On a Rate-Distortion Model for Color Images using a Correlation-Based Approach

Although most image compression algorithms deal today with color images, the theory behind the compression process is based mainly on monochrome tools. The common approach to color image coding is to decrease the high inter-color correlations in the RGB domain by transforming the color primaries into a de-correlated color space prior to coding. In this work we present a different approach, called Correlation Based Approach (CBA). Instead of de-correlating the color primaries, we exploit the inter-color correlation to approximate two of the color components as a polynomial function of the third color component, or the base color. We then suggest to code the expansion coefficients of the polynomial functions and at least partly the approximation errors. We use the DCT (Discrete Cosine Transform) block transform to enhance the algorithm´s performance. Thus the approximation of two of the colors relative to the base color is performed for each DCT subband separately. We also use the Rate-Distortion theory of subband transform coders to optimize the algorithm´s bit allocation to each subband and also to find the optimal color components transform to be applied prior to coding. This pre-processing stage may further enhance the algorithm´s performance. Simulation results are provided showing that the new CBA algorithm is superior to algorithms based on the common de-correlation approach, such as JPEG, when using the same tools for image coding.