一种新的保持分形特征的分形变形方法

A new study on fractal morphing method with fractal feature preserved

针对IFS吸引子变形过程中间出现的分形特征退化的问题,提出基于局部吸引子的近似凸包及旋转匹配的特征对应方法。IFS吸引子的局部吸引子可由独立的IFS生成,IFS中每个压缩仿射映射存在不动点,构造所有不动点的凸包,即得到局部近似凸包;证明了局部近似凸包间的相似对应等价于局部吸引子间的相似对应,并提出了通过旋转匹配的特征对应方法实现局部近似凸包的配对,最后计算所有配对下相似度最高的一组局部近似凸包匹配,确定局部吸引子间的特征对应,即IFS特征对应。对两个IFS进行线性插值可实现保持分形特征的分形变形。

According to the appearance of fractal feature degeneration during fractal morphing, a new feature corresponding method based on local attractor＇ s approximate convex hull （LAA） and revolving matching method （RMM） is introduced. The local attractor, part of the whole IFS attractor, is indicated by an independent IFS code, whose internal contractive affine transformations have unique fixed points, and the LAA is constructed by contouring the convex hull of all the fixed points of the IFS. It is proved that the similarity between different IFS＇ s LAAs is equivalent to the similarity of its local attractors, so the feature corresponding can be built upon the LAAs. The matching between two LAAs is based on RMM and the matching order is restricted clockwise or anticlockwise. Then, the feature corresponding between two IFS＇ s local attractors is determined by searching for the most similar matching of the LAAs. Finally, the parameters of the iterated function are linearly interpolated to finish the morphing procedure of two IFS＇ s fraetal attractors and to perform the fraetal morphing with fractal feature preserved.