Note however that depending on as well as the distribution of colours in the palette, there may not always be an exact solution for any given . Instead we’ll say that we want to minimise the absolute error between and some linear combination , or .
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Another way to approach dithering is to analyse the input image in order to make informed decisions about how best to perturb pixel values prior to quantisation. Error-diffusion dithering does this by sequentially taking the quantisation error for the current pixel (the difference between the input value and the quantised value) and distributing it to surrounding pixels in variable proportions according to a diffusion kernel . The result is that input pixel values are perturbed just enough to compensate for the error introduced by previous pixels.