  In this paper we propose a modified cross correlation method to align images
from the same class in single-particle electron microscopy of highly
non-spherical structures. In this new method, First we coarsely align
projection images, and then re-align the resulting images using the cross
correlation (CC) method. The coarse alignment is obtained by matching the
centers of mass and the principal axes of the images. The distribution of
misalignment in this coarse alignment can be quantified based on the
statistical properties of the additive background noise. As a consequence, the
search space for re-alignment in the cross correlation method can be reduced to
achieve better alignment. In order to overcome problems associated with false
peaks in the cross correlations function, we use artificially blurred images
for the early stage of the iterative cross correlation method and segment the
intermediate class average from every iteration step. These two additional
manipulations combined with the reduced search space size in the cross
correlation method yield better alignments for low signal-to-noise ratio images
than both classical cross correlation and maximum likelihood(ML) methods.
