This can lead to magnification changes or deformations in the recorded projections.
The result is that the geometric relationships between the object and the obtained
projections are not precisely known initially. Thus, a step of image alignment of
these projection images is mandatory prior to compute accurate reconstructions. In
this chapter, we will discuss different approaches to perform image alignment used
with the aim of correcting most of the deviations from an ideal projection geometry.
This means to describe methods to determine the geometrical relationships existing
between the different projections of a tomographic tilt series.
Different approaches have been used to perform image alignment. The most
classical one, frequently used to correct shifts between projections, is based on the
maximisation of the cross-correlation existing between images [2–4]. However,
this approach does not consider the existence of magnification changes or
deformations cross-correlation, so that it is not good enough to align projections
when shrinkage or change of focus occurs during the acquisition process which is
not unusual in biological samples which are sensible to damages induced by the
electron beam. A second way to perform image alignment, frequently used in
biological samples, is to add fiducial gold colloidal markers to the sample. As gold
beads can be localized very accurately, due to their spherical shape and high
contrast, the alignments base on these markers are very accurate. In addition, if a
large number of beads is used, the errors in their localization are averaged [5]. The
marker-based methods have another advantage as it will generate a 3D model of
their positions which guarantees a consistent alignment among the images from
the full range of tilt angles. This 3D model can also be adapted to correct
deformations induced in the sample during imaging. However, it is not always
possible to use fiducial gold colloidal markers as they can interfere with reconstruction process (streak artifact for example [6]). Moreover, even if markers are
added during sample preparation before observation, sometimes they are not
uniformly distributed, being absent (or numbering not enough) in the region of
interest for the reconstruction. To deal with this problem, approaches based on
feature recognition have been developed. Thus, instead of adding external markers
to the sample characteristic features are automatically extracted and tracked along
the projection images of tilt-series before building 3D models prior to determine
alignment parameters ().
7.2 Standard Alignment Process
As aforementioned, the acquisition of tilt series under the transmission electron
microscope suffers from the goniometer and sample instabilities which main effects
leads to shifts and in-plane rotations. To evaluate the accuracy of different alignment processes and algorithms it is frequent to use numerical phantoms which
values are perfectly determined and which precisely simulate the different shifts,
rotations or deformations to be corrected. Thus, it is possible to compare the
parameters determined by algorithms or process to the simulated values included in
7 Alignment of Tilt Series
185
The result is that the geometric relationships between the object and the obtained
projections are not precisely known initially. Thus, a step of image alignment of
these projection images is mandatory prior to compute accurate reconstructions. In
this chapter, we will discuss different approaches to perform image alignment used
with the aim of correcting most of the deviations from an ideal projection geometry.
This means to describe methods to determine the geometrical relationships existing
between the different projections of a tomographic tilt series.
Different approaches have been used to perform image alignment. The most
classical one, frequently used to correct shifts between projections, is based on the
maximisation of the cross-correlation existing between images [2–4]. However,
this approach does not consider the existence of magnification changes or
deformations cross-correlation, so that it is not good enough to align projections
when shrinkage or change of focus occurs during the acquisition process which is
not unusual in biological samples which are sensible to damages induced by the
electron beam. A second way to perform image alignment, frequently used in
biological samples, is to add fiducial gold colloidal markers to the sample. As gold
beads can be localized very accurately, due to their spherical shape and high
contrast, the alignments base on these markers are very accurate. In addition, if a
large number of beads is used, the errors in their localization are averaged [5]. The
marker-based methods have another advantage as it will generate a 3D model of
their positions which guarantees a consistent alignment among the images from
the full range of tilt angles. This 3D model can also be adapted to correct
deformations induced in the sample during imaging. However, it is not always
possible to use fiducial gold colloidal markers as they can interfere with reconstruction process (streak artifact for example [6]). Moreover, even if markers are
added during sample preparation before observation, sometimes they are not
uniformly distributed, being absent (or numbering not enough) in the region of
interest for the reconstruction. To deal with this problem, approaches based on
feature recognition have been developed. Thus, instead of adding external markers
to the sample characteristic features are automatically extracted and tracked along
the projection images of tilt-series before building 3D models prior to determine
alignment parameters ().
7.2 Standard Alignment Process
As aforementioned, the acquisition of tilt series under the transmission electron
microscope suffers from the goniometer and sample instabilities which main effects
leads to shifts and in-plane rotations. To evaluate the accuracy of different alignment processes and algorithms it is frequent to use numerical phantoms which
values are perfectly determined and which precisely simulate the different shifts,
rotations or deformations to be corrected. Thus, it is possible to compare the
parameters determined by algorithms or process to the simulated values included in
7 Alignment of Tilt Series
185