Abstract: Optimal color quantization of true-color images is very important for various multimedia applications. We used MacAdam color space, where all color distances are Euclidean, to realize quantization girds that are optimal in respect to human vision. Simple fractionally-bilinear (FB) approximations are proposed for strictly non-linear MacAdam formulae that describe the transformation of usual color space to MacAdam space. Optimal coefficients of FB functions are found for the inner part of the color triangle. Using of FB functions gives the possibility to find explicit color quantization for true-color real-world images in MacAdam space. Both rectangular and hexagonal quantization grids were used in our experiments. Visual tests have shown that the quality of a true-color image displayed on the screen of computer monitor remained very high up to mesh sizes of 8-10 just noticeable differences. Color entropy of quantized images was in this case about 5-6. This means the possibility to compress their colors about 3 times with the help of standard statistical methods. More complicated compression methods that remove spatial correlation of the neighboring image pixels can be used to reach much higher compression ratios. !6
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