二维数字图形计盒分维的改进算法和X射线衍射谱线分维计算

MODIFIED METHOD OF BOX-COUNTING DIMENSION FOR 2-D DIGITAL IMAGE AND THE CALCULATION OF FRACTAL DIMENSION FOR XRD PATTERNS

通过增加图像大小调整模块,根据所选标尺的大小,在二值图的右边和下面补充最少数量的背景色,使得二值图正好能被标尺正方形完全覆盖,改进了二维数字图像计盒分维的计算方法,并利用Matlab实现了分形图形计盒分维的更精确计算。利用改进的程序对8代Koch曲线计盒分维的计算证实了该程序的有效性。XRD谱线具有某种自相似性,利用该程序计算出了合金NdAlSi的XRD谱线的计盒分维值,发现该合金的XRD谱线的分维是1.1484,因而证实了XRD谱线具有分形特征。XRD谱线分维计算方法为进一步研究影响合金XRD谱线的因素与XRD谱线分形的关系提供了研究方法。

We improve the algorithm of box-counting dimension for 2-D digital image which can improve the accuracy of fractal dimension based on Matlab. The algorithm resizes the binary image by adding the module to make sure that the image can be completely covered with box by adding the least background color pixels at the right side and the bottom of image. The algorithm has proved to be worked well on the 8-th generation Koch curve. At the same time, it can be found that X-ray power diffraction pattern has self-similarity. The box-counting dimension of NdAlSi XRD pattern was calculated to be 1.1484 by the improved algorithm and results show that XRD patterns are fractal. The calculation of XRD pattern fractal dimension can be a new method to discover the factors of XRD pattern and the relations of XRD pattern fractal dimension.