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Our fast alignment method relies on fast rotational matching.
To achieve this goal, we first identify a keypoint in the target complex whose relative location is invariant to rigid transformations and serves as the center of rotation in the fast rotational matching of the two subtomograms.
By expressing the structural information in Spherical Harmonics (SH) Expansion, it is possible to formulate the rotational alignment as a fast rotational matching, which simultaneously calculates alignment scores of all rotations using FFT.
The fast rotational alignment is based on sampling of simultaneously over all rotations R. To do so, we apply a fast 3D volumetric rotational matching (Kovacs and Wriggers, 2002; Xu et al., 2012).
It is therefore beneficial to formulate fast rotational matching in real space.
However, formulating the fast rotational matching in reciprocal space has some limitations.
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Sohl and Spohn (1997) essentially took a single compositional model due to Wänke and Dreibus (1988) and relied on either the chondritic Fe/Si ratio (1.71) to fix the bulk the mantle/core partitioning of iron (and thus the oxidation state of the mantle) or relied on matching the rotational moment of inertia, C, to its upper limit of 0.366×M r 2 as then known from available data.
Figure 1 gives an example of block matching using translational and rotational motion model.
Figure 1 An example of block matching using translational and rotational motion model.
Application of cone-beam CT (CBCT) for patient localization was superior to 2D matching techniques for detecting rotational setup errors.
We assessed the accuracy and reproducibility of our method by investigating the influence of the segmentation and matching procedure on translational and rotational side-to-side differences of the distal poles.
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