A novel domain optimization technique in fractal image compression

Abstract

Fractal image compression is a lossy compression scheme that exploits the affine redundancy in images and represents them in the form of mathematical model. The scheme has capability of very high compression ratio, high resolution and fast decoding time. The encoding procedure, however, is computationally very expensive and thus requires long encoding time. The encoding procedure consists of dividing the image into range blocks and domain blocks, and then it takes a range block and matches it with the domain block by properly aligning the domain block. It repeats the above procedure for the entire domain pool and then encodes the range block in terms of domain block that is most similar to it. This paper is an effort to reduce complexity and accuracy of first part of the algorithm, i.e. range and domain block alignment and matching. The computation complexity of this process is mainly achieved by doing alignment and matching in Fourier domain using fast convolution technique. The accuracy is achieved by the ability if algorithm to find rotation angles that is not restricted to 90°, 180°, 270° and 360° and also we are able to find the translation of domain block with respect to range block that is often ignored in many fractal encoders in aligning and matching domain block with the range block.