In the imaging process for nanometer-scale electron tomography, misalignment between the actual projection parameters and the theoretical ones is inevitable due to mechanical precision of the instrument. Effective alignment remains a challenge. Currently, marker-based alignment approaches complicate the sample preparation process and worsen the sample shrinking issue. Marker-free approaches suffer from either low accuracy or long computation time.

In this paper, we formulate an analytical problem for marker-free alignment by minimizing the reprojection error. The reprojection error involves the projection operator, which is a complicated functional with the projection parameters as the variables. To solve this optimization problem, we derive a gradient-based approach by decomposing the original problem with auxiliary parameters and by linearizing a subproblem with Taylor expansion. The approach is computational friendly, especially when comparing to an exhaustively parameter tuning approach in previous practice. The results show that our method is capable of accurate alignment without fiducial markers and obtains a 16.7\(\times \) speedup over the existing exhaustive approach, which makes fine reconstruction of ROI almost instantly ready after data collection. A preliminary FPGA design for the method’s bottleneck process shows 6.6\(\times \) speed-up over well-optimized GPU program.


Electron tomography Automatic alignment Functional optimization 


  1. 1.
    Fernandez, J.J.: Computational methods for electron tomography. Micron 43(10), 1010–1030 (2012)CrossRefGoogle Scholar
  2. 2.
    Guckenberger, R.: Determination of a common origin in the micrographs of tilt series in three-dimensional electron microscopy. Ultramicroscopy 9(1–2), 167–173 (1982)CrossRefGoogle Scholar
  3. 3.
    Han, R., Bao, Z., Zeng, X., et al.: A joint method for marker-free alignment of tilt series in electron tomography. Bioinformatics 35(14), i249–i259 (2019)CrossRefGoogle Scholar
  4. 4.
    Herman, G.T.: Fundamentals of Computerized Tomography: Image Reconstruction from Projections, pp. 64–68. Springer, London (2009). Scholar
  5. 5.
    Houben, L., Sadan, M.B.: Refinement procedure for the image alignment in high-resolution electron tomography. Ultramicroscopy 111(9–10), 1512–1520 (2011)CrossRefGoogle Scholar
  6. 6.
    Leis, A., Rockel, B., Andrees, L., et al.: Visualizing cells at the nanoscale. Trends Biochem. Sci. 34(2), 60–70 (2009)CrossRefGoogle Scholar
  7. 7.
    Lucas, B.D., Kanade, T.: An iterative image registration technique with an application to stereo vision (1981)Google Scholar
  8. 8.
    Mastronarde, D.N., Held, S.R.: Automated tilt series alignment and tomographic reconstruction in IMOD. J. Struct. Biol. 197(2), 102–113 (2017)CrossRefGoogle Scholar
  9. 9.
    Natterer, F.: The Mathematics of Computerized Tomography. SIAM, Philadelphia (1986)zbMATHGoogle Scholar
  10. 10.
    Tian, Q., Öfverstedt, L.G.,: Unit USSCB. Semi-automatically aligned tilt images in electron tomography. In: 2017 International Conference on Intelligent Informatics and Biomedical Sciences (ICIIBMS), pp. 71–75. IEEE (2017)Google Scholar
  11. 11.
    Trampert, P., Bogachev, S., Marniok, N., et al.: Marker detection in electron tomography: a comparative study. Microsc. Microanal. 21(6), 1591–1601 (2015)CrossRefGoogle Scholar
  12. 12.
    Sorzano, C.O.S., Messaoudi, C., Eibauer, M., et al.: Marker-free image registration of electron tomography tilt-series. BMC Bioinform. 10(1), 124 (2009)CrossRefGoogle Scholar
  13. 13.
    Winkler, H., Taylor, K.A.: Accurate marker-free alignment with simultaneous geometry determination and reconstruction of tilt series in electron tomography. Ultramicroscopy 106(3), 240–254 (2006)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Center for Energy-efficient Computing and ApplicationsPeking UniversityBeijingChina

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