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.

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