In order to improve the efficiency and speed of match seeking in fractal compression, this paper presents an Average-Variance function which can make the optimal choice more efficiently. Based on it, we also present a fast optimal choice fractal image compression algorithm and an optimal method of constructing data tree which greatly improve the performances of the algorithm. Analysis and experimental results proved that it can improve PSNR over 1 dB and improve the coding speed over 30-40% than ordinary optimal choice algorithms such as algorithm based on center of gravity and algorithm based on variance. It can offer much higher optimal choice efficiency, higher reconstructive quality and rapid speed. It's a fast fractal encoding algorithm with high performances.

This paper present three characteristic functions which can express the luminance distribute characteristic much better. Based on these functions a region classification algorithm is presented. The algorithm can offer more information on regions' similarity and greatly improve the efficiency and performance of match seeking in fractal coding. It can be widely applied to many kinds of fractal coding algorithms. Analysis and experimental results proved that it can offer more information on luminance distribute characteristics among regions and greatly improve the decoding quality and compression ratio with holding the running speed.