Matching criteria in fractal image compression

Fractal image compression techniques are being developed due to the recognition that fractals can describe natural scenes better than shapes of traditional geometry. One of the most efficient fractal methods is based on iterated function systems (IFS). The basic principle is that an image can be reconstructed by using the self-similarities in the image itself. When encoding an image, the algorithm partitions the image into a number of square blocks (domain blocks). After this there is a new partition into smaller blocks (range blocks). For every range block the best matching domain block is searched among all domain blocks by performing a set of transformations on the blocks. The compression is obtained by storing only the descriptions of these transformations. While rapid compression algorithm exists, the compression process is extremely time consuming. A crucial point in the encoding procedure is to be able to determine the "best matching" domain block for every range block. So, the matching criterion or the distortion measure represents an important part in the encoding process. This paper investigates the collage theorem upon which is built the fractal image compression method in order to determine the best matching measure for fractal compression. The results prove that the linear correlation coefficient gets the best reconstruction image quality in addition to rapid convergence in the decoding. However, different matching criteria are employed between image partitions.