数字图像相关方法中匹配及过匹配形函数的误差分析

发布时间：2019-06-07 08:52

【摘要】：基于图像子区的数字图像相关方法需采用合适的形函数来近似目标图像子区的真实变形。由于实际测量时目标子区的局部变形往往是未知的,实际采用的不同阶次(零阶、一阶和二阶)的形函数不可避免地产生误匹配(欠匹配和过匹配)问题,从而引入位移测量的系统或随机误差。尽管由欠匹配形函数引起的系统误差已被充分认识,由过匹配形函数引起的位移误差仍缺少理论解释。本文首先推导出采用一阶和二阶形函数的数字图像相关方法的随机误差理论公式,随后采用一系列数值实验验证了理论公式的准确性。结果显示:过匹配形函数不会引入额外的系统误差,但会增加随机误差,且二阶形函数的随机误差是一阶形函数的二倍。考虑到由欠匹配一阶形函数引入的系统误差往往远大于过匹配二阶形函数的随机误差,因此在未能确知变形的情况下,推荐使用二阶形函数。
[Abstract]:The digital image correlation method based on image sub-region needs to use appropriate shape function to approximate the real deformation of target image sub-region. Because the local deformation of the target subregion is often unknown in the actual measurement, the shape functions of different orders (zero order, first order and second order) inevitably lead to the problem of mismatching (undermatching and overmatching). Thus, the system or random error of displacement measurement is introduced. Although the systematic error caused by undermatched shape function has been fully understood, the displacement error caused by overmatched shape function is still lack of theoretical explanation. In this paper, the theoretical formula of random error of digital image correlation method using first-order and second-order shape functions is derived, and then a series of numerical experiments are used to verify the accuracy of the theoretical formula. The results show that the overmatched shape function does not introduce additional systematic error, but increases the random error, and the random error of the second order shape function is twice as much as that of the first order shape function. Considering that the systematic error introduced by the undermatched first-order shape function is often much larger than the random error of the overmatched second-order shape function, it is recommended to use the second-order shape function if the deformation is not known.
【作者单位】：北京航空航天大学固体力学所;
【基金】：国家自然科学基金(11272032,11322220,11427802) 北京市科技新星计划(xx2014B034)资助的课题
【分类号】：O348

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