Feature Difference Classification in Fractal Image Coding

Fractal image coding suffers from its long encoding time. Block classification is often used to speed up coding processing, which uses some mechanism of classification when coding an image and only does match job for domain and range blocks with some similar features. D. Saupe’s classification algorithm of nearest neighbor search in feature space seems to have the best rate-distortion property among all state-of-the-art classification schemes. However, the algorithm is always bothered with the problem that more time is needed for better fidelity, which is contradictory to the original goal of classification. A scheme using the notion of feature difference in Saupe algorithm is proposed in this paper. This scheme dramatically speeds up matching process in fractal coding without fidelity lost. The kernel idea of this scheme is based on the natural contraction property of fractal image coding. Note that the scale parameter s in a conventional affine transformation between domain and range blocks should satisfy |s|<1 in an ideal environment, but this property is neglected in nowadays classification schemes. Conventional algorithms usually compute the value of s and do a truncation if |s|>1, which not only loses computation precision but also wastes computation time. If the contraction property is properly employed in coding process, much better rebuilt image quality can be obtained with equivalent coding speed; or, reversely, an equivalent PSNR value can be obtained with much shorter coding time. Therefore, We propose the notion of “feature difference” as a feature factor of a block in fractal image coding. It can be easily shown that the domain block always has a bigger feature difference than the range block in a good domain-range match pair. So, when doing domain-range match, for a predefined threshold, only domain blocks with bigger feature differences than the target range block need further regression analysis while others are all discarded. Calculation of feature difference is very simple and adds no complexity to the whole algorithm. Since many “pseudo matched blocks” are effectively precluded, a better rebuilt image quality or a shorter coding time can be expected. Experimenal results show that the improved Saupe algorithm using difference feature can effectively avoid a lot of unnecessary computation and find optimal domain-range match very efficiently. It costs only less than half of the matching time to give equivalent PSNR value in the same compression ratio level of both high and low bit rate image coding. The feature difference decision criterion effectively solves the problem of contradiction between coding time and fidelity of reconstructed image and generates much better rebuilt image quality with same or less coding time. The notion of feature difference is simple but effective. It can also be successfully applied to many other classification algorithms.