分形编码算法的研究

【作者】 沈志超；

【导师】 李莉；

【作者基本信息】 上海师范大学 ， 通信与信息系统， 2003， 硕士

【摘要】 本文主要是对分形编码算法进行研究，并介绍和实现了一种新的图像压缩算法：基于小波的分形图像压缩算法。首先本文介绍了分形的理论及其用于图像压缩的一般算法。其次研究了分形编码的参数。通过对8种几何变换研究发现，它们并不是传统分形图像压缩编码中固有的不可缺少的一部分，可以通过直接在图像内部增加定义域块扩大搜索空间的方法来替代用8种几何变换构造的搜索空间。由于灰度偏移量g分布相当随机，一直没有有效的方法对其进行再压缩。因此我们采用一种新的参数（值域块均值）来代替它。采用值域块均值作为分形编码的参数可加快分形编码的速度，提高压缩比和加快分形图像压缩解码的收敛速度。然后对值域块方差、比例因子s和均方误差之间的关系进行了研究，从理论上说明了为什么当s的取值超过1以后可以获得较好的重构图像。最后基于分形图像编码的收敛特性和比例因子s的取值特点提出了特征值算法。实验证明采用上述方法可显著减少编码时间。更多还原

【Abstract】 The paper mainly studies the algorithm of fractal image compression, then introduces and implements a new algorithm of image compression: fractal image coding based on wavelet.Firstly, the theory of fractal and the common algorithm of fractal image compression is presented. Secondly, we studied the fractal coding parameters. Based on the study of 8 geometry transforms, the result shows that the transforms are not an intrinsic part of fractal image coding. We can increase the domain blocks directly to enlarge the search pools. It may replace the search pools of 8 geometry transforms. There is not an effective method to compress the parameter g, because the distribution of it is fairly random. So we adopt the mean of range block as the parameter of fractal coding to replace the g. With the mean of range block, the compression ratio is improved, the coding time and reconstruction time are decreased. Then we discuss the relations among range blocks covariance, contrast scaling s and MSE. The analysis shows why a better reconstruction image is obtained when the range of contrast scaling s is larger than one.　 Finally, an algorithm of characteristic value is given based on the convergence characteristics of fractal image coding and the effect of different values of contrast scaling s. Experimental results show that the coding time is decreased obviously.更多还原