Fuzzy algorithms for combined quantization and dithering

Color quantization reduces the number of the colors in a color image, while the subsequent dithering operation attempts to create the illusion of more colors with this reduced palette. In quantization, the palette is designed to minimize the mean squared error (MSE). However, the dithering that follows enhances the color appearance at the expense of increasing the MSE. We introduce three joint quantization and dithering algorithms to overcome this contradiction. The basic idea is the same in two of the approaches: introducing the dithering error to the quantizer in the training phase. The fuzzy C-means (FCM) and the fuzzy learning vector quantization (FLVQ) algorithms are used to develop two combined mechanisms. In the third algorithm, we minimize an objective function including an inter-cluster separation (ICS) term to obtain a color palette which is more suitable for dithering. The goal is to enlarge the convex hull of the quantization colors to obtain the illusion of more colors after error diffusion. The color contrasts of images are also enhanced with the proposed algorithm. We test the results of these three new algorithms using quality metrics which model the perception of the human visual system and illustrate that substantial improvements are achieved after dithering.