广义Mandelbrot集和Logistic映射在图像压缩中的应用

Image Compression Using Generalized Mandelbrot Collection and Logistic Mapping

目的在构造压缩字典时,改变传统的一幅图像固定一张量化表、一幅图像对应一个压缩字典的分形图像压缩方法,将广义M集和Logistic映射应用于分形图像压缩编码.方法采用函数f(z)=z3+c,生成M集曲线,使用Logistic混沌映射生成的量化表量化M集曲线,生成图像块,构成压缩字典.将自适应合并算法应用于图像的分类,将量化后的M集图像块与压缩字典中的图像块进行匹配,选出满足条件的图像块,然后对该图像块进行编码;解码时读取压缩字典,重建图像.结果实验证明本算法实现简单、可行,图像压缩比高、重建图像质量好.结论该算法生成的图像块数量多、种类全,构造的压缩字典丰富,解码图像质量高,并且比传统分形图像压缩算法压缩比高,解码速度快.

When constructing the compression dictionary, we create a new method to change the fact that an image has a fixed quantification table and an image has a one - to - one compression dictionary. The method advances the fractal image compression algorithm based on Mandelbrot collection and Logistic mapping. The function f（z） = z3 ＋ c with different z can create different curves. The paper used the quantification table coming from Logistic mapping to quantify the curves and then obtained many image blocks, thus an abundant compression dictionary was built. Self - adapt combination arithmetic was applied to sorting the image. We matched the image blocks in the compression dictionary, then the image blocks satisfying the conditions were encoded. When decoding, the compression was read to reconstruct the former image. This algorithm is simple and feasible, and it provides higher compression ratio, faster decoding and perfect decoded image.