Skip to main content

Multifractality in Imaging: Application of Information Entropy for Observation of Inner Dynamics Inside of an Unlabeled Living Cell in Bright-Field Microscopy

  • Chapter

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 14))

Abstract

The theoretical background of bright field optical microscopy is not described to the extent that would allow the extraction of as many features of the original object from the image as possible. In this article, we present the determination of image features based on a general assumption that images transmitted by an optical microscope have multifractal character. In order to determine the borders of the determinable point spread function, we derived a Point Divergence Gain (PDG α,x(l),y(l)) variable from the Renyi entropy. This variable calculates image points that carry the same information in consequent images captured upon moving the object along the lens’ optical axis (z-scan). In this way, we may precisely identify the border of the point spread function of immovable identifiable objects.

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

Buying options

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
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Braat, J.J.M., Dirksen, P., Janssen, A.J.E.M.: Assessment of an Extended Nijboer-Zernike Approach for the Computation of Optical Point-Spread Functions. J. Opt. Soc. Am. A 19, 858–870 (2002)

    Article  Google Scholar 

  2. Stys, D., Urban, J., Vanek, J., Cisar, P.: Analysis of Biological Time-Lapse Microscopic Experiment from the Point of View of the Information Theory. Micron 42, 360–365 (2011)

    Article  Google Scholar 

  3. Štys, D., Jizba, P., Papáček, Š., Náhlík, T., Císař, P.: On Measurement of Internal Variables of Complex Self-Organized Systems and Their Relation to Multifractal Spectra. In: Kuipers, F.A., Heegaard, P.E. (eds.) IWSOS 2012. LNCS, vol. 7166, pp. 36–47. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Tkacik, G., Garrigan, P., Ratliff, C., Milcinski, G., Klein, J.M., Seyfarth, L.H., Sterling, P., Brainard, D.H., Balasubramanian, V.: Natural Images from the Birthplace of the Human Eye. PLoS One 6(6), e20409 (2011)

    Google Scholar 

  5. http://www.expertomica.eu/software.php

  6. Abbe, E.: Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung. Archiv für Mikroskopische Anatomie 9(1), 469–480 (1874)

    Article  Google Scholar 

  7. Lichtscheidel, I.K., Foissner, I.: Video Microscopy of Dynamic Plant Cell Organelles: Principles of the Technique and Practical Application. J. Microsc.-Oxford 181, 117–128 (1996)

    Article  Google Scholar 

  8. Zernike, F.: The Concept of Degree of Coherence and Its Application to Optical Problems. Physica 5, 785–795 (1938)

    Article  Google Scholar 

  9. Nijboer, B.R.A.: The Diffraction Theory of Aberrations. Ph.D. dissertation, University of Groningen, Groningen, The Netherlands (1942)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Renata Rychtarikova .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Rychtarikova, R. et al. (2015). Multifractality in Imaging: Application of Information Entropy for Observation of Inner Dynamics Inside of an Unlabeled Living Cell in Bright-Field Microscopy. In: Sanayei, A., E. Rössler, O., Zelinka, I. (eds) ISCS 2014: Interdisciplinary Symposium on Complex Systems. Emergence, Complexity and Computation, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-10759-2_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-10759-2_27

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10758-5

  • Online ISBN: 978-3-319-10759-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics