Fuzzy Grammars in Syntactic Recognition of Skeletal Maturity from X-Rays

A hierarchical three-stage syntactic recognition algorithm using six-tuple fuzzy and seven-tuple fractionally fuzzy grammars is described for identifying different stages of maturity of bones from X-rays of hand and wrist. The primitives considered are "dot," "straight line," and "arc" as obtained elsewhere. For each arc, its memberships in the sets of "sharp," "fair," and "gentle" arcs have been considered in order to describe and interpret the structural development of epiphysis and metaphysis with growth of a child. The two algorithms are illustrated with the help of the radiograph of a 10-12-year old boy along with some "noisy" versions of the radiograph, which was artificially generated by taking into account possible variations in shape of the relevent contours in the radiograph. Relative merits of the two algorithms with respect to each other and as well as the existing nonfuzzy approach are also discussed.