A dual interpretation for direct binary search and its implications for tone reproduction and texture quality

The direct binary search (DBS) algorithm employs a search heuristic to mini mize the mean-squared perceptually filtered error between the halftone and continuous-tone original images. Based on an efficient method for evaluatin g the effect on mean squared error of trial changes to the halftone image, we show that DBS also minimizes in a pointwise sense the absolute error und er the same visual model, but at twice the viewing distance associated with the mean-squared error metric. This dual interpretation sheds light on the convergence properties of the a lgorithm, and clearly explains the tone bias that has long been observed wi th halftoning algorithms of this type. It also demonstrates how tone bias a nd texture quality are linked via the scale parameter, the product of print er resolution and viewing distance. Finally, we show how the tone bias can be eliminated by tone-correcting the continuous-tone image prior to halfton ing it.