Error diffusion

Error diffusion is a type of halftoning in which the quantization residual is distributed to neighboring pixels that have not yet been processed.

Richard Howland Ranger received United States patent 1790723 for his invention, "Facsimile system".

The patent, which issued in 1931, describes a system for transmitting images over telephone or telegraph lines, or by radio.

[1] Ranger's invention permitted continuous-tone photographs to be converted first into black and white, then transmitted to remote locations, which had a pen moving over a piece of paper.

Floyd and Steinberg described a system for performing error diffusion on digital images based on a simple kernel[2] where "

Nearly concurrently, J. F. Jarvis, C. N. Judice, and W. H. Ninke of Bell Labs disclosed a similar method, which they termed "minimized average error" using a larger kernel[3] Error diffusion takes a monochrome or color image and reduces the number of quantization levels.

[4] A popular application of error diffusion involves reducing the number of quantization states to just two per channel.

One-dimensional error diffusion tends to have severe image artifacts that show up as distinct vertical lines.

Rather than use a single threshold to produce binary output, the closest permitted level is determined, and the error, if any, is diffused as described above.

When an image has a transition from light to dark, the error-diffusion algorithm tends to make the next generated pixel be black.