A partial realization algorithm for finite‐size two‐dimensional arrays
Tsuyoshi Matsuo, Yasumichi Hasegawa, Yoshikuni Okada · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1995
Abstract The following figure realization problem has already been posed. “For arbitiarily given figure (two‐dimensional array), find the (mathematical) model that realizes (describes) the figure. If there exist two or more models, show that they are isomorpric.” As a solution to the problem, the figure realization theorem is obtained as follows. “For any given figure, there always exists a canonical commutative linear representation system that realizes the figure, which is unique except for the isomorphism.” There also are studies to analyze the finite‐dimensional canonical commutative linear representation system. Based on those results, this paper discusses the partial realization (faithful description) problem for the finite‐size two‐dimensional array. an algorithm is given which derives the minimum‐dimensional commutative linear representation system that partially realizes (faithfully describes) the given finite‐size two‐dimensional array. As an application example, the dyeing and weaving patterns are considered and the usefulness of the proposed algorithm is shown. the proposed method is a processing to compress the information of the finite‐size two‐dimensional array by maximally utilizing the regularity of the finite‐size two‐dimensional array considering the vertical and horizontal positions.