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Tracing microtubule centerlines in serial section electron tomography requires microtubules to be stitched across sections, that is lines from different sections need to be aligned, endpoints need to be matched at section boundaries to establish a correspondence between neighboring sections, and corresponding lines need to be connected across multiple sections. We present computational methods for these tasks: 1) An initial alignment is computed using a distance compatibility graph. 2) A fine alignment is then computed with a probabilistic variant of the iterative closest points algorithm, which we extended to handle the orientation of lines by introducing a periodic random variable to the probabilistic formulation. 3) Endpoint correspondence is established by formulating a matching problem in terms of a Markov random field and computing the best matching with belief propagation. Belief propagation is not generally guaranteed to converge to a minimum. We show how convergence can be achieved, nonetheless, with minimal manual input. In addition to stitching microtubule centerlines, the correspondence is also applied to transform and merge the electron tomograms. We applied the proposed methods to samples from the mitotic spindle in C. elegans, the meiotic spindle in X. laevis, and sub-pellicular microtubule arrays in T. brucei. The methods were able to stitch microtubules across section boundaries in good agreement with experts’ opinions for the spindle samples. Results, however, were not satisfactory for the microtubule arrays. For certain experiments, such as an analysis of the spindle, the proposed methods can replace manual expert tracing and thus enable the analysis of microtubules over long distances with reasonable manual effort.
Automated 3D Crack Detection for Analyzing Damage Processes in Concrete with Computed Tomography
(2012)
We present a software-assisted workflow for the alignment and matching of filamentous structures across a 3D stack of serial images. This is achieved by combining automatic methods, visual validation, and interactive correction. After an initial alignment, the user can continuously improve the result by interactively correcting landmarks or matches of filaments. Supported by a visual quality assessment of regions that have been already inspected, this allows a trade-off between quality and manual labor. The software tool was developed to investigate cell division by quantitative 3D analysis of microtubules (MTs) in both mitotic and meiotic spindles. For this, each spindle is cut into a series of semi-thick physical sections, of which electron tomograms are acquired. The serial tomograms are then stitched and non-rigidly aligned to allow tracing and connecting of MTs across tomogram boundaries. In practice, automatic stitching alone provides only an incomplete solution, because large physical distortions and a low signal-to-noise ratio often cause experimental difficulties. To derive 3D models of spindles despite the problems related to sample preparation and subsequent data collection, semi-automatic validation and correction is required to remove stitching mistakes. However, due to the large number of MTs in spindles (up to 30k) and their resulting dense spatial arrangement, a naive inspection of each MT is too time consuming. Furthermore, an interactive visualization of the full image stack is hampered by the size of the data (up to 100 GB). Here, we present a specialized, interactive, semi-automatic solution that considers all requirements for large-scale stitching of filamentous structures in serial-section image stacks. The key to our solution is a careful design of the visualization and interaction tools for each processing step to guarantee real-time response, and an optimized workflow that efficiently guides the user through datasets.