by kragen | 2025-10-28 01:05:01+00:00
The major dithering algorithm that's missing from this list is blue-noise dithering. This is very similar to "ordered dithering"; you can think of ordered dithering as either thresholding the pixel values with a different threshold value on each pixel, following a regular pattern, or as adding a different offset value to each pixel, following a regular pattern, and thresholding the result with a constant threshold. Blue-noise dithering replaces the regular pattern with a random pattern that's been high-pass filtered. This has all the advantages of ordered dithering, in particular avoiding "crawling" patterns during animation, but avoids the repetitive patterns and line artifacts it introduces.

https://nelari.us/post/quick_and_dirty_dithering/ is the best quick introduction to the technique that I've seen. There's a more comprehensive introduction at https://momentsingraphics.de/BlueNoise.html. https://bartwronski.com/2016/10/30/dithering-part-three-real... also demonstrates it, comparing it to other dithering algorithms.

Ulichney introduced blue noise to dithering in 01988 as a refinement of "white-noise dithering", also known as "random dithering", where you just add white noise before thresholding: https://cv.ulichney.com/papers/1988-blue-noise.pdf. Ulichney's paper is also a pretty comprehensive overview of dithering algorithms at the time, and he also makes some interesting observations about high-pass prefiltering ("sharpening", for example with Laplacians). Error-diffusion dithering necessarily introduces some low-pass filtering into your image, because the error that was diffused is no longer in the same place, and high-pass prefiltering can help. He also talks about the continuum between error-diffusion and non-error-diffusion dithering, for example adding a little bit of noise to your error-diffusion algorithm.

But Ulichney is really considering blue noise as an output of conventional error-diffusion algorithms; as far as I can tell from a quick skim, nowhere in his paper does he propose using a precomputed blue-noise pattern in place of the white-noise pattern for "random dithering". That approach has really only come into its own in recent years with real-time raytracing on the GPU.

An interesting side quest is Georgiev and Fajardo's abstract "Blue-Noise Dithered Sampling" from SIGGRAPH '16 http://web.archive.org/web/20170606222238/https://www.solida..., sadly now memory-holed by Autodesk. Georgiev and Fajardo attribute the technique to the 02008 second edition of Lau and Arce's book "Modern Digital Halftoning", and what they were interested in was actually improving the sampling locations for antialiased raytracing, which they found improved significantly when they used a blue-noise pattern to perturb the ray locations instead of the traditional white noise. This has a visual effect similar to the switch from white to blue noise for random dithering. They also reference a Ulichney paper from 01993, "The void-and-cluster method for dither array generation," which I haven't read yet, but which certainly sounds like it's generating a blue-noise pattern for thresholding images.

Lau, Arce, and Bacca Rodriguez also wrote a paper I haven't read about blue-noise dithering in 02008, saying, "The introduction of the blue-noise spectra—high-frequency white noise with minimal energy at low frequencies—has had a profound impact on digital halftoning for binary display devices, such as inkjet printers, because it represents an optimal distribution of black and white pixels producing the illusion of a given shade of gray," suggesting that blue-noise dithering was already well established in inkjet-land long before it became a thing on GPUs.

Maxime Heckel has a nice interactive WebGL demo of different dithering algorithms at https://blog.maximeheckel.com/posts/the-art-of-dithering-and..., with mouse-drag orbit controls, including white-noise dithering, ordered dithering, and blue-noise dithering. Some of her examples are broken for me.

It's probably worth mentioning the redoubtable https://surma.dev/things/ditherpunk/ and the previous discussion here: https://news.ycombinator.com/item?id=25633483.