Optimum parent pruning in fractal compression

Abstract

We consider the rate/distortion benefits of aspects of fractal image compression, and introduce a new method of pruning the pool of parent blocks for optimum performance. Previous work questioned the value of searching in fractal compression, and found that the code used to represent block offsets was not compensated for by decreased error. This was because the searching process predominantly chose local parent blocks. Here we revisit this question using improved basis functions and orthogonalized parent blocks. The basis function is a limited number of DCT coefficients which has very low complexity compared to wavelet transforms or full DCTs. A zero-searching fractal transform in which the parent block is centred over the child block improves the basis function approximation. With orthogonalized parent blocks, searching of the image gives a slight PSNR benefit at higher compression ratios. A new scheme, in which the pool of parent blocks is pruned according to a rate/distortion criterion, gives greater improvement, and guarantees optimal use of the parent pool. The method advances the technique of fractal image compression and shows how to use fractal terms to improve the rate/distortion performance of image coding by any basis approximation.