Fast Fractal Image Encoding

Abstract

This thesis focuses on fast fractal image encoding. Fractal image encoding has a lot of advantages such as high speed decoding, competitive distortion-compression rate, and resolution independent decoding. However, it suffers from long search time to find a close match between a range block and a large pool of domain blocks. Furthermore, each pair of range-domain match involves time-consuming mean square error (MSE) calculation, since each calculation needs a lot of time to get contrast scaling by a complicated formula. In this study we propose two new techniques to reduce the number of MSE calculations and the time to accomplish an MSE calculation, which, in turn, speed up the encoding time. First, MSE criterion is adopted to prune similar domain blocks in advance so that consequent searching time during encoding can be reduced dramatically. Note that when the size of the image increases, the size of domain pool increases exponentially. However, the proposed pruning method only increases the size of domain pool in nearly linear order. Second, a simple equation to approximate contrast scaling is derived on the basis of regression analysis so that the time taken to calculate each MSE can be dropped. Moreover, the estimated contrast scaling can be used to modify the adaptive search rule [1] so that the adaptive search rule can be performed more efficiently. In a summary, the proposed method achieves good speed-up while maintaining the quality of compression. Various experimental results show that our method yields superior performance over other existing fractal encoding methods.