Instead of perturbing each pixel in the input image at random, we can choose to dither by a predetermined amount depending on the pixel’s position in the image. This can be achieved using a threshold map; a small, fixed-size matrix where each entry tells us the amount by which to perturb the input value , producing the dithered value . This matrix is tiled across the input image and sampled for every pixel during the dithering process. The following describes a dithering function for a 4×4 matrix given the pixel raster coordinates :
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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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