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苏勇,张青川*.数字图像相关的噪声导致系统误差及散斑质量评价标准[J].实验力学,2017,32(5):699~717
数字图像相关的噪声导致系统误差及散斑质量评价标准
Noise-Induced Bias and Evaluation Criterion of Speckle Quality in Digital Image Correlation
投稿时间: 2017-06-16  最后修改时间: 2017-08-07
DOI:10.7520/1001-4888-17-304
中文关键词:  数字图像相关  散斑质量评价  噪声导致系统误差
英文关键词:digital image correlation  speckle pattern assessment  noise-induced bias
基金项目:国家自然科学基金(11332010, 11627803, 11472266)和国家重点基础研究发展计划(2011CB302105)资助
作者单位
苏勇 中国科学技术大学 近代力学系 中科院材料力学行为和设计重点实验室 合肥 230027 
张青川* 中国科学技术大学 近代力学系 中科院材料力学行为和设计重点实验室 合肥 230027 
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中文摘要:
      数字图像相关中散斑质量评价标准应该综合考虑系统误差和随机误差的作用。之前的工作考虑了无图像噪声情况下插值引起的系统误差,本文则进一步研究了有图像噪声情况的系统误差,并与随机误差综合考虑提出了完善的散斑质量评价参数。本文推导了有噪声情况下系统误差的解析形式,揭示了噪声引入系统误差产生的内在本质在于插值引起噪声不确定性对亚像素位置的依赖。依据理论分析,插值噪声耦合函数的概念被引入,它由插值基函数平移平方和的斜率决定,表征了噪声引入系统误差随亚像素位置的变化。插值耦合函数将之前的研究成果纳入统一的理论体系,并从本质上解释了高阶B-样条插值对应的噪声引起系统误差较小的现象。数值模拟与本文的理论分析显示一致,在真实的亚像素平移实验验证中,本文将公式推广到非均匀噪声情况,并与实验结果获得了较好的吻合。基于对系统误差的理论分析,综合考虑系统误差和随机误差影响,提出了两种计算误差评估参数:总误差的最大值和平方平均值,并提出了快速估计算法且通过数值模拟进行了验证。计算误差评估参数实际也是一种散斑质量评价参数,提出的评估参数弥补了现存散斑质量评价参数未足够考虑插值影响的缺陷,是更完善的散斑质量评价标准。本文应用新提出的散斑评价参数对一些常见散斑图进行了评价,并将其用于对模拟散斑图的优化。
英文摘要:
      In digital image correlation (DIC), the evaluation criteria of speckle quality should comprehensively consider the effect of systematical error and effect of random error. Our previous works consider the systematical error caused by interpolation under no image noise condition. In this paper, the systematical error produced by image noise is studied further, and improved speckle quality evaluation parameters are put forward by taking into account the random error. In this paper, an analytical form of systematical error in the presence of noise is derived, and the intrinsic nature of systematical error introduced by noise is revealed, that is the dependence of interpolation-induced noise uncertainty on the sub-pixel location. According to theoretical analysis, the concept of interpolating noise coupling function is introduced. It is determined by the slope of translation square sum of interpolation basis function, which characterizes the variation of niose-induced systematical error along with the sub-pixel position change. The interpolated coupling function incorporates previous study achievement into a unified theoretical system, the phenomenon of noise-induced smaller systimatical error which is corresponding to the higher order B-spline interpolation is also explained. The numerical simulation is consistent with the theoretical analysis in this paper. In real experimental verification of sub-pixel translation, the formula is extended to the case of nonuniform noise, and the results are in good agreement with the experimental results. Based on the theoretical analysis of systematical error, and considering the effect of systematical error and random error, two evaluation parameters of calculation error are proposed, that are the maximum total error and square mean error. A fast estimation algorithm is proposed and validated by numerical simulation. Calculation of error evaluation parameter is actually also a kind of speckle quality evaluation parameter. The proposed evaluation parameters make up the defects, that is in existing speckle quality evaluation parameters, the influence of interpolation is not considered sufficiently. It is a more perfect standard for speckle quality evaluation. In this paper, some common speckle patterns are evaluated by the newly proposed speckle evaluation parameters, and are applied to the optimization of simulated speckle patterns.
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