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Markerless Alignment in Electron Tomography

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Electron Tomography

Abstract

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.

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References

  • 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 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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 

  • Brandt, S. S. and Ziese, U. (2006). Automatic TEM image alignment by trifocal geometry. J. Microsc. 222:1–14.

    Article  PubMed  CAS  Google Scholar 

  • Coleman, T. F. and Li, Y. (1996). An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6:418–445.

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Faugeras, O. and Luong, Q.-T. (2001). Geometry of Multiple Images. MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Frank, J., Shimkin, B. and Dowse, H. (1981a). SPIDER—a modular software system for electron image processing. Ultramicroscopy 6: 343–357.

    Google Scholar 

  • Frank, J., Verschoor, A. and Boublik, M. (1981b). Computer averaging of electron micrographs of 40S ribosomal subunits. Science 214:1353–1355.

    Article  PubMed  CAS  Google Scholar 

  • Gonzalez, R. C. and Woods, R. E. (1993). Digital Image Processing. Addison Wesley.

    Google Scholar 

  • Guckenberger, R. (1982). Determination of a common origin in the micrographs of tilt series in three-dimensional electron microscopy. Ultramicroscopy 9:167–174.

    Article  Google Scholar 

  • Harris, C. and Stephens, M. (1988). A combined corner and edge detector. In Proceedings of the 4th Alvey Vision Conference, pp. 147–151

    Google Scholar 

  • Hartley, R. and Zisserman, A. (2000). Multiple View Geometry in Computer Vision. Cambridge University Press.

    Google Scholar 

  • Huber, P. J. (1981). Robust Statistics. Wiley.

    Google Scholar 

  • 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 

  • Joyeux, L. and Penczek, P. A. (2002). Efficiency of 2D alignment methods. Ultramicroscopy 92:33–46.

    Article  PubMed  CAS  Google Scholar 

  • Kak, A. C. and Slaney, M. (1988). Principles of Computerized Tomographic Imaging. IEEE Press.

    Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Kuipers, J. B. (2002). Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality. Princeton University Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • Lim, J. S. (1990). Two-dimensional Signal and Image Processing. Prentice Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  • Liu, Y., Penczek, P. A., McEwen, B. and Frank, J. (1995). A marker-free alignment method for electron tomography. Ultramicroscopy 58:393–402.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Mastronarde, D. N. (1997). Dual-axis tomography: an approach with alignment methods that preserve resolution. Journal of Structural Biology 120:343–352.

    Article  PubMed  CAS  Google Scholar 

  • 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 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Penczek, P., Marko, M., Buttle, K. and Frank, J. (1995). Double-tilt electron tomography. Ultramicroscopy 60: 393–410.

    Article  PubMed  CAS  Google Scholar 

  • Penczek, P., Radermacher, M. and Frank, J. (1992) Three-dimensional reconstruction of single particles embedded in ice. Ultramicroscopy 40:33–53.

    Article  PubMed  CAS  Google Scholar 

  • Quan, L. (1996) Self-calibration of an affine camera from multiple views. Int. J. Comput. Vis. 19:93–105.

    Article  Google Scholar 

  • Saxton, W. O. (1994). Accurate alignment of sets of images. J. Microsc. 174:61–68.

    Google Scholar 

  • Saxton, W.O., Baumeister, W. and Hahn, M. (1984) Three-dimensional reconstruction of imperfect two-dimesional crystals. Ultramicroscopy 13:57–70.

    Article  PubMed  CAS  Google Scholar 

  • Saxton, W. O. and Frank, J. (1977). Motif detection in quantum noise-limited electron micrographs by cross-correlation. Ultramicroscopy 2:219–227.

    Article  PubMed  CAS  Google Scholar 

  • Schmid, C., Mohr, R. and Bauckhage, C. (2000). Evaluation of the interest point detectors. Int. J. Comput. Vis. 37:151–172.

    Article  Google Scholar 

  • Schmid, C. and Zisserman, A. (2000). The geometry and matching of curves over multiple views. Int. J. Comput. Vis. 40:199–233.

    Article  Google Scholar 

  • Shan, Y. and Zhang, Z. (2002). New measurements and corner-guidance for curve matching with probabilistic relaxation. Int. J. Comput. Vis. 46:199–233.

    Article  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Tomasi, C. and Kanade, T. (1992). Shape and motion from image streams under orthography: a factorisation approach. Int. J. Comput. Vis. 9:137–154.

    Article  Google Scholar 

  • 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 

  • van Heel, M. (1987). Angular reconstitution: a posteriori assignment of projection directions for 3D reconstruction. Ultramicroscopy 21:111–124.

    Article  PubMed  Google Scholar 

  • van Heel, M., Schatz, M. and Orlova, E. (1992). Correlation functions revisited. Ultramicroscopy 46:307–316.

    Article  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • Xu, G. and Zhang, Z. (1996). Epipolar Geometry in Stereo, Motion and Object Recognition. Kluwer.

    Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  Google Scholar 

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Brandt, S.S. (2007). Markerless Alignment in Electron Tomography. In: Frank, J. (eds) Electron Tomography. Springer, New York, NY. https://doi.org/10.1007/978-0-387-69008-7_7

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