This algorithm attempts to minimise numerically. Because of this, the quality of the dither produced by Knoll’s algorithm is much higher than any other of the N-candidate methods we have covered so far. It is also the slowest however, as it requires a greater per-pixel to be really effective. More details are given in Knoll’s now expired patent[3]. I have put together a GPU implementation of Knoll’s algorithm on Shadertoy here.
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This approach shares a lot in common with the idea of multivariate interpolation over scattered data. Multivariate interpolation attempts to estimate values at unknown points within an existing data set and is often used in fields such as geostatistics or for geophysical analysis like elevation modelling. We can think of our colour palette as the set of variables we want to interpolate from, and our input colour as the unknown we’re trying to estimate. We can borrow some ideas from multivariate interpolation to develop more effective dithering algorithms.
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