Scale selection in roughness based color quantization

Color quantization is an important operation with many applications in image compression and image analysis. Through color quantization, millions of colors in original images are compressed to a limited palette while guaranteeing the display quality. Synthesizing color spatial distribution into the traditional histogram, rough set theory is utilized to design the roughness measure for color quantization. Although the superiority of the roughness-based color quantization has been proved, the basic roughness measure tends to over focus on the homogeneity of noisy points and is still not precise enough to represent the homogeneous color regions. To weaken the interference of noise, we improve the existing roughness measure through filtering the local color differences with the linear scale-space kernel. The filtering process actually forms a group of multi-scale approximations of color components and leads to the multilevel roughness. Therefore it is required to decide the reasonable scales for roughness-based quantization. A strategy of scale selection based on the information measurement is also proposed in this paper, which uses the change of the generalized entropies in linear scale-spaces to interpret the varying region homogeneity and detect the optimal scales for color quantization. Abundant experimental results demonstrate the validity of the scale selection strategy. Under the selected scales, the color quantization induced from the roughness measure has good performances on most testing images.