Markerless Alignment in Electron Tomography

  • Sami S. Brandt


In computing high-accuracy reconstructions from transmission electron microscope (TEM) tilt series, image alignment currently has an important role. Though most are automated devices today, the imaging systems have certain non-idealities which give rise to abrupt shifts, rotations and magnification changes in the images. Thus, the geometric relationships between the object and the obtained projections are not precisely known initially. In this chapter, image alignment refers to the computation of the projection geometry of the tilt series so that most of the above deviations from the assumed ideal projection geometry could be rectified by using simple 2D geometric transformations for the images before computing a tomographic reconstruction.


Feature Point Alignment Method Common Line Alignment Problem Alignment Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Brandt, S. (2002). Theorems and Algorithms for Multiple View Geometry with Applications to Electron Tomography. Doctoral thesis for the degree of Doctor of Science in Technology, Helsinki University of Technology.Google Scholar
  2. Brandt, S., Heikkonen, J. and Engelhardt, P. (2001a). Automatic alignment of transmission electron microscope tilt-series without fiducial markers. J. Struct. Biol. 136:201–213.PubMedCrossRefGoogle Scholar
  3. Brandt, S., Heikkonen, J. and Engelhardt, P. (2001b). Multiphase method for automatic alignment of transmission electron microscope images using markers. J. Struct. Biol. 133:10–22.PubMedCrossRefGoogle Scholar
  4. Brandt, S. S. and Kolehmainen, V. (2004). Motion without correspondence from tomographic projections by Bayesian inversion theory. In Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2004) Vol. I. Washington, DC, pp. 582–587.Google Scholar
  5. Brandt, S. S. and Palander, K. (2005). A Bayesian approach for affine auto-calibration. In Proceedings of the 14th Scandinavian Conference on Image Analysis. Joensuu, Finland, pp. 577–578.Google Scholar
  6. Brandt, S. S. and Ziese, U. (2006). Automatic TEM image alignment by trifocal geometry. J. Microsc. 222:1–14.PubMedCrossRefGoogle Scholar
  7. Coleman, T. F. and Li, Y. (1996). An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6:418–445.CrossRefGoogle Scholar
  8. Cong, Y., Kovacs, J.A. and Wiggers, W. (2003). 2D fast rotational matching for image processing of biophysical data. J. Struct. Biol. 144:51–60.PubMedCrossRefGoogle Scholar
  9. Crowther, R.A. (1971). Procedures for three-dimensional reconstruction of spherical viruses by Fourier synthesis from electron micrographs. Philos. Trans. R. Soc. B 261:221.CrossRefGoogle Scholar
  10. Crowther, R.A., Amos, L.A., Finch, J. T., De Rosier, D. J. and Klug, A. (1970). Three dimensional reconstructions of spherical viruses by Fourier synthesis from electron micrographs. Nature 226:421–425.PubMedCrossRefGoogle Scholar
  11. Dengler, J. (1989). A multi-resolution approach to the 3D reconstruction from an electron microscope tilt series solving the alignment problem without gold particles. Ultramicroscopy 30:337–348.CrossRefGoogle Scholar
  12. Engelhardt, P. (2000). Electron tomography of chromosome structure. In Encyclopaedia of Analytical Chemistry (R. A. Meyers, ed.), Vol. 6. John Wiley & Sons Ltd, pp. 4948–4984.Google Scholar
  13. Faugeras, O. and Luong, Q.-T. (2001). Geometry of Multiple Images. MIT Press, Cambridge, Massachusetts.Google Scholar
  14. Fishler, M. and Bolles, L. (1981). Random sample consensus. A paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24:381–385.CrossRefGoogle Scholar
  15. Frank, J. (1980). The role of correlation techniques in computer image processing. In Computer Processing of Electron Microscope Images (P. W. Hawkes, ed.). Springer-Verlag, Berlin, pp. 187–222.Google Scholar
  16. Frank, J. and McEwen, B. F. (1992). Alignment by cross-correlation. In Electron Tomography: Three-Dimensional Imaging with the Transmission Electron Microscope (J. Frank, ed.). Plenum Press, New York. pp. 205–213.Google Scholar
  17. Frank, J., McEwen, B. F., Radermacher, M., Turner, J. N. and Rieder C. L. (1987). Three-dimensional tomographic reconstruction in high voltage electron microscopy. J. Electron Microsc. Tech. 6:193–205.CrossRefGoogle Scholar
  18. Frank, J., Radermacher, M., Penczek, P., Zhu, J., Li, Y., Ladjadj, M. and Leith, A. (1996). SPIDER and WEB: processing and visualization of images in 3D electron microscopy and related fields. J. Struct. Biol. 116:190–199.PubMedCrossRefGoogle Scholar
  19. Frank, J., Shimkin, B. and Dowse, H. (1981a). SPIDER—a modular software system for electron image processing. Ultramicroscopy 6: 343–357.Google Scholar
  20. Frank, J., Verschoor, A. and Boublik, M. (1981b). Computer averaging of electron micrographs of 40S ribosomal subunits. Science 214:1353–1355.PubMedCrossRefGoogle Scholar
  21. Gonzalez, R. C. and Woods, R. E. (1993). Digital Image Processing. Addison Wesley.Google Scholar
  22. Guckenberger, R. (1982). Determination of a common origin in the micrographs of tilt series in three-dimensional electron microscopy. Ultramicroscopy 9:167–174.CrossRefGoogle Scholar
  23. Harris, C. and Stephens, M. (1988). A combined corner and edge detector. In Proceedings of the 4th Alvey Vision Conference, pp. 147–151Google Scholar
  24. Hartley, R. and Zisserman, A. (2000). Multiple View Geometry in Computer Vision. Cambridge University Press.Google Scholar
  25. Huber, P. J. (1981). Robust Statistics. Wiley.Google Scholar
  26. Irani, M. and Anadan, P. (2000). Factorization with uncertainty. In Proceedings of the 6th European Conference on Computer Vision, Dublin, Ireland, pp. 539–553.Google Scholar
  27. Joyeux, L. and Penczek, P. A. (2002). Efficiency of 2D alignment methods. Ultramicroscopy 92:33–46.PubMedCrossRefGoogle Scholar
  28. Kak, A. C. and Slaney, M. (1988). Principles of Computerized Tomographic Imaging. IEEE Press.Google Scholar
  29. Kenney, J., Karsenti, E., Gowen, B. and Fuller, S. D. (1997). Three-dimensional reconstruction of the mammalian centriole from cryoelectron micrographs: the use of common lines for orientation and alignment. J. Struct. Biol. 120:320–328.PubMedCrossRefGoogle Scholar
  30. Kremer, J. R., Mastronarde, D. N. and McIntosh, J. R. (1996). Computer visualization of three-dimensional image data using IMOD. J. Struct. Biol. 116:71–76.PubMedCrossRefGoogle Scholar
  31. Kuipers, J. B. (2002). Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality. Princeton University Press.Google Scholar
  32. Lauren, P. D. and Nandhakumar, N. (1997). Estimating the viewing parameters of random, noisy projections of asymmetric objects for tomographic reconstruction. IEEE Trans. Pattern Anal. Machine Intell. 19:417–430.CrossRefGoogle Scholar
  33. Lawrence, M. C. (1983). Alignment of images for three-dimensional reconstruction of nonperiodic objects. In Proceedings of the Electron Microscopy Society of Southern Africa, Vol. 13, pp. 19–20.Google Scholar
  34. Lawrence, M.C. (1992). Least-squares method of alignment using markers. In Electron Tomography: Three-Dimensional Imaging with the Transmission Electron Microscope (J. Frank, ed.). Plenum Press, New York, pp. 197–204.Google Scholar
  35. Lim, J. S. (1990). Two-dimensional Signal and Image Processing. Prentice Hall, Englewood Cliffs, New Jersey.Google Scholar
  36. Liu, Y., Penczek, P. A., McEwen, B. and Frank, J. (1995). A marker-free alignment method for electron tomography. Ultramicroscopy 58:393–402.PubMedCrossRefGoogle Scholar
  37. Lindahl, M. (2001). Strul—A method for 3D alignment of single-particle projection based on common line correlation in Fourier space. Ultramicroscopy 87:165–175.PubMedCrossRefGoogle Scholar
  38. Mastronarde, D. N. (1997). Dual-axis tomography: an approach with alignment methods that preserve resolution. Journal of Structural Biology 120:343–352.PubMedCrossRefGoogle Scholar
  39. Mühlich, M. and Mester, R. (2001). Subspace methods and equilibration in computer vision. In Proceedings of the 12th Scandinavian Conference on Image Analysis. Bergen, Norway, pp. 415–422.Google Scholar
  40. Owen, C. H. and Landis, W. J. (1996). Alignment of electron tomographic series by correlation without the use of gold particles. Ultramicroscopy 63:27–38.PubMedCrossRefGoogle Scholar
  41. Penczek, P., Grassucci, R. A. and Frank, J. (1994). The ribosome at improved resolution: new techniques for merging and orientation refinement in 3D cryo-electron microscopy of biological particles. Ultramicroscopy 53:251–270.PubMedCrossRefGoogle Scholar
  42. Penczek, P., Marko, M., Buttle, K. and Frank, J. (1995). Double-tilt electron tomography. Ultramicroscopy 60: 393–410.PubMedCrossRefGoogle Scholar
  43. Penczek, P., Radermacher, M. and Frank, J. (1992) Three-dimensional reconstruction of single particles embedded in ice. Ultramicroscopy 40:33–53.PubMedCrossRefGoogle Scholar
  44. Quan, L. (1996) Self-calibration of an affine camera from multiple views. Int. J. Comput. Vis. 19:93–105.CrossRefGoogle Scholar
  45. Saxton, W. O. (1994). Accurate alignment of sets of images. J. Microsc. 174:61–68.Google Scholar
  46. Saxton, W.O., Baumeister, W. and Hahn, M. (1984) Three-dimensional reconstruction of imperfect two-dimesional crystals. Ultramicroscopy 13:57–70.PubMedCrossRefGoogle Scholar
  47. Saxton, W. O. and Frank, J. (1977). Motif detection in quantum noise-limited electron micrographs by cross-correlation. Ultramicroscopy 2:219–227.PubMedCrossRefGoogle Scholar
  48. Schmid, C., Mohr, R. and Bauckhage, C. (2000). Evaluation of the interest point detectors. Int. J. Comput. Vis. 37:151–172.CrossRefGoogle Scholar
  49. Schmid, C. and Zisserman, A. (2000). The geometry and matching of curves over multiple views. Int. J. Comput. Vis. 40:199–233.CrossRefGoogle Scholar
  50. Shan, Y. and Zhang, Z. (2002). New measurements and corner-guidance for curve matching with probabilistic relaxation. Int. J. Comput. Vis. 46:199–233.CrossRefGoogle Scholar
  51. Taylor, K. A., Tang, J., Cheng, Y. and Winkler, H. (1997). The use of electron tomography for structural analysis of disordered protein arrays. J. Struct. Biol. 120:372–386.PubMedCrossRefGoogle Scholar
  52. Tomasi, C. and Kanade, T. (1992). Shape and motion from image streams under orthography: a factorisation approach. Int. J. Comput. Vis. 9:137–154.CrossRefGoogle Scholar
  53. Triggs, B., McLauchlan, P., Hartley, R. and Fitzgibbon, A. (2000). Bundle adjustment-a modern synthesis. In Vision Algorithms: Theory and Practice (B. Triggs, A. Zisserman and R. Szeliski, eds), Vol. 1883 of LNCS. Springer, pp. 298–372.Google Scholar
  54. van Heel, M. (1987). Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction. Ultramicroscopy 21:111–124.PubMedCrossRefGoogle Scholar
  55. van Heel, M., Schatz, M. and Orlova, E. (1992). Correlation functions revisited. Ultramicroscopy 46:307–316.CrossRefGoogle Scholar
  56. Winkler, H. and Taylor, K.A. (2003). Focus gradient correction appied to tilt series image data used in electron tomography. J. Struct. Biol. 143:24–32.PubMedCrossRefGoogle Scholar
  57. Xu, G. and Zhang, Z. (1996). Epipolar Geometry in Stereo, Motion and Object Recognition. Kluwer.Google Scholar
  58. Yang, C, Ng, E.G. and Penczek, P. A. (2005). Unified 3-D structure and projection orientation refinement using quasi-Newton algorithm. J. Struct. Biol. 149:53–64.PubMedCrossRefGoogle Scholar
  59. Zhang, Z., Deriche, R., Faugeras, O. and Luong, Q. (1994). A robust technique for matching two uncalibrated through the recovery of the unknown epipolar geometry. Artif. Intell. 78:87–119.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Sami S. Brandt
    • 1
  1. 1.Laboratory of Computational EngineeringHelsinki University of TechnologyTKKFinland

Personalised recommendations