Skip to main content

OK-Quantization Theory and Its Relationship to Sampling Theorem

  • Conference paper
Computer Vision – ACCV 2006 (ACCV 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3852))

Included in the following conference series:

Abstract

OK-Quantization Theory for the digitization in value ensures the reconstructivity of the probabilistic density function of the image. This paper shows some experimental demonstrations to reduce the number of the gray levels, and shows mainly that there is a necessary analytical relationship between sampling and quantization based on the equivalence relationship between two kinds of the integral, Riemann and Lebesgue integrals for calculating the volume of the image. Experimental demonstrations are also shown in this paper.

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

Access this chapter

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. Shannon, C.E., et al.: The Mathematical Theory of Communication. Univ. Illinois Press (1949)

    Google Scholar 

  2. Hasegawa, J., et al.: The Mathematical Theory of Communication, Meiji Tosho (1969)

    Google Scholar 

  3. Nakata, K.: Vector Quantization of Vowel and Image Signals. Journal of Measurement and Control 25(6), 517–552 (1986)

    MathSciNet  Google Scholar 

  4. Isomichi, Y.: Exercise in Information Theory, pp. 53–55. Corona Publishing Company (1983)

    Google Scholar 

  5. Koshimizu, H., et al.: A Practical Method for Estimating Aliasing Error in Image Processing. Trans. IEICE 61-D(6), 443–444 (1978)

    Google Scholar 

  6. Koshimizu, H., et al.: Proposal of Quantization Theorem. In: Proc. VIEW 2002, December 2002, p. 1, Yokohama (2002)

    Google Scholar 

  7. Oteru, O.: Basic Electric Measurement, pp. 236–237. Ohm Publishing Company (1966)

    Google Scholar 

  8. Iijima, T.: Considerations on OK-Quantization Therem by Examples (Feburary 18, 2003)

    Google Scholar 

  9. Koshimizu, H.: On A Mathematical Theory of Quantization — How should image gray value be digitized? In: FCV 2003, Jeju, Korea (Feburary 6, 2003) Invited paper

    Google Scholar 

  10. Koshimizu, H.: On Proposal Of Quantization Theorem and Its Experimental Consideration- Theory of image gray scale dispersion, IEICE(PRUM 2003-66) (May 2003)

    Google Scholar 

  11. Tanaka, Y., Fujiwara, T., Koshimizu, H., Iijima, T.: A Relationship between OK-Quantization and Sampling Theorem and Its Experimental Consideration. In: QCAV 2005, May 2005, pp. 399–404 (2005)

    Google Scholar 

  12. Tanaka, Y., Fujiwara, T., Koshimizu, H., Numada, M.: OK-Quantization Method and Its Theoretical and Experimental Properties. In: MIRU 2005, July 2005, pp. 1495–1502 (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Tanaka, Y., Fujiwara, T., Koshimizu, H., Iijima, T. (2006). OK-Quantization Theory and Its Relationship to Sampling Theorem. In: Narayanan, P.J., Nayar, S.K., Shum, HY. (eds) Computer Vision – ACCV 2006. ACCV 2006. Lecture Notes in Computer Science, vol 3852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11612704_48

Download citation

  • DOI: https://doi.org/10.1007/11612704_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31244-4

  • Online ISBN: 978-3-540-32432-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics