Fast sinogram computation and the sinogram-based alignment of images

A direct Fourier method (DFM) to compute sinograms is described. Since the DFM is much faster than the customary rotation and projection process, novel uses of sinograms can be devised. As an example and an exercise on the properties of sinograms, a fast sinogram-based method to align large sets of images is described. The method is based on shift-invariant functions to detect rotations, and on tomographic reconstructions of cross-correlation functions to detect relative shifts. It has been implemented in a novel library, SIGNAL, used to align images of macromolecular assemblies observed in the electron microscope. A comparative analysis of the complexity of sinogram- and imagebased methods, as well as quite a few tests with EM images, show that SIGNAL runs faster, the accuracy being the same.