An adaptive fractal-based algorithm for image compression

The use of fractal theory in the area of image compression is a relatively new and intriguing concept. Its theoretical basis is well established in the theory of iterated function systems, and particularly in partitioned iterated function systems. However, there are still numerous questions about its practical implementation to be answered. The main problem with this method is that of reducing the complexity of an otherwise very promising concept. We describe a simple and efficient adaptive fractal-based algorithm for image compression. The algorithm uses horizontal-vertical (HV) partitioning of an image into rectangular blocks of different sizes. The partitioning information is used in the encoding process for determining both the range and the domain image blocks. Neither the ranges nor the domains are determined in advance. Instead, the image is fully partitioned into small areas not larger than some predetermined size. The ranges and the corresponding domains are then determined in an adaptive manner, by comparing the rectangular image blocks with different scales. The proposed algorithm attempts to find a good cover for the ranges as large as possible and it then proceeds toward smaller ranges only if an optimal cover is not found with the larger scale. The method allows the total number of finally chosen ranges to be reduced, which is an essential requirement for achieving high compression ratios. The proposed algorithm gives roughly one-half the number of ranges compared to that given by the quad-tree based partitions yielding significant improvement in the compression ratio.