Languages of Encoded Line Patterns

By treating patterns as statements in a two-dimensional language, it is possible to apply linguistic theory to pattern analysis and recognition. In this paper, line patterns are encoded into string form using the chain code developed by Freeman. A class of patterns, or pattern language, encodes to a set of strings that is examined using theory that exists for string languages and automata. Pattern languages formed on the basis of equations in two variables and various pattern properties are related to the hierarchy of string language classes. The known relationships between classes of string languages and classes of automata can then be applied to determine bounds on the time and memory required to recognize the various patterns. Results can be extended to other forms of pattern encoding provided that a suitable translator can be constructed.