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中文摘要：
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．
英文摘要：
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.
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