III.G. IMAGE ANALYZING REAL SPACE AND OTHER RECONSTRUCTION METHODS

Although Fourier methods of image processing are still widely used, several other methods are practiced and maybe preferred for studying certain specimens. The rotational and translational photographic superposition methods (Horne & Markham, 1972) are quite popular because the theory and application of these methods are simple and straightforward. These methods lead to results comparable with those obtained by optical (digital) filtering and digital, rotational filtering. In addition, the experimental apparatuses are inexpensive and easy to construct.

The main purpose of the photographic superposition methods is to produce an averaged image by forming on a single photographic plate (print) a composite image of the symmetry equivalent parts of the specimen image. The micrograph (or photographic print) is rotated or translated to superimpose the images of individual symmetric units in the specimen. The results of such manipulations are erroneous if an incorrect symmetry is enforced or if the correct symmetry is applied incorrectly (e.g. by rotating about a point of the symmetry axis or by translating in the wrong direction). A major disadvantage of these methods is that they can be too subjective. Of course, any method applied incorrectly will produce erroneous results. Fourier methods divide image analysis into two, objective steps. The superposition methods are reliable and powerful when the specimen symmetry is obvious or well-established by other methods, or when they are performed in conjunction with information obtained by optical digital diffraction. Diffraction patterns (or power spectra) provide a direct and objective way to determine how superpositions should be performed.

Three-dimensional reconstructions may be determined directly from projected images with a variety of real- space processing procedures. Some of these procedures generated much controversy and theoretical discussion in the early image processing literature. In these methods, 3D reconstructions are calculated by directly recombining the set of 2D projections (views) of the specimen. The algebraic algorithms required to perform such reconstructions offer some computational advantages compared to the Fourier methods, but they are generally less familiar to electron microscopists who typically use the Fourier transform algorithms adopted from X-ray crystallographers. The application of real space, back-projection methods to biological problems has mostly been limited to the study of phage tail structures (e.g. Mikhailov & Vainshtein1972) Dokl. Biophys. 203:36-39) and non- crystalline enzyme molecules (e.g. Kiselev (1978) Proc. Ninth Int. Cong.lec. Microsc. (Toronto) 3:94-106).