Information
entropy and biological microscopy

Jan Urban, Jan
Vaněk, Petr Císař, Tomáš Náhlík and Dalibor Štys

Institute
of Physical Biology, University of South Bohemia, Zámek 136, Nové Hrady 37333,
CZ

In
cell biology experiments there are increasingly popular time-lapse movies
created from sequences of thousand of images, captured by digital device using
different microscopy techniques in predefined time interval. The captured
images become as input for evaluation of their content in preprocessing phase of
analysis. Parameters, observed and described in image may produce relevant
information in some mathematical model for cell life cycle. Unfortunately there
is no general image segmentation method able to recognize cell or even the cell
organells, properly in significant number of case. Each experiment require own
parametrisation and/or manual selection of important points in image matrix.
Those operations are time consuming and may differ to each other by selected
order of parameters thresholding or by independent observer.

One
of the promising ways for automation whole process of proper parameters
selection is using equations for information entropy, defined by Shannon as
measure of surprise, generalised by Rényi for conditional probability
distributions or Tsalis, Havrda and Charvát (THC) in non-extensive cases. This
method is rational also since it properly represents the stochastic nature of
the observed signal which in each case is an incomplete representation of
inherently stochastic Gibbs energy or, rather, a Rényi- or THC- type of
distribution function. In the literature
are described many algorithms based on Shannon entropy for one dimensional
thresholding and filtering. The more theoretically justified Rényi or THC type
distributions are seldom considered. Main practical reason for that is the
computational intensiveness.

**ACKNOWLEDGEMENTS**

This work was supported by
South Bohemia University
grant GAJU 091/2008/P and HCTFOOD A/CZ0046/1/0008 of EEA funds.

**REFERENCES**

[1] I. Glauche, R. Lorenz, D. Hasenclever, I.
Roeder (2008): A novel view on stem cell development:
Analyzing the shape of cellular genealogies, Cell Proliferation

[2] Yuguang Xiong, Padmini Rangamani1, Benjamin Dubin-Thaler, Michael P.
Sheetz, Ravi

Iyengar; A three-dimensional stochastic
spatio-temporal model of isotropic phase of cell spreading; Nature Preceedings : doi:10.1038/npre.2007.62.2 : Posted 3 Dec 2007

[3] Carpenter et al.: „CellProfiler: image analysis
software for identifying and quantifying cell phenotypes “, Genome Biology, 7:R100, 2006

[4] A. Rényi (1961). "On measures of
information and entropy". Proceedings of the 4th Berkeley Symposium on
Mathematics, Statistics and Probability 1960: 547-561.

[5] P.Jizba,
Toshihico Arimitsu; The World according to Renyi: Thermodynamics of
multifractal systems. Annals Phys.312:17-57,2004.

[6] A.O. Hero; B. Ma; O.Michel, and J. Gorman:
Alpha-Divergence for Classification, Indexing and Retrieval; Communications and
Signal Processing Laboratory Technical Report CSPL- 328 2001

[7] Beucher S.: „Applications of mathematical morphology in material
sciences: A review of recent developments“, International Metallography Conference, pp. 41-46, 1995

**[8] Atkins P., de Paula J.,
Physical Chemistry, Oxford University Press 2006**

**[9] **Gokcay, D.; Bowers,
D.; Rochardson, C.; Desai, A.; **Use of
local entropy changes as a measure for identification of facial expressions; **IEEE
International Conference on Processing, 2000. ICASSP Volume 6, Page(s):2334 -
2337 vol.4

[10] Urban J., Vanek J., Štys D. Preprocessing of
microscopy images via Shannon's entropy,

In Proc. of Pattern Recognition
and Information Processing, pp.183-187, Minsk, Belarus,

(2009).