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.

Three different implementations of the 3-pass algorithm of image and volume data rotation are illustrated and discussed. The three protocols use interpolation in real domain, with a peculiar implementation of the Shannon reconstruction, or phase shifts in Fourier domain. Accuracy and speed of the three methods are compared with corresponding values obtained with a 1-pass method. The results indicate that for low or moderate accuracy, 1-pass is more convenient than 3-pass rotation for both accuracy and speed. Very accurate rotations can be obtained in reasonable time if all steps of 3-pass rotation are performed in the Fourier domain.

A single projection of a helical distribution of matter allows one to obtain the complete three-dimensional reconstruction of the structure. This task is usually performed by a Fourier-Bessel algorithm, which is more efficient than a customary fast Fourier transform inversion. This article describes how to achieve such a result by a direct Fourier method in a reasonable time. Once the two-dimensional transform of the projection is obtained from the source image, it is possible to build up the three-dimensional transform array, in Cartesian coordinates, that yields the reconstruction by a straightforward Fourier inversion. Images of projected helices should be studied with high sampling rates to enhance the resolution, and the segments of helix should be long enough to give a satisfactory signal-to-noise ratio. These conditions result in three-dimensional transform arrays that would require one or more gigabytes of storage. The strategy proposed here requires much less storage and is fast enough to allow the reconstruction to be performed with different parameters and filters in a very short time without any sacrifice in resolution.

Biological computing is generally organized as standalone implementation on a PC-type computer or on a central facility (e.g. a university computer center). Services provided by central facilities need to be tailored to the user community. Unless very work-intensive individual contacts are used, the feedback must be collected with generalized tools, such as questionnaires distributed in the form of a newsletter. We have developed a method to have such polls automated and tailored, as well as having multiple-choice questions combined with branching after fundamental questions. As the evaluation of the results needs to know the questions asked, we have also included a method to process the answers and give detailed tables on the answers. SUPER was applied in a poll to query the academic usership in Switzerland on the usage of molecular biology databases.

FT3D is a self-contained package of tools for three-dimensional Fourier analysis, written in the C language for Unix workstations. It can evaluate direct transforms of three-dimensional real functions, inverse transforms, auto- and cross-correlations and spectra. The library has been developed to support three-dimensional reconstructions of biological structures from projections obtained in the electron microscope. This paper discusses some features of the library, which has been implemented in such a way as to profit from the resources of modern workstations. A table of elapsed times for jobs of different dimensions with different RAM buffers is reported for the particular hardware used in the authors' laboratory.