Fractal Image Compression through Weighted Error Minimisation in the Frequency Domain

IFS compression technique, proposed by Barnsley [1], has been widely studied because of its potentially high compression rates. Usually IFS code is determined by minimizing the rms error between a given image and its collage. As rms error is not a physiological metric, images obtained through the standard IFS coding evidence a lot of noise (blocking effect, bad definition). In order to reduce this feeling of noise without incurring in any compression loss, we applied IFS method to minimize the weighted error between the DCT of the given image, partitioned in 8 x 8 sub-blocks, and the DCT of its collage; the weighting is performed through the JPEG matrix. This metric allows us to take into account the physiological properties of human eye and to obtain images which we feel to be more similar to the original than the ones achieved through standard IFS with the rms metric.