| 粗糙面分形计算理论研究进展 |
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| 引用本文： | 李业学,高明忠,马亢.粗糙面分形计算理论研究进展[J].数学进展,2012(4):397-408. |
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| 作者姓名： | 李业学 高明忠 马亢 |
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| 作者单位： | 湖北文理学院建筑工程学院;四川大学水利水电学院;新加坡国立大学工学院土木与环境工程系 |
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| 基金项目： | 国家自然科学基金资助项目(No.50974091);湖北省自然科学基金资助项目(No.2011CDC037);湖北省教育厅自然科学基金资助项目(No.Q20122503);襄阳市自然科学基金项目(汽车零部件表面形貌研究) |
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| 摘 要： | 为提出一种工程上适用可靠的粗糙面分形维数计算方法,在分形曲线的维数计算方法(码尺法,盒维法)基础上,先后提出了星积分形曲面的维数计算方法、三角形棱柱表面积法、投影覆盖法、立方体覆盖法、改进的立方体覆盖法、分形的增变量描述法等曲面分形维数理论.鉴于上述方法的共有缺陷——获取三维坐标的激光表面仪器的扫描尺度限制,研究者提出了粗糙面图像维数计算理论,包括二值化图像维数、灰度图像维数、RGB图像维数计算理论.最后,本文展望了分形维数计算理论领域内亟待解决的三大问题.
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| 关 键 词： | 分形 维数 图像维数 立方体覆盖法 投影覆盖法 |
Developments in Calculation Theory of Fractal Dimension of Rough Surface |
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| LI Yexue,GAO Mingzhong,MA Kang.Developments in Calculation Theory of Fractal Dimension of Rough Surface[J].Advances in Mathematics,2012(4):397-408. |
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| Authors: | LI Yexue GAO Mingzhong MA Kang |
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| Institution: | (2,3) (1.School of Civil Engineering and Architecture,Hubei University of Arts and Science,Xiangyang, Hubei,441053,P.R.China;2.College of Water Resources and Hydropower,Sichuan University, Chengdu,Sichuan,610065,P.R.China;3.Department of Civil and Environmental Engineering, Faculty of Engineering,National University of Singapore,117576,Singapore) |
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| Abstract: | In order to present an applicable and reliable calculation method of rough surface,based on calculation methods of fractal dimension of curved line(scale method and box-counting method),fractal dimension theories of rough curved surface,such as calculation method of dimension of star product fractal surface,triangular prism surface area method,projective covering method,cubic covering method,improved cubic covering method and variogram method, were proposed.Due to the common drawback of the above methods,i.e.,the limited scanning scope of a laser profilimeter obtaining three-dimensional coordinate data,investigators presented calculation theories of image dimension of rough surface,including binary image dimension,grayscale image dimension and RGB image dimension.Finally,three unsolved problems of fractal dimension theory are presented. |
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| Keywords: | fractal dimension image dimension cubic covering method projective covering method |
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