Direct Binary Search with Adaptive Search and Swap

Grayscale halftoning is the technique of approximating a grayscale image by a black-and-white image. Black-and-white printers use halftoning to replicate grayscale images on paper. The printers have only the black of ink and the white of paper as the colors at their disposal. Although the printers may vary the size of dots they drop, they cannot vary the intensity of the droplets. All droplets are black. The printers therefore actually produce black-and-white halftones instead of grayscale prints. The task is to make the black-and-white image indistinguishable from the grayscale one. We consider a halftoned image to be a good approximation to the original grayscale in the obvious sense: perceptually, the images look like one another. How to quantify this metric, however, is less than obvious. A complete model for the human visual system is an open research problem and must take many things into account: for example, how the eye blurs together nearby pixels, the sensitivity of the eye to changes in texture and luminescence, the attenuated response of the eye to changes along diagonal directions, and how optical illusions fool the brain. Understanding that the approximation problem must take into account visual perception, we define the grayscale halftoning problem: