Advertisement

A characterization of digital disks by discrete moments

  • Joviša Žunić
  • Nataša Sladoje
Poster Session I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1296)

Abstract

In this paper our studies are focused on the digital disks and problems of their characterization (coding) with an appropriate number of bits, and reconstruction of the original disk from the code that is used. Even though the digital disks appear very often in practice of the computer vision and image processing, only the problem of their recognition has been solved till now. In this paper a representation by constant number of integers, requireing optimal number of bits, is presented. One-to-one correspondence between the digital disks and their proposed codes, consisting of:
  • - the number of points of the digital disk

  • - the sum of x-coordinates of the points of digital disk

  • - the sum of y-coordinates of the points of digital disk, is proved.

The efficiency of the reconstruction of the original disk from the proposed code is analysed. It is shown that the errors in estimating the radius of the disk, and the coordinates of its center, tend to zero while the radius of the disk tends to infinity. More precisely, if a disk, having the radius equal to r, is digitized and proposed coding scheme is applied, then the radius and the center position of the original disk can be reconstructed (from the obtained code) with relative errors bounded by \(\mathcal{O}\left( {\tfrac{1}{{r \cdot \sqrt[3]{r}}}} \right)\), and absolute errors bounded by \(\mathcal{O}\left( {\tfrac{1}{{\sqrt[3]{r}}}} \right)\).

The numerical data strongly confirm the theoretical results. The illustration by several experimental results is given.

Key words

pattern analysis low level processing and coding shape representation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. Dorst and A.W.M. Smeulders, “Discrete representation of straight lines”, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 450–463, 1984.Google Scholar
  2. [2]
    A. Ivić, “Introduction in Analytic Number Theory”, (in Serbian), Novi Sad, 1996.Google Scholar
  3. [3]
    C. E. Kim, “Digital disks”, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, pp. 372–374, 1984.Google Scholar
  4. [4]
    R. Klette, I. Stojmenović and J. Žunić, “A parametrization of digital planes by least square fits and generalizations”, Graphical Models and Image Processing, vol. 58, no. 3, pp. 295–300, 1996.CrossRefGoogle Scholar
  5. [5]
    V. A. Kovalevsky, “New definition and fast recognition of digital straight segments and arcs”, Proc. of the tenth international conference on pattern recognition, IEEE Proc. 10662, pp. 31–34, 1990.Google Scholar
  6. [6]
    M. Lindenbaum and J. Koplowitz, “A new parametrization of digital straight lines”, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 847–852, 1991.CrossRefGoogle Scholar
  7. [7]
    R. A. Melter, I. Stojmenović and J. Žunić, “A new characterization of digital lines by least square fits”, Pattern Recognition Letters, vol. 14, pp. 83–88, 1993.CrossRefGoogle Scholar
  8. [8]
    A. Nakamura and K. Aizawa, “Digital circles”, Computer Vision, Graphics Image Processing, vol. 26, pp. 242–255, 1984.Google Scholar
  9. [9]
    P. Sauer, “On the recognition of digital circles in linear time”, Computational Geometry: Theory and Applications, vol. 2, pp. 287–302, 1993.Google Scholar
  10. [10]
    M. Worring and A.W.M Smeulders, “Digitized Circular Arcs: Characterization and Parameter Estimation”, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17 pp. 587–597, 1995.CrossRefGoogle Scholar
  11. [11]
    J. Žunić and D.M. Acketa, “Least Squares Fitting of Digital Polynomial Segments”, Lecture Notes in Computer Science: Discrete Geometry for Computer Imagery vol. 1176. pp. 17–23, 1996.Google Scholar
  12. [12]
    J. Žunić and N. Sladoje, “Efficiency of Characterizing Ellipses and Ellipsoids by Discrete Moments”, submitted.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Joviša Žunić
    • 1
  • Nataša Sladoje
    • 1
  1. 1.Faculty of EngineeringUniversity of Novi SadNovi SadYugoslavia

Personalised recommendations