Interpolation bias for the inverse compositional Gauss–Newton algorithm in digital image correlation. (January 2018)

• Record Type: Journal Article
• Authors: Su, Yong; Zhang, Qingchuan; Xu, Xiaohai; Gao, Zeren; Wu, Shangquan
• Is Part Of: Optics and lasers in engineering. Volume 100(2018)
• Page Start: 267
• Page End: 278
• Publication Date: 2018-01
• Subjects: Digital image correlation -- Interpolation bias -- Inverse compositional Gauss–Newton algorithm -- Fourier analysis -- Gradient estimator; 00-01 -- 99-00; Lasers in engineering -- Periodicals; Optical measurements -- Periodicals; Optics -- Periodicals; Lasers en ingénierie -- Périodiques; Mesures optiques -- Périodiques; Optique -- Périodiques; 621.36605
• DOI: 10.1016/j.optlaseng.2017.09.013
• Languages: English
• ISSNs: 0143-8166

Abstract

Highlights: The interpolation biases of FA-NR algorithm and IC-GN algorithm can be significantly different. The reference image gradient estimation can strongly influence the interpolation bias. The formulas of interpolation bias for the IC-GN algorithms are derived. The role of gradient estimation is thoroughly studies. Source codes are uploaded. Abstract: It is believed that the classic forward additive Newton–Raphson (FA-NR) algorithm and the recently introduced inverse compositional Gauss–Newton (IC-GN) algorithm give rise to roughly equal interpolation bias. Questioning the correctness of this statement, this paper presents a thorough analysis of interpolation bias for the IC-GN algorithm. A theoretical model is built to analytically characterize the dependence of interpolation bias upon speckle image, target image interpolation, and reference image gradient estimation. The interpolation biases of the FA-NR algorithm and the IC-GN algorithm can be significantly different, whose relative difference can exceed 80%. For the IC-GN algorithm, the gradient estimator can strongly affect the interpolation bias; the relative difference can reach 178%. Since the mean bias errors are insensitive to image noise, the theoretical model proposed remains valid in the presence of noise. To provide more implementation details, source codes are uploaded as a supplement.