The Clustering and Recognition of Patterns

ABSTRACT This work is concerned with the processing of line patterns in general, and of hand-written numbers in particular. A mathematical model of the space of hand-written numerals constrained to be a bounded portion of a plane is developed first. Each numeral is transformed into a real function of a real variable by means of a procedure involving horizontal and vertical scanning of the pattern. The functions thus obtained are defined in an interval normalized to [0, 1], are uniformly bounded, piecewise continuous and non-negative. They form a sub-set of the Hilbert space L 2[0, 1 ]. An operator technique in L 2 is then employed to achieve clustering and recognition. When there are m classes S i of patterns, the outcome of the application of the ith operator H i (followed by a normalization) decides if an unclassified pattern belongs or not to S i . The operators are abstracted from a learning set composed of representative samples of the classes. This requires the determination of functions F i and G i...