrabarti, P.P.: Distance functions in digital geometry. Information Sciences 42, 113–136 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  15. Das, P.P., Chakrabarti, P.P., Chatterji, B.N.: Generalized distances in digital geometry. Information Sciences 42, 51–67 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  16. Fazekas, A., Hajdu, A., Hajdu, L.: Lattice of generalized neighbourhood sequences in nD and ∞D. Publicationes Mathematicae Debrecen 60, 405–427 (2002)

    MATH  MathSciNet  Google Scholar 

  17. Nagy, B.: Distance functions based on neighbourhood sequences. Publicationes Mathematicae Debrecen 63(3), 483–493 (2003)

    MATH  MathSciNet  Google Scholar 

  18. Das, P.P.: Best simple octagonal distances in digital geometry. Journal of Approximation Theory 68, 155–174 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  19. Das, P.P., Chatterji, B.N.: Octagonal distances for digital pictures. Information Sciences 50, 123–150 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  20. Mukherjee, J., Das, P.P., Kumar, M.A., Chatterji, B.N.: On approximating Euclidean metrics by digital distances in 2D and 3D. Pattern Recognition Letters 21, 573–582 (2000)

    Article  Google Scholar 

  21. Hajdu, A., Hajdu, L.: Approximating the Euclidean distance using non-periodic neighbourhood sequences. Discrete Mathematics 283, 101–111 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  22. Danielsson, P.: 3D octagonal metrics. In: Proceedings of 8th Scandinavian Conference on Image Analysis, Tromsø, Norway, pp. 727–736 (1993)

    Google Scholar 

  23. Hajdu, A., Nagy, B.: Approximating the Euclidean circle using neighbourhood sequences. In: Proceedings of 3rd Hungarian Conference on Image Processing, Domaszék, pp. 260–271 (2002)

    Google Scholar 

  24. Strand, R., Nagy, B.: Some properties for distances based on neighbourhood sequences in the face-centered cubic grid and the body-centered cubic grid. Technical report, Centre for Image Analysis, Uppsala University, Sweden (2005); Internal report 39

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Faculty of Informatics, University of Debrecen, PO Box 12, 4010, Debrecen, Hungary

    Benedek Nagy

  2. Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain

    Benedek Nagy

  3. Centre for Image Analysis, Uppsala University, Lägerhyddsvägen 3, SE-75237, Uppsala, Sweden

    Robin Strand

Authors
  1. Benedek Nagy
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  2. Robin Strand
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Editor information

Editors and Affiliations

  1. Institute for Transport Research, German-Aerospace Center (DLR), Rutherfordstr. 2, 12489, Berlin, Germany

    Ralf Reulke

  2. Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, 20146, Hamburg

    Ulrich Eckardt

  3. Dresden University of Technology,  

    Boris Flach

  4. Institut für Informatik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Uwe Knauer

  5. FU Berlin, Arnimallee 3, 14195, Berlin, Germany

    Konrad Polthier

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© 2006 Springer-Verlag Berlin Heidelberg

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Nagy, B., Strand, R. (2006). Approximating Euclidean Distance Using Distances Based on Neighbourhood Sequences in Non-standard Three-Dimensional Grids. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds) Combinatorial Image Analysis. IWCIA 2006. Lecture Notes in Computer Science, vol 4040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11774938_8

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  • DOI: https://doi.org/10.1007/11774938_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35153-5

  • Online ISBN: 978-3-540-35154-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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