基于布朗曲面模型的图像分形维计算方法

Method of calculating image fractal dimension based on fractal Brownian model

针对差分盒维数DBC(differential box counting)算法中空盒子对计算图像分形维数的影响,分析了DBC算法和其一种改进算法最小盒维数计算方法MBC(minimum box counting)剔除所有空盒子的不足,提出了一种新算法——真实差分盒维数算法ADBC(actual differential box-counting),将差分盒方法中存在的空盒子分为真实空盒子和潜在盒子。在计算盒子数量时,引入图像分形布朗曲面模型,通过模拟图像差分盒子覆盖真实事物(极限分辨率的图像)的情况,结合DBC算法和MBC算法寻找空盒子为潜在盒子的期望,用期望的形式最大程度求出基于图像和分形布朗模型的精确盒子数。实验结果表明,该方法使分形维数计算精度得到了明显提高。

Aimed at the influence of empty boxes existing in DBC （differential box-counting）, after analysis the deficient of the DBC and one of its advanced method MBC （minimum box counting）, which abandoned all the empty boxes, a new approach ADBC （actual differential box-counting） is proposed, in which the empty boxes are classified into two categories including real empty boxes and potential ones. Then, the probability of the empty boxes being potential ones when the boxes are covering the real thing （equals the image with infinite resolution） is calculated by bringing fractal Brownian surface model and with DBC and MBC. It derives the greatest extent of the exact number of boxes with the probability in the form of image and fractal Brownian model. The experimental tests indicate that ADBC can effectively improve the accuracy of fractal dimension. Experiments show that this method makes the fractal dimension calculation accuracy improved significantly.