Kronecker乘积生成分形图形和放大图像.pdf

16 2 V o l16 N o2 2011 4 JOURNA L O F HAR BIN UN IVER SITY OF SCIENCE AND TE CHNOLOGY A pr. 2011 K ronecker 韩 伟 ( , 02400 1 : 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K ronecker乘积, 通过构造 不同的矩阵, 生成了 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K ronecker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. : K ronecker乘积; 分形图形; 自相似结构; 图像放大 : TP391 : A : 1007- 2683( 2011 02- 0049- 04 Gene rat ing Fracta l G raphics and Zoom ing Image Us ing K ronecke r P roduct HAN W e i ( M athem atics Co llege, C h ifeng U n ivers ity, Ch ifeng 02400 1, Ch ina Abs tract: F racta l g raph ics generation is one o f the m a in fields in fractal geom etry. In this paper, d ifferent fracta l graph ics are generated by u sing K ronecker product o f m atrix. T hese graph ics show fine se lfsmi ilar struc tures. Com pared w ith Iteration Function System and Lsystem w hich generates fracta l graph ics, se lfsmi ilar struc tures o f fractal graph ics are m ore comp licated w hich are based on K ronecker product. S mi ultaneou sly, a m ethod o f selecting product m atr ix adaptively acco rd ing to mi age content is g iven by Kronecker product of m atrix. Ourm ethod obtains idea l results o f mi age m agn ification. Com pared w ith mi age zoom ing m ethod based on fracta l mi age coding, the m ethod proposed in th is paper has low calcu lation cost and better mi age zoom ing effects. K ey