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Open Access Highly Accessed Research article

3D time series analysis of cell shape using Laplacian approaches

Cheng-Jin Du1*, Phillip T Hawkins2, Len R Stephens2 and Till Bretschneider1

Author Affiliations

1 Warwick Systems Biology Centre, University of Warwick, Coventry CV4 7AL, UK

2 The Babraham Institute, Cambridge CB22 3AT, UK

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BMC Bioinformatics 2013, 14:296  doi:10.1186/1471-2105-14-296

Published: 4 October 2013



Fundamental cellular processes such as cell movement, division or food uptake critically depend on cells being able to change shape. Fast acquisition of three-dimensional image time series has now become possible, but we lack efficient tools for analysing shape deformations in order to understand the real three-dimensional nature of shape changes.


We present a framework for 3D+time cell shape analysis. The main contribution is three-fold: First, we develop a fast, automatic random walker method for cell segmentation. Second, a novel topology fixing method is proposed to fix segmented binary volumes without spherical topology. Third, we show that algorithms used for each individual step of the analysis pipeline (cell segmentation, topology fixing, spherical parameterization, and shape representation) are closely related to the Laplacian operator. The framework is applied to the shape analysis of neutrophil cells.


The method we propose for cell segmentation is faster than the traditional random walker method or the level set method, and performs better on 3D time-series of neutrophil cells, which are comparatively noisy as stacks have to be acquired fast enough to account for cell motion. Our method for topology fixing outperforms the tools provided by SPHARM-MAT and SPHARM-PDM in terms of their successful fixing rates. The different tasks in the presented pipeline for 3D+time shape analysis of cells can be solved using Laplacian approaches, opening the possibility of eventually combining individual steps in order to speed up computations.