A criterion to evaluate three dimensional reconstructions from projections of unknown structures.

The recent discoveries of algorithms for three dimensional reconstructions from projections (Cormack, 1963; De Rosier & Klug, 1968; Crowther, De Rosier & Klug, 1970; Vainshtein, 1970; Gordon, Bender & Herman, 1970; Berry & Gibbs, 1970; Ramachandran & Lakshminarayanan, 1971; Goitein, 1971; Matulka & Collins, 1971; Gilbert, 1972; Cormack, 1973; Sweeney & Vest, 1973; Smith,.Peters & Bates, 1973) are of great interest to biologists because of the possibility of applying them to reconstruct threedimensional structures from electron micrographs and radiographs. However, it has been shown that when the number of projections is limited the reconstruction problem is intrinsically indetermined (Frieder & Herman, 1971). In addition it has been realized that the actual processing of real data introduces anisotropy, erroneous contrast and noise amplification, which produces further elements of uncertainty (Goodman, 1968; De Rosier, 1970; Bellman, Bender, Gordon & Rowe, 1971; Herman, Lent & Rowland, 1973). Given this situation it is extremely important to have a quantitative criterion to evaluate a posteriori the reconstruction itself. Gordon et al. (1970) propose as a criterion the iS-measure and, regarding the statement of Crowther & Klug (1971) that "6 is not a good measure because it reaches a low value once the large scale features are correct and it is relatively insensitive to errors in fine details", Frieder & Herman (1971)