Fractal image compression is one of the efficient structure-based methods in applications where images are compressed only once but decoded several times due to its resolution-independent feature and fast reconstruction time. However, it has high computational complexity restricting practical use most of the time. Although several methods have been developed to speed up the compression process, these do not satisfy the compression time or the decoded image quality requirements. The affine transforms of image blocks used in fractal coding require a huge number of multiplications and additions and are very expensive in computation that may also slow down the compression process. This paper presents a novel fractal image compression using a fast affine transform and hierarchical classification scheme. The applied affine transform computation algorithm of image blocks uses relationships among neighboring pixels of transformed image block that significantly reduces the number of multiplication and addition operations. Then, this strategy with hierarchical classification and class-wise domain sorting is applied in fractal coding with quad-tree and horizontal vertical partitioning schemes to reduce compression time. Experimental results show that the quad-tree-based fractal coding with the proposed scheme can significantly speed up the compression process keeping image quality and compression ratio almost unchanged.

分形图像压缩是一种有效的基于结构的方法，在这些应用中，由于其与分辨率无关的特征和快速的重建时间，图像仅压缩一次但解码多次。然而，它具有很高的计算复杂度，在大多数情况下限制了实际使用。虽然已经开发了几种方法来加速压缩过程，但这些方法都不能满足压缩时间或解码图像质量的要求。分形编码中使用的图像块的仿射变换需要大量的乘法和加法，并且计算非常昂贵，这也可能会减慢压缩过程。本文提出了一种使用快速仿射变换和分层分类方案的新型分形图像压缩。应用的图像块仿射变换计算算法利用变换后的图像块的相邻像素之间的关系，显着减少了乘法和加法运算的次数。然后，将这种具有分层分类和逐类域排序的策略应用于具有四叉树和水平垂直分区方案的分形编码，以减少压缩时间。实验结果表明，采用所提出方案的基于四叉树的分形编码可以显着加快压缩过程，同时保持图像质量和压缩率几乎不变。这种具有分层分类和逐类域排序的策略应用于具有四叉树和水平垂直分区方案的分形编码，以减少压缩时间。实验结果表明，采用所提出方案的基于四叉树的分形编码可以显着加快压缩过程，同时保持图像质量和压缩率几乎不变。这种具有分层分类和逐类域排序的策略应用于具有四叉树和水平垂直分区方案的分形编码，以减少压缩时间。实验结果表明，采用所提出方案的基于四叉树的分形编码可以显着加快压缩过程，同时保持图像质量和压缩率几乎不变。