Glossary of terms used in image processing and
Further information is available in the book
by Joachim Frank
Three-Dimensional Electron Microscopy of Macromolecular Assemblies
Oxford University Press, (February 2006)
- Angular reconstitution: a common-lines method designed
to determine the relative angles between three projections of an
object with arbitrary symmetry [van Heel,
1987a]. The method works on the basis of comparing sinograms,
which are plots of line projections as a function of angle.
- Astigmatism(axial): an electron-optical lens aberration
that causes the defocus to be a function of azimuth, and the
contrast transfer function to deviate from circular symmetry about
the optical axis. As a consequence, the Thon rings deform into
elliptic or hyperbolic patterns, depending on the size of defocus
and the size of the astigmatic defocus difference. See
astigmatism as defined by SPIDER
- Classification: separation of
an image set into subsets according to the similarity of features
[Frank, 1990]. Automated classification can be
done directly on the image set, based on [generalized] Euclidean
distances, or on a representation of the image set in a coordinate
system with reduced dimensionality, obtained by principal component
analysis or correspondence analysis. There are two often-used
classification methods: K-means and hierarchical ascendant
classification (HAC). In K-means, the data set is split into K (a
given number) subsets in such a way that each subset is maximally
compact, as measured by the intra-subset variance.
- Eulerian angles: a set of three angles that define an orientation, or
direction, in space. It goes back to the mathematician Euler, and
was used to describe motions in celestial mechanics.
- Pixel size: the number of Angstroms
per pixel in the digitized micrograph. Pixel size is computed as
ps (A/p) = [10,000(A/u) * SR(u) * DF] / M
where ps = pixelsize, SR = scanning resolution, DF = decimation
factor, M = magnification
(units: A = Angstroms, p = pixels,
u = microns). Thus, if the images were acquired at 50,000
magnification, scanned at 7 microns, then reduced in size by 2,
the pixel size would be (10000 * 7 * 2)/50000 or 2.8 Angstroms/pixel.
- Three-dimensional projection matching: a
method of refinement in reconstructing single particles from their
projections [Penczek et al., 1994]. A
preliminary 3D map, obtained by random-conical reconstruction or
angular reconstitution, is used to compute "predicted projections"
on a grid in angular space, which are held in the computer memory.
One by one, the experimental projections are now compared (by
cross-correlation, See CCF) with the set of predicted projections,
to find the best Eulerian angles representing their projection
direction. Next, a refined 3D map is computed, and again this is
used to compute "predicted projections," etc. For self-consistent,
homogeneous data sets, this procedure converges in a
higher-resolution 3D map.
Boettcher, B., Wynne, S.A. and Crowther, R.A.
(1997) Nature 386, 88-91.
Frank, J. (1990) Quart. Rev. Biophys.
Frank, J. (1996)
Three-dimensional Electron Microscopy of Macromolecular
Assemblies. Academic Press, San Diego.
Frank, J., Verschoor, A., and Boublik, M.
(1981) Science 214, 1353-1355.
Malhotra, A., Penczek, P., Agrawal, R.K.,
Gabashvili, I.S., Grassucci, R.A., Juenemann, R., Burkhardt, N.,
Nierhaus, K.H., and Frank, J. (1998) J. Mol. Biol. 280,
Penczek, P., Grassucci, R.A. and Frank, J.
(1994) J. Ultramicroscopy 53, 251-270.
Radermacher, M., Wagenknecht, T.,
Verschoor, A., and Frank, J. (1987) J. Microsc. 146,
Saxton, W.O. and Baumeister, W. (1982)
J. Microsc. 127, 127-138.
van Heel, M. (1987a) Ultramicroscopy
Unser, M., Trus, B.L., and Steven, A.C.
(1987) Ultramicroscopy 30, 429-434.
van Heel, M. (1987b) Ultramicroscopy
Zhu, J., Penczek, P., Schroder, R., and Frank, J.
(1997) J Struct Biol 118, 197-219.
Last update: 14 Nov. 2015
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