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A method of representing a binary pictorial pattern is developed. Its original idea comes from a sequence of terminal symbols of a context-free grammar. It is a promising technique of data compression for ordinary binary-valued pictures such as texts, documents, charts, etc. Fundamental notions like complexity, primitives, simplifications, and other items about binary-valued pictures are introduced at the beginning. A simple context-free grammar G is also introduced. It is shown that every binary-valued picture is interpretable as a terminal sequence of that G. The DF-expression is defined as the reduced terminal sequence of G. It represents the original picture in every detail and contains no surplus data for reproducing it. A quantitative discussion about the total data of a DF-expression leads to the conclusion that any binary-valued picture with complexity less than 0.47 is expressed by the DF-expression with fewer data than the original ones. The coding algorithm of original data into the DF-expression is developed. It is very simple and recursively executable. Experiments were carried out using a PDS (photo digitizing system), where test pictures were texts, charts, diagrams, etc. with 20 cm × 20 cm size. Data compression techniques in facsimile were also simulated on the same test pictures. Throughout these studies it was made clear that the DF-expression is a very effective technique as a data compression for binary pictorial patterns not only because it yields high data compression but also because its coding and decoding algorithms are very feasible.
Kawaguchi et al. (Tue,) studied this question.