一种用于MEMS动态测量的最优盒计数分形维数算法

在微机电系统（micro electromechanical system，MEMS）的动态测量中，利用分形插值法可以提高MEMS器件面内位移测量的精度，利用图像边缘的分形特征，还可以实现离面位移和旋转角度的测试。而分形维数（fractal dimension）的计算又是这些方法的关键。在研究目前最常用的分形维数计算方法差分盒计数法（difference box counting, DBC）的基础上，提出了一种对“空盒子”不予计数的最优盒计数分形维数算法，克服了差分盒计数法存在“空盒子”被计数的缺陷。理论分析和实验结果表明，该算法获得的分形维数更接近于理论维数。

A novel optimal box counting fractal dimension algorithm

In MEMS dynamic measurement, fractal interpolation method can improve the accuracy of measurement for MEMS devices in plane displacement. Also by using the fractal characteristics of the image edge, the surface displacement and the rotating angle can be measured. So, calculating the fractal dimension accurately is very important in these methods. In this paper, the difference box counting method which is the most favorite fractal dimension estimation method is researched and a novel optimal box counting fractal dimension algorithm is presented to overcome the problem of difference box counting to reduce the effect of the empty boxes. Both theoretical analysis and experimental results show that the fractal dimension obtained by this algorithm is closer to the theoretical dimension.