Kronecker乘积生成分形图形和放大图像

摘要

Fractal graphics generation is one of the main fields in fractal geometry. In this paper, different fractal graphics are generated by using Kronecker product of matrix. These graphics show fine self-similar structures. Compared with Iteration Function System and L-system which generates fractal graphics, self-similar structures of fractal graphics are more complicated which are based on Kronecker product. Simultaneously, a method of selecting product matrix adaptively according to image content is given by Kronecker product of matrix. Our method obtains ideal results of image magnification. Compared with image zooming method based on fractal image coding,the method proposed in this paper has low calculation cost and better image zooming effects.%分形图形生成是分形几何学研究的主要内容之一.利用矩阵的Kronecker乘积,通过构造不同的矩阵,生成了各种不同的分形图形.这些图形呈现出了精细的自相似结构.与生成分形图形的L系统和迭代函数系统相比,基于Kronecker乘积生成的分形图的自相似结构更为复杂.同时,借助矩阵的Kronecker乘积,给出了一种根据图像内容自适应选取乘积矩阵的方法,很好地实现了图像的放大.与基于分形图像编码的图像放大方法相比,本文的图像放大方法计算简单,放大效果好.