Error bounds for error diffusion and related digital halftoning algorithms

Abstract

We study error bounds of error diffusion and related digital halftoning algorithms. We define a large class of error diffusion algorithms and give sufficient and necessary conditions for the existence of an error diffusion algorithm with bounded error. In particular, we show that there exists an error diffusion algorithm with bounded errors if and only if the input colors lie in the convex hull of the output colors. We discuss boundedness of a human visual system based error. In addition, we discuss the relationship between digital halftoning and some classical mathematical problems such as the chairman assignment problem. © 2001 IEEE.