MATLAB环境下图像分形维数的计算
详细信息 本馆镜像全文    |  推荐本文 | | 获取馆网全文
摘要
利用MATLAB的图像处理和数值计算功能,对大气可吸入颗粒物的场发射电镜(FESEM)图像进行处理,得到颗粒物边界的二值图像;编制MATLAB程序,统计一系列以不同像素数量为边长的正方形块覆盖二值图像时的个数,根据像素数量和正方形块个数之间的关系,确定图像的计盒维数.结果表明:MATLAB对分形图像的处理简单、方便,通过科赫曲线、谢宾斯基填料等有规分形图形分形维数的计算表明该方法计算出的结果准确、可靠.对大气颗粒物的分形维数的计算表明,不同不规则程度的颗粒物有不同的分形维数,可以通过颗粒物分形维数的计算分析颗粒物的来源和输运过程.
The functions of MATLAB in image processing and numerical calculation were employed to process the images of atmosphere sniffable particles obtained by the field emission scanning electron microscope(FESEM).With the MATLAB program,the binary images of the particles border were acquired,the numbers of a series of square blocks whose lengths were different pixelquantitiesto cover the binary image were counted,and the box-counting dimensions of these images werecalculated according to the mathematics relationship of the pixelquantities and the numbers of square blocks.The resultsshowed that the processing of fractal images by MATLAB is simple and convenient,and the calculating results of fractal dimensions tested by some fractal curves such as the Koch curve and the Sierpinski gasket are accurate and believable The particles with different irregularities have different fractal dimensions,and the sources and transportprocesses of particles can be indicated by their fractal dimensions.
引文
[1]MANDELBROT B B.The fractal geometry of nature[M].San Francisco:Freeman,1982.
    [2]彭瑞东,谢和平,鞠杨.二维数字图像分形维数的计算方法[J].中国矿业大学学报,2004,33(1):19-25.PENG Rui-dong,XIE He-ping,JU Yang.Computa-tion method of fractal dimension for 2-D digital image[J],Journal of China University of Mining&Tech-nology,2004,33(1):19-25.
    [3]李女丰刀,朱金兆,朱清科.分形维数计算方法研究进展[J].北京林业大学学报,2002,24(2):71-78.LI Jie,ZHU Jin-zhao,ZHU Qing-ke.Review onmethods of calculating fractal dimension[J].Journalof Beijing Forestry University,2002,24(2):71-78.
    [4]王印培,陈进,孙晓明,等.珠光体球化的分形研究[J].理化检验-物理分册,2003,39(3):129-133.WANG Yin-pei,CHEN Jin,SUN Xiao-ming,et al.Investigation on the fractal dimension of pearlitespheroidization[J].PTCA(Part A:Physical Tes-ting),2003,39(3):129-133.
    [5]FERNANDEZ E,JELINEK H F.Use of fractal the-ory in neuroscience:methods,advantages,and po-tential problems[J].METHODS,2001,24:309-321.
    [6]屈朝霞,张汉谦.材料科学中的分形理论应用进展[J].宇航材料工艺,1999(5):5-9.QU Zhao-xia,ZHANG Han-qian.Progress of appli-cation of fractal theory to material science[J].As-trogation Material and Process,1999(5):5-9.
    [7]杨志远,曲建林,周安宁.超细煤粉颗粒形状分形维数与球磨工艺的研究[J].煤炭学报,2004,29(3):342-345.YANG Zhi-yuan,QU Jian-lin,ZHOU An-ning.Study on the relationships between the profile fractaldimensions of coal ultra fine powders and their grind-ing technologies[J].Journal of China Coal Society,2004,29(3):342-345.
    [8]曾凡桂,王祖讷.煤粉碎过程中颗粒形状的分形特征[J].煤炭转化,1999,22(11):27-30.ZENG Fan-gui,WANG Zu-na.Fractal characteris-tics of particle shape in coal comminiting process[J].Coal Conversion,1999,22(11):27-30.
    [9]张怀亮,邱显焱,卜英勇.基于真彩色的磨粒分形维数计算系统的设计[J].中南工业大学学报,2002,33(3):285-288.ZHANG Huai-liang,QIU Xian-yan,BU Ying-yong.The design of fractal dimension computing system a-bout the wear particle based on real color[J].Jour-nal of Cent-South University of Technology,2002,33(3):285-288.
    [10]武生智,魏春玲,马崇武,等.沙粒粗糙度和粒径分布的分形特性[J].兰州大学学报:自然科学版,1999,35(3):53-56.WU Sheng-zhi,WEI Chun-ling,MA Chong-wu,etal.Fractal analysis of the roughness and grading ofsands[J].Journal of Lanzhou University:NaturalSciences,1999,35(3):53-56.
    [11]KAYE B H.分形漫步[M].徐新阳,康雁,陈旭,等译.沈阳:东北大学出版社,1994:41-66.
    [12]KOREN I,GANOR E,JOSEPH J H.Dynamicthreshold and fractal analysis of desert dust aerosol[J].Journal of Aerosol Science,2000,31(Supp.):224-225.
    [13]COLBECK I,ATKINSON B,JOHAR Y.TheMorphology and optical properties of soot producedby different fuels[J].Journal of Aerosol Science,1997,28(5):715-723.
    [14]EVANS D E,HARRISON R M,AYRES J G.The generation and characterization of elementalcarbon aerosols for human challenge studies[J].Journal of Aerosol Science,2003,34:1023-1041.
    [15]ALLEN M,BROWN G J,MILES N J.Measure-ment of boundary fractal dimensions:review of cur-rent techniques[J].Powder Technology,1995,84:1-14.
    [16]冯志刚,周宏伟.图像的分形维数计算方法及其应用[J].江苏理工大学学报:自然科学版,2001,22(6):92-96.FENG Zhi-gang,ZHOU Hong-wei.Computingmethod of fractal dimension of image and its applica-tion[J].Journal of Jiangsu University of Scienceand Technology:Natural Science,2001,22(6):92-96.
    [17]丁保华,李文超,王福明.分形图像分析与分形维数计算程序的设计[J].北京科技大学学报,1999,21(3):304-307.DING Bao-hua,LI Wen-chao,WANG Fu-ming.A-nalysis of fractal image and design of fractal dimen-sion calculation program[J].Journal of Universityof Science and Technology of Beijing,1999,21(3):304-307.
    [18]黄小葳.分形维数计算程序的设计及其应用[J].北京联合大学学报:自然科学版,2004,18(4):33-37.HUANG Xiao-wei.The design and application offractal dimension calculation program[J].Journal ofBeijing Union University:Natural Sciences,2004,18(4):33-37.
    [19]李海涛,邓樱.MATLAB程序设计教程[M].北京:高等教育出版社,2002.
    [20]陈杨,陈荣娟,郭颖辉.MATLAB 6.X图形编程与图像处理[M].西安:西安电子科技大学出版社,2002.
    [21]陈颙,陈凌.分形几何学[M].北京:地震出版社,1998:67.

版权所有:© 2023 中国地质图书馆 中国地质调查局地学文献中心