Han Renmin, Li Guojun, Gao Xin
Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao 266237, China.
King Abdullah University of Science and Technology (KAUST), Computational Bioscience Research Center (CBRC), Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, Thuwal 23955-6900, Saudi Arabia.
Bioinformatics. 2021 Apr 9;37(1):107-117. doi: 10.1093/bioinformatics/btaa1098.
Electron tomography (ET) has become an indispensable tool for structural biology studies. In ET, the tilt series alignment and the projection parameter calibration are the key steps toward high-resolution ultrastructure analysis. Usually, fiducial markers are embedded in the sample to aid the alignment. Despite the advances in developing algorithms to find correspondence of fiducial markers from different tilted micrographs, the error rate of the existing methods is still high such that manual correction has to be conducted. In addition, existing algorithms do not work well when the number of fiducial markers is high.
In this article, we try to completely solve the fiducial marker correspondence problem. We propose to divide the workflow of fiducial marker correspondence into two stages: (i) initial transformation determination, and (ii) local correspondence refinement. In the first stage, we model the transform estimation as a correspondence pair inquiry and verification problem. The local geometric constraints and invariant features are used to reduce the complexity of the problem. In the second stage, we encode the geometric distribution of the fiducial markers by a weighted Gaussian mixture model and introduce drift parameters to correct the effects of beam-induced motion and sample deformation. Comprehensive experiments on real-world datasets demonstrate the robustness, efficiency and effectiveness of the proposed algorithm. Especially, the proposed two-stage algorithm is able to produce an accurate tracking within an average of ⩽ 100 ms per image, even for micrographs with hundreds of fiducial markers, which makes the real-time ET data processing possible.
The code is available at https://github.com/icthrm/auto-tilt-pair. Additionally, the detailed original figures demonstrated in the experiments can be accessed at https://rb.gy/6adtk4.
Supplementary data are available at Bioinformatics online.
电子断层扫描（ET）已成为结构生物学研究中不可或缺的工具。在电子断层扫描中，倾斜序列对齐和投影参数校准是实现高分辨率超微结构分析的关键步骤。通常，会在样品中嵌入基准标记以辅助对齐。尽管在开发从不同倾斜显微图像中找到基准标记对应关系的算法方面取得了进展，但现有方法的错误率仍然很高，因此必须进行人工校正。此外，当基准标记数量较多时，现有算法效果不佳。
在本文中，我们试图完全解决基准标记对应问题。我们建议将基准标记对应工作流程分为两个阶段：（i）初始变换确定，以及（ii）局部对应细化。在第一阶段，我们将变换估计建模为对应对查询和验证问题。利用局部几何约束和不变特征来降低问题的复杂性。在第二阶段，我们通过加权高斯混合模型对基准标记的几何分布进行编码，并引入漂移参数来校正束流诱导运动和样品变形的影响。在真实数据集上进行的综合实验证明了所提算法的稳健性、效率和有效性。特别是，所提的两阶段算法即使对于具有数百个基准标记的显微图像，也能够在平均每张图像⩽100毫秒内产生准确的跟踪结果，这使得实时电子断层扫描数据处理成为可能。
代码可在https://github.com/icthrm/auto-tilt-pair获取。此外，实验中展示的详细原始图像可在https://rb.gy/6adtk4访问。
补充数据可在《生物信息学》在线获取。
