Picture Graphs, Grammars, and Parsing

Abstract

This paper is concerned with the syntactic description and analysis of pictures when graphs are employed as the primary description formalism. The present state of development, a number of significant open problems, and the advantages and limitations of this approach are discussed under the following three headings: (a) representation of pictures by graphs, (b) graph languages and grammars, and (c) parsing of graphs and pictures. In (a) we investigate transformations from pictures to graphs based on n-ary relations $(n \geq 1)$ that exist among picture components, both at the primitive pattern level and among higher level subpictures; n-ary relations are reduced when $n>2$ or expanded when $n=1$ to binary relations. Several grammatical schemes for generating graph descriptions are then evaluated with respect to their descriptive adequacy, complexity, and practical and theoretical tractability. Syntax-directed analysis of graphss and pictures is treated from two points of view - how to parse efficiently and how to enlist the descriptive mechanism as an aid in the difficult lower level pattern recognition tasks. The latter point is particularly emphasized with the aim of promoting a more systematic approach to contextual recognition.