Traditional fractal image coding is highly time consuming. However

according to the sub-block feature

the approach is very effective in accelerating encoding speed. This study proposes a new sub-block feature function to accelerate coding speed and improve coding performance. This study proves a theorem that unifies theoretical approaches from other documents. This theorem describes the relationship among trace length

trace distribution

and encoding performance. The advantages of multiple documents are compared

and a new block feature is defined on the basis of the theorem. Experimental results show that the proposed algorithm has improved the main diagonal sum feature. Moreover

the local cross trace feature in coding performance has a short encoding time under the same PSNR and has high PSNR under the same encoding time. In the same search radius

the algorithm could determine a large number of optimal matching blocks. That the R-block is a neighbor of the D-block according to block feature is a necessary but insufficient condition to obtain the best matching error. When 10% of the codebook capacity is searched

only approximately 25% of all R-blocks can find their best matching blocks. When half of the codebook capacity is searched

the number of such R-blocks can reach approximately 80%. The proposed algorithm has better coding performance and decoding image quality than the main diagonal sum and local cross trace features.