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In this report three thinning algorithms are developed: one each for use with rectangular, hexagonal, and triangular arrays. The approach to the development of each algorithm is the same. Pictorial results produced by each of the algorithms are presented and the relative performances of the algorithms are compared. It is found that the algorithm operating with the triangular array is the most sensitive to image irregularities and noise, yet it will yield a thinned image with an overall reduced number of points. It is concluded that the algorithm operating in conjunction with the hexagonal array has features which strike a balance between those of the other two arrays. [ABSTRACT FROM AUTHOR]

There are situations in the natural sciences and medicine (e.g. in electron microscopy and X-ray photography in which it is desirable to estimate the gray levels of a digital picture at the individual points from the sums of the gray levels along straight tines (projections) at a Few angles. Usually, in such situations, the picture is far from determined and the problem is to find the "most representative" picture. Three algorithms are described (all using Monte Carlo methods which were designed to solve this problem. The algorithms are applicable in a large and varied number of fields. The most important uses may he the reconstruction of possibly asymmetric particles from electron micrographs and three-dimensional X-ray analysis. [ABSTRACT FROM AUTHOR]