The futility of square isometries in fractal image compression

In fractal image compression an image is partitioned into a set of image blocks, called ranges. The ranges are matched with blocks taken from a codebook of filtered and subsampled domain image blocks up to an affine transformation of intensity values. It is common practise in fractal image compression to include all 8 isometric versions of a codebook block in the codebook. It is reasoned that such enlarged domain pools yield better rate-distortion curves. However, this is not a valid argument supporting the use of isometries. A fair test must compare the performance of the method using a codebook including isometries with that obtained when using a plain codebook of the same size. We have performed such analysis and our results show that codebooks with isometries offer no advantages in terms of fidelity-in contrast to the prevalent belief. A similar study is carried out for the effects of including respectively excluding negative scaling factors in the fractal code