A language for two-dimensional digital picture processing

Abstract

A new system, that of matrix grammars, for two-dimensional pattern processing, is introduced. A hierarchy, induced on Chomsky's is found. Language operations such as union, catenation (row and column), Kleene's closure (row and column), and homomorphisms are investigated. It is found that the smallest class of these languages may serve as the class of regular arrays, which is defined as the smallest class of arrays closed under union, catenation (row and column) and Kleene's closure (row and column). Eight possible ways of defining a matrix language are discussed and it is suggested that one of them may lead to a normal form for matrix grammars. The method is advantageous over others on several points. Perhaps the most interesting of all is that it provides a compromise between sequential methods which take too much time for large arrays and parallel methods which usually take too much hardware for large arrays.