Summarizing, the algorithm SIFT is used to find common features between two
images. These features are then used to find the parameters to align these two
images. Since, tomography involves the alignment of a series of images acquired
with different tilts angles, the detection step and the descriptor creation step must be
performed for each image in the tilts series. The alignment step occurs once the
matching of the descriptors associated to interest points have been determined for
each couple of images in the tilts series. To align the images in the tilts series, an
additional step of chain creation is needed. This mechanism consists in the tracking
of each point of interest based on the results of the matching. The obtained chain
can begin and end on any image. The chains of each point of interest along the
sequence of images are used during the final alignment. The alignment model,
allowing to determine the orientation of the tilt axis, that can be used in tomography
is detailed in Sect. 2.2.
7.4 Extension to Data Other than Tilt Series
7.4.1 Data Alignment in Multiple-Axis Tomography
The impossibility to acquire a full 180° tilt series under the electron microscope
generate a lack of information. To compensate this limitation two approaches are
frequently used: N-axis tomography and sub-tomogram averaging. Both of then
consist in combine reconstructed volumes in a single final reconstruction but they
differ in the origin of data. In N-axis tomography several tomograms of a single
object are combined whereas in sub-tomogram averaging tomograms of several
objects are fused.
7.4.1.1 N-Axis Tomography
N-axis tomography, allows to get back some of the missing information by
acquiring multiple tilt series. The simplest approach is dual-axis tomography in
which two tilt series are recorded with perpendicular tilt-axes [36, 37]. The use
more than two axis has also been proposed [38, 39], but the higher dose and
complexity of post-processing, compared to the gain of information is not valuable
enough.
The reconstruction of data from N-axis tomography is performed by independent
alignment and reconstruction of each tilt series followed by the determination of the
geometric relationships between the different reconstructions. These relationships are
computed using methods similar to those described in this chapter: correlation-based
or landmarks-based approaches, but in three dimensions. Most of the time, software,
such as imod [40], uses gold beads correspondences between the reconstructions to
solve shifts, rotations and deformations such as shrinkage. Once aligned, tomograms
7 Alignment of Tilt Series
203
images. These features are then used to find the parameters to align these two
images. Since, tomography involves the alignment of a series of images acquired
with different tilts angles, the detection step and the descriptor creation step must be
performed for each image in the tilts series. The alignment step occurs once the
matching of the descriptors associated to interest points have been determined for
each couple of images in the tilts series. To align the images in the tilts series, an
additional step of chain creation is needed. This mechanism consists in the tracking
of each point of interest based on the results of the matching. The obtained chain
can begin and end on any image. The chains of each point of interest along the
sequence of images are used during the final alignment. The alignment model,
allowing to determine the orientation of the tilt axis, that can be used in tomography
is detailed in Sect. 2.2.
7.4 Extension to Data Other than Tilt Series
7.4.1 Data Alignment in Multiple-Axis Tomography
The impossibility to acquire a full 180° tilt series under the electron microscope
generate a lack of information. To compensate this limitation two approaches are
frequently used: N-axis tomography and sub-tomogram averaging. Both of then
consist in combine reconstructed volumes in a single final reconstruction but they
differ in the origin of data. In N-axis tomography several tomograms of a single
object are combined whereas in sub-tomogram averaging tomograms of several
objects are fused.
7.4.1.1 N-Axis Tomography
N-axis tomography, allows to get back some of the missing information by
acquiring multiple tilt series. The simplest approach is dual-axis tomography in
which two tilt series are recorded with perpendicular tilt-axes [36, 37]. The use
more than two axis has also been proposed [38, 39], but the higher dose and
complexity of post-processing, compared to the gain of information is not valuable
enough.
The reconstruction of data from N-axis tomography is performed by independent
alignment and reconstruction of each tilt series followed by the determination of the
geometric relationships between the different reconstructions. These relationships are
computed using methods similar to those described in this chapter: correlation-based
or landmarks-based approaches, but in three dimensions. Most of the time, software,
such as imod [40], uses gold beads correspondences between the reconstructions to
solve shifts, rotations and deformations such as shrinkage. Once aligned, tomograms
7 Alignment of Tilt Series
203