On a Method of Binary-Picture Representation and Its Application to Data Compression

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.