摘要： 提出一种基于Julia-CK集和Logistic映射的非线性分形压缩算法。用Carotid-Kundalini函数生成Julia-CK集，并用Logistic映射生成伪随机数填充量化表。将量化后的Julia-CK集分割成4 4的小图像块，再变换成圆盘。圆盘经过旋转后重新变换为正方形，对Julia-CK集进行适当的分类。编码时在同类中寻找匹配的图像块，扩充了原有的仿射变换，得到一个丰富且可通用的压缩字典，有效地打破图像和数据字典之间的一一对应关系。实验表明，相比于Barnsley提出的经典分形压缩方法，新算法使压缩比提高约36%，重建图像的峰值信噪比提高约27%，具有良好的压缩比，获得了高质量的解码图像。

关键词: Julia-CK集, Logistic映射, 圆盘, 分形压缩, 数据字典

Abstract: This paper presents a new nonlinear fractal compression algorithm based on Julia-CK set and Logistic map. Carotid-Kundalini function is used to generate the Julia-CK set and Logistic map is applied to engender pseudo-number to fill the quantized table. Julia-CK set is divided into
4×4 square image blocks, afterwards they are changed into disks. After the disks are rotated, they are changed into square blocks again and classified appropriately. In the course of coding, it is only to search the matching image square in the same category. The traditional affine maps are largely extended and a very abound, universal and fixed dictionary is obtained. Moreover, the problem that the image and digital dictionary should be corresponded with each other can be effectively solved. Experimental results show that compared with the traditional fractal compression method brought by Barnsley, the new algorithm can enhance the compression rate by about 36 percent and improve the PSNR of the rebuilt image by about 27 percent, so it has better compression results and high quality rebuilt image.

Key words: Julia-CK set, logistic map, disk, fractal compression, digital dictionary

中图分类号: 

• TP391