一种新的网格重叠差分盒分形模型

New Fractal Model of Grid Overlapping Differential Box-counting

分形维数一个最重要的特性是其维数大小与人眼感觉图像表面的粗糙程度有很大的相关性,分形在图像的纹理分析、图像的分割与分类等方面有着很多成功的运用。在基于分形理论提出的分形维数的估计方法中,差分盒法是一种经常被使用的分形维数估计技术。研究发现差分盒法对细致纹理的最小二乘法线性拟合度比较好,但是对较为粗糙的纹理其最小二乘法的线性拟合度不够理想,估计出的分形维数往往失真。为了解决这个问题,提出了一种网格重叠差分盒模型,用以计算差分盒的盒子数的网格在一定程度上重叠,计算整个图像统计自相似意义上的盒子数,其最小二乘法的线性拟合度比较好。为了进一步提高差分盒的盒子计数精度,提出了非整数盒子计数法,修正了缩放尺度,试验证明其能更真实地反映纹理的分形维数。

One of the most important feature of the fractal dimension is that its fractal dimension is largely correlated with the surface roughness of image feeled by the human eye.The fractal has many successful applications in analysis,segmentation and classification of images,the differential box-account method is often used in the fractal dimension estimation based on fractal theory.Least-squares is better for detailed textures,but is not satisfactory for more coarse textures,in order to solve this problem,overlapping grid differential box-account model was presented,the grids which the numbers of the boxes are calculated by are overlapped,the numbers of boxes of the whole image are calculated on the statistical self-similarity.Linear fit of least-square of this model is better,in order to improve the precision of box-coun-ting,non-integer box-counting and zoom-scale-fixing were presented,the fractal dimension of the image texture got by the model was validated,compared with differential box-account.