Open Access Research article

Variational attenuation correction in two-view confocal microscopy

Thorsten Schmidt1*, Jasmin Dürr2, Margret Keuper1, Thomas Blein23, Klaus Palme2456 and Olaf Ronneberger14

Author Affiliations

1 Department of Computer Science, Albert-Ludwigs-Universität, Georges-Köhler-Allee Geb. 52, 79110 Freiburg, Germany

2 Institute of Biology II, Albert-Ludwigs-Universität, Schänzlestr. 1, 79104 Freiburg, Germany

3 Current address: Institut Jean-Pierre Bourgin, Unité Mixte de Recherche 1318, Institut National de la Recherche Agronomique-AgroParisTech, Bâtiment 2, INRA Centre de Versailles-Grignon, 78026 Versailles Cedex, France

4 BIOSS, Centre for Biological Signalling Studies, Albert-Ludwigs-Universität, Albertstr. 19, 79104 Freiburg, Germany

5 FRIAS, Freiburg Center for Advanced Studies, Albert-Ludwigs-Universität Freiburg, Albertstr. 19, 79104 Freiburg, Germany

6 FRISYS, Faculty for Biology, Albert-Ludwigs-Universität Freiburg, Albertstr. 19, 79104 Freiburg, Germany

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BMC Bioinformatics 2013, 14:366  doi:10.1186/1471-2105-14-366

Published: 18 December 2013



Absorption and refraction induced signal attenuation can seriously hinder the extraction of quantitative information from confocal microscopic data. This signal attenuation can be estimated and corrected by algorithms that use physical image formation models. Especially in thick heterogeneous samples, current single view based models are unable to solve the underdetermined problem of estimating the attenuation-free intensities.


We present a variational approach to estimate both, the real intensities and the spatially variant attenuation from two views of the same sample from opposite sides. Assuming noise-free measurements throughout the whole volume and pure absorption, this would in theory allow a perfect reconstruction without further assumptions. To cope with real world data, our approach respects photon noise, estimates apparent bleaching between the two recordings, and constrains the attenuation field to be smooth and sparse to avoid spurious attenuation estimates in regions lacking valid measurements.


We quantify the reconstruction quality on simulated data and compare it to the state-of-the art two-view approach and commonly used one-factor-per-slice approaches like the exponential decay model. Additionally we show its real-world applicability on model organisms from zoology (zebrafish) and botany (Arabidopsis). The results from these experiments show that the proposed approach improves the quantification of confocal microscopic data of thick specimen.

Attenuation correction; Absorption; Confocal microscopy; Image restoration; Calculus of variations