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Med Image Anal. 2016 Aug;32:157-72. doi: 10.1016/j.media.2016.03.007. Epub 2016 Apr 4.

Automatic optimal filament segmentation with sub-pixel accuracy using generalized linear models and B-spline level-sets.

Author information

1
MOSAIC Group, Center for Systems Biology Dresden (CSBD), Dresden, Germany; Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany; Now at: European Research Center, Huawei Technologies, Munich, Germany.
2
Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, CT, USA.
3
Chair of Scientific Computing for Systems Biology, Faculty of Computer Science, TU Dresden, Dresden, Germany; MOSAIC Group, Center for Systems Biology Dresden (CSBD), Dresden, Germany; Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany. Electronic address: ivos@mpi-cbg.de.

Abstract

Biological filaments, such as actin filaments, microtubules, and cilia, are often imaged using different light-microscopy techniques. Reconstructing the filament curve from the acquired images constitutes the filament segmentation problem. Since filaments have lower dimensionality than the image itself, there is an inherent trade-off between tracing the filament with sub-pixel accuracy and avoiding noise artifacts. Here, we present a globally optimal filament segmentation method based on B-spline vector level-sets and a generalized linear model for the pixel intensity statistics. We show that the resulting optimization problem is convex and can hence be solved with global optimality. We introduce a simple and efficient algorithm to compute such optimal filament segmentations, and provide an open-source implementation as an ImageJ/Fiji plugin. We further derive an information-theoretic lower bound on the filament segmentation error, quantifying how well an algorithm could possibly do given the information in the image. We show that our algorithm asymptotically reaches this bound in the spline coefficients. We validate our method in comprehensive benchmarks, compare with other methods, and show applications from fluorescence, phase-contrast, and dark-field microscopy.

KEYWORDS:

Axoneme; B-spline; Filament segmentation; Level set; Light microscopy; Microtubule

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