Neugebauer revisited: Random dots in halftone screening

Abstract

The Neugebauer equations relate the color of a region of a halftone image to the colors and sizes of the ink dots within the region by considering the color to be a partitive mixture of the colors of the dots, the color of the paper, and the color of the dot overlaps. The amount of each color contributing to the mixture is the percent area covered by the color. In determining the percent area of each color, the Neugebauer equations implicitly assume that the dots of each screen are randomly positioned with respect to the dots of the other screens, and so the percent area of dot overlap is the product of the individual dot percent areas. With digital control of the printing process, however, the screens do not necessarily have statistical independence because the positions of the dots of each screen are completely determined. In this article, the halftone color is explicitly calculated as a function of the dot sizes for a bichromatic print. I define a correlation function that indicates statistical independence of the two screens and show that the Neugebauer equations result for zero correlation. It is shown that the condition for zero correlation depends on the angle between the screens. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 104–113, 1998