The Reconstruction of the Digital Hyperbola Segment from Its Code

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


It is known that a set consisting of the digital curves whose “original curves ” are graphs of continuous functions, having at most two ntersection points, pairwise, on a given interval, can be uniquely coded by five parameters. This result s applied to the set of digital hyperbola segments, corresponding to the hyperbolas of the form y = α/x-β+γ inscribed into the (m × m )-integer grid. An O (m · (log(m + |β| ))2) algorithm for recovering the digital hyperbola segment from its proposed code, is presented.


image processing pattern analysis reconstruct on digital hyperbola 


  1. 1.
    Blum, M., Floyd, R. W., Pratt, V., Rivest, R. L., Tarjan, R.E.:Time bounds for select on. J. Comput. System Sci.7(4).(1973) 448–461 164zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Dorst, L., Smeulders, A. W. M.:Discrete representat on of straight lines. IEEE Trans. Pattern Analysis and Mach ne Intelligence, Vol. 6. (1984) 450–463 159zbMATHCrossRefGoogle Scholar
  3. 3.
    Kim, C. E.:Digital d sks. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 6. (1984) 372–374zbMATHGoogle Scholar
  4. 4.
    Lindenbaum, M., Koplowitz, J.: A new parametrization of digital straight lines. IEEE Trans. Pattern Analysis and Machine Intelligence,Vol. 13. No. 4. (1991) 847–852CrossRefGoogle Scholar
  5. 5.
    Melter, R. A., Stojmenović, I.,. Žunić, J.: A new characterization of digital linesby least square fits. Pattern Recognition Letters, Vol.14. (1993) 83–88zbMATHCrossRefGoogle Scholar
  6. 6.
    Woring, M., Smeulders, A. W. M.: Digitized Circular Arcs:Characterization and Parameter Estimation. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 17. (1995) 587–597CrossRefGoogle Scholar
  7. 7.
    Žunić, J., Koplowitz, J.: A representat on of digital parabolas by least square fits. SPIE Proc.,Vol. 2356. (1994) 71–78 159Google Scholar
  8. 8.
    Žunić, J.: A cod ng scheme for certain sets of d gital curves. Pattern Recognition Letters, Vol. 16. (1995) 97–104 159,160,161,169CrossRefGoogle Scholar
  9. 9.
    Žunić, J.: A Representat on of D gital Hyperbolas y =1/xα+β. Pattern Recognition Letters, Vol. 17. (1996) 975–983 159CrossRefGoogle Scholar
  10. Žunić J., Sladoje, N.: Efficiency of Characterizing Ellipses and Ellipsoids by Discrete Moments. IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 22. (2000) 407–414 159,169CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Nataša Sladoje 
    • 1
  1. 1.Faculty of EngineeringNoviSadYugoslavia

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