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.
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 cov- ering 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, gray- scale image dimension and RCB image dimension. Finally, three unsolved problems of fractal dimension theory are presented.
出处
《数学进展》
CSCD
北大核心
2012年第4期397-408,共12页
Advances in Mathematics（China）
基金
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)
关键词
分形
维数
图像维数
立方体覆盖法
投影覆盖法
fractal
dimension
image dimension
cubic covering method
projective cov- ering method
