ソン　ショウシュウ   Shao Chin Sung   宋　少秋    所属   青山学院大学  理工学部 経営システム工学科    職種   教授
言語種別	日本語
発行・発表の年月	2006/03
形態種別	学術雑誌
標題	Distributing Distinct Inegers Uniformly over a Square Matrix with Application to Digital Halftoning
執筆形態	共同
掲載誌名	Journal HERMIS - International Journal of Computer Mathematics and its Application
巻・号・頁	1-11頁
著者・共著者	T. Asano, S. Choe, S. Kashima, Y. Kikuchi, *S.C. Sung
概要	This paper considers how to distribute n2 integers between 0 to n2-1 as uniformly as possible over an n × n square matrix. We introduce a discrepancy-based measure to evaluate the uniformity. More precisely, we take a sum of matrix elements over every k × k contiguous submatrix and define the discrepancy of the matrix as the matrix as the largest difference among those sums. It is known that if n and k are both even integers then we can construct zero-discrepancy matrices. In this paper we present a scheme for achieving a new discrepancy bound 2n when n is odd and k is 2. This is an improvement from the previous bound 4n. We borrow basic ideas behind orthogonal Latin squares and semi-magic squares. An n-ary number system also plays an improtant part. This problem is closely related to digital halftoning. Low discrepancy matrices would impprove the quality of commonly used ordered dither algorithm.