A fast fiducial marker tracking model for fully automatic alignment in electron tomography

Automatic alignment, especially fiducial marker-based alignment, has become increasingly important due to the high demand of subtomogram averaging and the rapid development of large-field electron microscopy. Among the alignment steps, fiducial marker tracking is a crucial one that determines the quality of the final alignment. Yet, it is still a challenging problem to track the fiducial markers accurately and effectively in a fully automatic manner.In this paper, we propose a robust and efficient scheme for fiducial marker tracking. Firstly, we theoretically prove the upper bound of the transformation deviation of aligning the positions of fiducial markers on two micrographs by affine transformation. Secondly, we design an automatic algorithm based on the Gaussian mixture model to accelerate the procedure of fiducial marker tracking. Thirdly, we propose a divide-and-conquer strategy against lens distortions to ensure the reliability of our scheme. To our knowledge, this is the first attempt that theoretically relates the projection model with the tracking model. The real-world experimental results further support our theoretical bound and demonstrate the effectiveness of our algorithm. This work facilitates the fully automatic tracking for datasets with a massive number of fiducial markers.The C/C ++ source code that implements the fast fiducial marker tracking is available at https://github.com/icthrm/gmm-marker-tracking. Markerauto 1.6 version or later (also integrated in the AuTom platform at http://ear.ict.ac.cn/) offers a complete implementation for fast alignment, in which fast fiducial marker tracking is available by the