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.

Quantization errors are generally hidden by performing a dithering operation on the image. A common method is to utilize error diffusion. However, this method is prone to error accumulation, resulting in color impulses and streaks. This paper presents a new approach to error diffusion dithering through a fuzzy error diffusion algorithm. In this method, the amount of error to be diffused is determined by considering the relative location of the pixel not only to the closest codebook vector, but to all other palette entries. The goal is to hide the quantization errors by error diffusion, while preventing the excess accumulation of errors. This is achieved through an attraction-repulsion schema according to a fuzzy membership function. We also explored methods to speed up the fuzzy error diffusion process through a L-filter approach by determining a fixed set of membership values. We have implemented the fuzzy error diffusion algorithm for color images and achieved drastic improvements, resulting in superior quality dithered images and significantly lower mean squared error values. A different error measure modeling the characteristic of the human visual system also indicates the superiority of our method.

Quantization errors are generally hidden by performing a dithering operation on the image. A common method is to utilize error diffusion. However, this method is prone to error accumulation, resulting in color impulses and streaks. This paper presents an improvement on error diffusion dithering through a fuzzy error diffusion algorithm. In this method, the amount of error to be diffused is determined by considering the relative location of the pixel not only to the closest codebook vector, but also to the color cluster it belongs to. The goal is to hide the quantization errors by error diffusion, while preventing the excess accumulation of errors. This is achieved through an attraction-repulsion schema according to a fuzzy membership function. We have implemented the fuzzy error diffusion algorithm for color images and achieved drastic improvements, resulting in superior quality dithered images and significantly lower mean squared error values.

Quantization and dithering operations are generally performed sequentially: first quantization and then, dithering. The latter is aware of the former. Dithering manipulates the quantization error to hide it. The same can not be said about the quantizer. The quantizer often works to minimize the quantization error without regard to the fact that the results will be changed by the ditherer. We aim to increase the overall image quality by designing the quantizer in such a way that better results will be obtained after dithering.