Data from: Automated stitching of microtubule centerlines across serial electron tomograms

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.

在连续切片电子断层成像（serial section electron tomography）中追踪微管中心线（microtubule centerlines）时，需对不同切片内的微管实施跨切片拼接操作：具体包括对齐不同切片中的线条、在切片边界处匹配端点以建立相邻切片间的对应关系，以及将多切片中的对应线条进行跨段连接。
针对上述任务，我们提出了一套完整的计算方法：1） 借助距离兼容性图（distance compatibility graph）计算初始对齐结果；2） 随后采用迭代最近点算法（iterative closest points algorithm）的概率变体完成精细化对齐，我们通过在概率建模中引入周期随机变量，将该方法扩展至可处理线条的方向信息；3） 将端点匹配问题建模为马尔可夫随机场（Markov random field）问题，并通过置信传播（belief propagation）求解最优匹配。通常而言，置信传播无法保证收敛至极小值点，我们证明了仅需极少量人工输入即可实现收敛。
除实现微管中心线的跨切片拼接外，我们还将该对应关系应用于电子断层图像的变换与融合。我们将所提方法应用于三类样本：秀丽隐杆线虫（C. elegans）的有丝分裂纺锤体、非洲爪蟾（X. laevis）的减数分裂纺锤体，以及布氏锥虫（T. brucei）的表膜下微管阵列。对于纺锤体类样本，本方法可实现微管的跨切片拼接，且与专家手动标注的结果吻合度较高；但对于表膜下微管阵列样本，其效果并不理想。在部分实验场景中，例如纺锤体分析，本方法可替代专家手动追踪，从而在合理的人工投入下完成长距离微管的分析。