一种改进的图像盒子维计算方法

An improved box-counting method for calculating image fractal dimension

分形维是图像的一种有用的特征,在许多领域中用于图像纹理分析、分割以及分类.盒子维方法由于其实现简单,成为估计图像分形维最常用的一种方法,但是该方法存在计数精度不高、稳定性较差等问题,为此提出了一种新的盒子维估计算法.首先对数字图像的离散灰度曲面进行适当插点补充,使插点后的曲面相对更接近连续的情况,使得在最小尺度下也能实现对不同图像的区分.然后直接采用最小尺度下的盒子数估计分形维,不进行拟合.该算法简单、直观、易于实现.实验结果表明,该方法具有更好的估计精度和稳定性.对于一些特殊测试图像,如尖峰脉冲图像,仍能得到合理的估计值.另外,由于本方法不需要计算多个尺度下的盒子数,因此计算量也相对较小.

A fractal dimension is a useful feature parameter for texture analysis,segmentation and classification in many fields.The differential box-counting method is frequently used to estimate image fractal dimension because of its simplicity.However this method is flawed with lack of accuracy and stability.A new box-counting method is presented.First,more nodes are into the discrete intensity surface of a digital image to make it relatively more approximate to a continuous surface.This step makes it possible to distinguish different images at the smallest scale.Then,the fractal dimension of the digital image is estimated directly according to the box number at the smallest scale without the fitting step.Experimental results show that this method is more accurate and stable compared with some typical methods.For some special test images,such as pulse images,the proposed method outperormed unreasonable estimates.In addition,because there is no need to calculate the box numbers at other scales,the computational complexity of our method is lower.