Skip to main content
SpringerLink
Log in

Approximation of Digital Circles by Regular Polygons

  • Conference paper
Pattern Recognition and Data Mining (ICAPR 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3686))

Included in the following conference series:

Abstract

In this paper, we show that an ideal regular (convex) polygon corresponding to a digital circle is possible for some of the digital circles, especially for the ones having smaller radii. For a circle whose ideal regular polygon is not possible, an approximate polygon, tending to the ideal one, is possible, in which the error of approximation can be controlled by the number of vertices of the approximate polygon. These (ideal or approximate) polygonal enclosures of digital circles have several applications in approximate point set pattern matching. We have reported the conditions under which an ideal regular polygon definitely exists corresponding to a digital circle, and the conditions under which the existence of an ideal regular polygon becomes uncertain. Experimental results have been given to exhibit the possibilities of approximation and the tradeoff in terms of error versus approximation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bhowmick, P., Bhattacharya, B.B.: Approximate Fingerprint Matching Using Kd-tree. In: ICPR 2004, vol. 1, pp. 544–547 (2004)

    Google Scholar 

  2. Bresenham, J.E.: A Linear Algorithm for Incremental Digital Display of Circular Arcs. Communications of the ACM 20(2), 100–106 (1977)

    Article  MATH  Google Scholar 

  3. Chung, P.C., Tsai, C.T., Chen, E.L., Sun, Y.N.: Polygonal Approximation Using a Competitive Hopfield Neural Network. PR 27(11), 1505–1512 (1994)

    Google Scholar 

  4. Davis, T.: Fast Decomposition of Digital Curves into Polygons Using the Haar Transform. IEEE Trans. PAMI 21(8), 786–790 (1999)

    Google Scholar 

  5. Gupta, A.K., Chaudhury, S., Parthasarathy, G.: A new approach for aggregating edge points into line segments. PR 26(7), 1069–1086 (1993)

    Google Scholar 

  6. Hosur, P.I., Ma, K.K.: A Novel Scheme for Progressive Polygon Approximation of Shape Contours. In: IEEE 3rd Workshop Multimedia Sig. Proc., pp. 309–314 (1999)

    Google Scholar 

  7. Perez, J.C., Vidal, E.: Optimum polygonal approximation of digitized curves. PRL 15, 743–750 (1994)

    MATH  Google Scholar 

  8. Pikaz, A., Dinstein, I.: Optimal Polygonal Approximation of Digital Curves. PR 28(3), 373–379 (1995)

    Google Scholar 

  9. Debled-Rennesson, I., Tabbone, S., Wendling, L.: Fast Polygonal Approximation of Digital Curves. In: Proc. ICPR 2004, pp. 465–468 (2004)

    Google Scholar 

  10. Rosin, P.L.: Techniques for Assessing Polygonal Approximation of Curves. IEEE Trans. PAMI 19(6), 659–666 (1997)

    Google Scholar 

  11. Salotti, M.: Improvement of Perez and Vidal Algorithm for the Decomposition of Digitized Curves into Line Segments. In: Proc. ICPR 2000, pp. 878–882 (2000)

    Google Scholar 

  12. Sarfraz, M., Asim, M.R., Masood, A.: Piecewise Polygonal Approximation of Digital Curves. In: Proc. 8th Intl. Conf. Information Visualisation (IV 2004), pp. 991–996 (2004)

    Google Scholar 

  13. Schröder, K., Laurent, P.: Efficient Polygon Approximations for Shape Signatures. In: Proc. ICIP 1999, pp. 811–814 (1999)

    Google Scholar 

  14. Worring, M., Smeulders, A.W.M.: Digitized Circular Arcs: Characterization and Parameter Estimation. IEEE Trans. PAMI 17(6), 587–598 (1995)

    Google Scholar 

  15. Yin, P.Y.: Genetic Algorithms for Polygonal Approximation of Digital Curves. IJPRAI 13, 1061–1082 (1999)

    Google Scholar 

  16. Yin, P.Y.: A Tabu Search Approach to Polygonal Approximation of Digital Curves. IJPRAI 14(2), 243–255 (2000)

    Google Scholar 

  17. Yin, P.Y.: Ant Colony Search Algorithms for Optimal Polygonal Approximation of Plane Curves. PR 36, 1783–1797 (2003)

    MATH  Google Scholar 

  18. Yin, P.Y.: A discrete particle swarm algorithm for optimal polygonal approximation of digital curves. J. Visual Comm. Image Reprsn. 15(2), 241–260 (2004)

    Article  Google Scholar 

  19. Zhu, Y., Seneviratne, L.D.: Optimal Polygonal Approximation of Digitised Curves. IEE Proc. Vis. Image Signal Process. 144(1), 8–14 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science and Technology Department, Bengal Engineering and Science University, Shibpur, Howrah, India

    Partha Bhowmick

  2. Center for Soft Computing Research, Indian Statistical Institute, Kolkata, India

    Bhargab B. Bhattacharya

Authors
  1. Partha Bhowmick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bhargab B. Bhattacharya
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research School of Infomatics, Loughborough, UK

    Sameer Singh

  2. ATR Lab, Research School of Informatics, University of Loughborough, Loughborough, UK

    Maneesha Singh

  3. IBM Corporation, 1133 Wetchester Avenue, White Plains, 10604, New York, United States

    Chid Apte

  4. Institute of Computer Vision and applied Computer Sciences, IBaI, Germany

    Petra Perner

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bhowmick, P., Bhattacharya, B.B. (2005). Approximation of Digital Circles by Regular Polygons. In: Singh, S., Singh, M., Apte, C., Perner, P. (eds) Pattern Recognition and Data Mining. ICAPR 2005. Lecture Notes in Computer Science, vol 3686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11551188_28

Download citation

  • DOI: https://doi.org/10.1007/11551188_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28757-5

  • Online ISBN: 978-3-540-28758-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation