Two-Dimensional Grammars And Their Applications To Artificial Intelligence

Abstract

During the past several years, the concepts and techniques of two-dimensional grammars1,2 have attracted growing attention as promising avenues of approach to problems in picture generation as well as in picture description3 representation, recognition, transformation and manipulation. Two-dimensional grammar techniques serve the purpose of exploiting the structure or underlying relationships in a picture. This approach attempts to describe a complex picture in terms of their components and their relative positions. This resembles the way a sentence is described in terms of its words and phrases, and the terms structural picture recognition, linguistic picture recognition, or syntactic picture recognition are often used. By using this approach, the problem of picture recognition becomes similar to that of phrase recognition in a language. However, describing pictures using a string grammar (one-dimensional grammar), the only relation between sub-pictures and/or primitives is the concatenation; that is each picture or primitive can be connected only at the left or right. This one-dimensional relation has not been very effective in describing two-dimensional pictures. A natural generaliza-tion is to use two-dimensional grammars. In this paper, two-dimensional grammars and their applications to artificial intelligence are presented. Picture grammars and two-dimensional grammars are introduced and illustrated by examples. In particular, two-dimensional grammars for generating all possible squares and all possible rhombuses are presented. The applications of two-dimensional grammars to solving region filling problems are discussed. An algorithm for region filling using two-dimensional grammars is presented together with illustrative examples. The advantages of using this algorithm in terms of computation time are also stated. A high-level description of a two-level picture generation system is proposed. The first level is the picture primitive generation using two-dimensional grammars. The second level is picture generation using either string description or entity-relationship (ER) diagram description. Illustrative examples are also given. The advantages of ER diagram description together with its comparison to string description are also presented. The results obtained in this paper may have useful applications in artificial intelligence, robotics, expert systems, picture processing, pattern recognition, knowledge engineering and pictorial database design. Furthermore, examples related to satellite surveillance and identifications are also included.