Abstract: Fractal image coding has received much interest over the past decade in the area of image processing，especially in the context of image compression.It is hardly useful in reality due to the fatal drawback of being quite time consuming during its encoding process.In order to shorten coding time，the fast scheme is proposed to limit the search space on the basis of an inequality linking the root-mean-square and newly-defined main diagonal sum features of normalized block.It can effectively confine the searching scope of best-matched block for an input range block to the neighbourhood of the initial-matched block（i.e.，the domain block having the closest main diagonal sum features to the input range block being encoded）.Moreover，the scheme further propose two strategies：One is all codebook blocks with small standard deviations can be excluded from the domain pool；the other is range blocks with small standard deviations are directly approximated by the intensity mean block.The algorithm is proved feasible in theroy，simulation test results demonstrate that，for three standard test images，the proposed scheme averagely obtain the speedup of 30 times or so，while can accomplish good quality of the reconstructed images against the full search method.

Key words: image compression, fractal, fractal image coding, main diagonal sum feature

摘要： 分形图像编码十余年来在图像处理尤其是图像压缩领域引起了人们的极大兴趣。但编码过程耗时长限制了它的应用范围。为了缩短编码时间，根据匹配均方根误差与新定义的规范块主对角和特征间的关系，提出了一个限制搜索空间的算法：对一个待编码range块，仅在与该range块主对角和特征值最接近的domain块的邻域范围内搜索它的最佳匹配块。同时融入两个措施：一是预先从码书Ω中排除小标准差domain块；二是对小方差range块用其均值块代替。该算法不仅从理论上证明是可行的，而且三幅标准测试图像的仿真实验结果也表明，它确实能够在重建图像质量略好的情况下，平均加快全搜索分形图像编码算法的编码速度30余倍。

关键词: 图像压缩, 分形, 分形图像编码, 主对角和特征