Efficiency of 2D alignment methods

In single particle analysis, the alignment of two-dimensional images is a fundamental step aimed at bringing into register various particle views of biological macromolecules observed with the electron microscope. The computational efficiency of this step is a deciding factor in design of alignment strategies for large sets of noisy data and in development of three-dimensional structure refinement methods. In addition, the accuracy of the alignment method varies depending on the numerical solutions adopted to efficiently perform exhaustive searches for three orientation parameters. The selected alignment methods are analyzed in terms of their computational complexity and the estimates of numbers of arithmetic operations for each method are given. The tests of alignment accuracy are performed using images simulated in accordance with the linear theory of image formation in the electron microscope. It is demonstrated that the efficiency of the alignment methods can be improved if approximate centers of gravity of particle views are known. The accuracy of the methods considered is largely affected, particularly for high noise levels, by the order in which interpolation steps are applied.