数字图像相关技术中插值偏差的理论估计

数字图像相关测量的普及提出了建立散斑质量评价体系要求,即发展针对不同的数字散斑图能够评估测量精度的标准方法.其中,数字图像相关计算中插值误差引起亚像素位移系统偏差(插值偏差)的估计是评价散斑质量的重要参数,然而至今插值偏差与散斑图结构及其插值方法之间的深层机制仍然不明,而且缺乏快速有效的手段估计插值偏差的量级.基于傅里叶方法获得了插值偏差的解析表达式.在满足采样定理的情况下,对其简化得到了插值偏差的带限近似形式和正弦近似形式.插值偏差的正弦近似形式解释了插值偏差随亚像素平移呈正弦形式变化的现象.基于插值偏差的正弦近似公式,提出了决定插值算法用于相关匹配优劣的插值偏差核概念,它表征了插值算法对散斑图特定频率的偏差响应,插值偏差是由插值偏差核与图像功率谱乘积的积分决定的.基于理论分析,提出了一种通过散斑频谱和插值偏差核估计插值偏差的简便有效算法,较之于传统的散斑图平移方法有明显的速度优势.分析了模板大小对估计精度的影响,并通过模拟进行了验证.解释了插值偏差产生的深层机理,解决了长久以来插值偏差难以快速估计的问题.不仅可以用于插值偏差估计,也可以用于插值算法优化,滤波模板选取等问题.对建立散斑质量评价体系,从而制作方便用户的水转印标准散斑也有推动作用. 

THEORETICAL ESTIMATION OF INTERPOLATION BIAS ERROR IN DIGITAL IMAGE CORRELATION

The popularity of digital image correlation technique have pointed out the urgent need to establish standard assessment criterion of speckle pattern quality, namely, the development of standard procedure to assess the metrological performance of various digital speckle patterns.The magnitude of digital image correlation calculation error due to subpixel interpolation(interpolation bias error) is an important parameter to evaluate the quality of speckle.However, there is no available method to estimate interpolation bias efficiently at present.In this paper, frequency method is employed to obtain the analytical expression of interpolation bias error.Band-limited and sinusoidal approximation forms are attained when sampling theorem is satisfied.The sinusoidal variation of interpretation bias error with respect to sub-pixel shift is explained.Based on sinusoidal approximation form of interpolation bias, this work introduces the concept of interpolation bias kernel.Interpolation bias kernel, which characterizes frequency bias response of specific speckle frequency, is exploited to decide the merits of the interpolation algorithm for correlation matching algorithm.Based on these theoretical results, this paper presents a method to estimate the interpolation bias error by speckle spectrum and interpolation bias kernel.This simple and effective algorithm has obvious speed advantage compared to traditional translation methods, and the simulation is conducted to verify this method.This work explains the inherent nature of interpolation bias and solves the problem of efficient interpolation bias estimation.This work could be used in interpolation optimization and filter size selection and contribute to the establishment of speckle quality assessment criterion as well.