测量分维的“数盒子”算法研究  

Research on the Box Counting Algorithm in Fractal Dimension Measurement

作　　者：梁东方[1] 李玉梁[1] 江春波[1] 

机构地区：[1]清华大学水利水电工程系,北京100084

出　　处：《中国图象图形学报（A辑）》2002年第3期246-250,共5页Journal of Image and Graphics

基　　金：国家自然科学基金项目 (5 0 0 790 10 )

摘　　要：在分析传统“数盒子”算法测量分形体分维缺陷的基础上 ,首先通过引入一个新的参数 η,提出了一种新的“数盒子”算法 ;然后通过具体算例 ,证实了该算法较传统算法的优越性 ,并且指出了它的局限性 ,同时还对“数盒子”算法测量的不确定性进行了讨论 ,进而提出了可行的提高测量精度的方法 ;最后应用平面激光诱发荧光 (PL IF)技术得到了圆柱尾流区域的浓度场图象 ,并由此提取得到尾流紊动 -非紊动界面 ,接着应用改进的算法对这一分界面的分维进行了测量 .测量结果与前人的结论相吻合 ,并且发现 ,在非恒定流动中 。The weakness of the conventional box counting algorithm in measuring the dimensions of fractals is analyzed. A novel improved box counting method is proposed by introducing a new parameter η , which is the ratio of fractal object's length in a box over the edge length of the box. For fractals having infinite self similar levels, η is also infinite which has no meaning in mathematics. But the fractals existed in the real world all have their scaling limits, so η is meaningful in practical measurement. Its advantage is proved by the examples in the paper, and its limits are also pointed out. The uncertainty in measuring the fractal dimension using box counting method is discussed, and the corresponding means to overcome them are also proposed. Planar laser induced fluorescence technique was employed to measure the concentration field in the near wake region of circular cylinder. Turbulence non turbulence interfaces were extracted from these images, and the new box counting algorithm is used to measure the fractal dimension of these interfaces. The measured results agree with those of other researchers, and it is found that the fractal dimensions vary little with time in an unsteady flow field.

关 键 词：分形体 “数盒子”算法 平面激光诱发荧光 尾流区 绕流特体 图象处理 分形几何 测量 分维 

分 类 号：O189[理学—数学] TP391.41[理学—基础数学]