Skip to main content
SpringerLink
Log in

Linear Time Constant-Working Space Algorithm for Computing the Genus of a Digital Object

  • Conference paper
Advances in Visual Computing (ISVC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5358))

Included in the following conference series:

Abstract

In recent years the design of space-efficient algorithms that work within a limited amount of memory is becoming a hot topic of research. This is particularly crucial for intelligent peripherals used in image analysis and processing, such as digital cameras, scanners, or printers, that are equipped with considerably lower memory than the usual computers. In the present paper we propose a constant-working space algorithm for determining the genus of a binary digital object. More precisely, given an m ×n binary array representing the image, we show how one can count the number of holes of the array with an optimal number of O(mn) integer arithmetic operations and optimal O(1) working space. Our consideration covers the two basic possibilities for object and hole types determined by the adjacency relation adopted for the object and for the background. The algorithm is particularly based on certain combinatorial relation between some characteristics of a digital picture.

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. Asano, T.: Constant-working space algorithm for image processing. In: Proc. of the First AAAC Annual Meeting, Hong Kong (April 2008) (to appear)

    Google Scholar 

  2. Asano, T.: Constant-working space image scan with a given angle. In: Proc. of the 24th European Workshop on Computational Geometry, Nancy, March 2008, pp. 165–168 (2008)

    Google Scholar 

  3. Asano, T., Biotu, S., Motoki, M., Usui, N.: In-place algorithm for image rotation. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 704–715. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Asano, T., Buzer, L.: Constant-working space algorithm for connected components counting with extension, personal communication (to appear, 2008)

    Google Scholar 

  5. Asano, T., Tanaka, H.: Constant-working space algorithm for connected components labeling, IEICE Technical Report, Special Interest Group on Computation, Japan, IEICE-COMP2008-1, vol. 108(1), pp. 1–8 (2008)

    Google Scholar 

  6. Asano, T., Tanaka, H.: Constant-working space algorithm for Euclidean distance transform, IEICE Technical Report, Special Interest Group on Computation, Japan, IEICE-COMP2008-2, vol. 108(1), pp. 9–14 (2008)

    Google Scholar 

  7. Blunck, H., Vahrenhold, J.: In-place algorithms for computing (layers of) maxima. In: Arge, L., Freivalds, R. (eds.) SWAT 2006. LNCS, vol. 4059, pp. 363–374. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Brimkov, V.E., Klette, R.: Curves, hypersurfaces, and good pairs of adjacency relations. In: Klette, R., Žunić, J. (eds.) IWCIA 2004. LNCS, vol. 3322, pp. 276–290. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  9. Brimkov, V.E., Klette, R.: Border and surface tracing - theoretical foundations. IEEE Transactions on Pattern Analysis and Machine Intelligence 30(4), 577–590 (2008)

    Article  Google Scholar 

  10. Brimkov, V.E., Maimone, A., Nordo, G.: Counting gaps in binary pictures. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 16–24. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Brönniman, H., Chan, T.M.: Space-efficient algorithms for computing the convex hull of a simple polygonal line in a linear time. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 162–171. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Brönniman, H., Iacono, J., Katajainen, J., Morin, P., Morrison, J., Toussaint, G.: In-place planar convex hull algorithms. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 197–205. Springer, Heidelberg (2002)

    Google Scholar 

  13. Chen, M.-H., Yan, P.-F.: A fast algorithm to calculate the Euler number for binary image. Pattern Recognition Letters 8(5), 295–297 (1988)

    Article  MATH  Google Scholar 

  14. Garey, M.S., Johnson, D.S.: Computers and Intractability: a Guide to the Theory of NP-Completeness. Freeman & Co., San Francisco (1979)

    MATH  Google Scholar 

  15. Geffert, V., Katajainen, J., Pasanen, T.: Asymptotically efficient in-place merging. Theoretical Computer Science 237(1-2), 159–181 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Katajainen, J., Pasanen, T.: In-place sorting with fewer moves. Information Processing Letters 70(1), 31–37 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Katajainen, J., Pasanen, T., Titan, G.: Sorting multisets stably in minimum space. Acta Informatica 31(4), 301–313 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  18. Klette, R., Rosenfeld, A.: Digital Geometry - Geometric Methods for Digital Picture Analysis. Morgan Kaufmann, San Francisco (2004)

    MATH  Google Scholar 

  19. Kong, T.Y.: Digital topology. In: Davis, L.S. (ed.) Foundations of Image Understanding, pp. 33–71. Kluwer, Boston (2001)

    Google Scholar 

  20. Pasanen, T.: In-place algorithms for sorting problems. ACM SIGACT News 30(2), 61 (1999)

    Article  Google Scholar 

  21. Rosenfeld, A.: Connectivity in digital pictures. Journal of the ACM 17(3), 146–160 (1970)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, SUNY Buffalo State College, Buffalo, NY 14222, USA

    Valentin E. Brimkov

  2. Department of Computer Science, SUNY Fredonia, NY 14063, USA

    Reneta Barneva

Authors
  1. Valentin E. Brimkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Reneta Barneva
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Digital Image Research Center, Kingston University, London, UK

    Paolo Remagnino

  6. Mitsubishi Electric Research Laboratories, P.O. Box 02139, Cambridge, MA, USA

    Fatih Porikli

  7. Computer and Information Science and Engineering, University of Florida, P.O. Box, FL 32611-6120, Gainsville, USA

    Jörg Peters

  8. IBM T.J. Watson Research Center, 19 Skyline Drive, NY 10532, Hawthorne, USA

    James Klosowski

  9. 128 Memorial Mall, Stewart B001, IN 47907, West Lafayette, USA

    Laura Arns

  10. Denver Museum of Nature and Space, 2001 Colorade Blvd. Denver,, CO 80205, USA

    Yu Ka Chun

  11. Departmen of Computer Science,, NC State University, Campus Box 8206, NC 27695-8206, Raleigh, USA

    Theresa-Marie Rhyne

  12. Los Alamos National Labs, P.O. Box 1663, NM 87545, Los Alamos, USA

    Laura Monroe

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brimkov, V.E., Barneva, R. (2008). Linear Time Constant-Working Space Algorithm for Computing the Genus of a Digital Object. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2008. Lecture Notes in Computer Science, vol 5358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89639-5_64

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89639-5_64

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89638-8

  • Online ISBN: 978-3-540-89639-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation