Geometry constrained correlation adjustment for stereo reconstruction in 3D optical deformation measurements

Zhilong Su; Zhilong Su; Lei Lu; Fujun Yang; Xiaoyuan He; Xiaoyuan He; Dongsheng Zhang; Dongsheng Zhang; Dongsheng Zhang

doi:10.1364/OE.392248

Optics Express
Vol. 28,
Issue 8,
pp. 12219-12232
(2020)
•https://doi.org/10.1364/OE.392248

Geometry constrained correlation adjustment for stereo reconstruction in 3D optical deformation measurements

Zhilong Su, Lei Lu, Fujun Yang, Xiaoyuan He, and Dongsheng Zhang

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Zhilong Su, Lei Lu, Fujun Yang, Xiaoyuan He, and Dongsheng Zhang, "Geometry constrained correlation adjustment for stereo reconstruction in 3D optical deformation measurements," Opt. Express 28, 12219-12232 (2020)

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Abstract

Recovering the geometric shape of deformable objects from images is essential to optical three-dimensional (3D) deformation measurements and is also actively pursued by researchers. Most of the existing techniques retrieve the shape data with triangulation based on pre-estimated stereo correspondences. In this paper, we instead propose to recover depth information directly from images of a binocular vision system for 3D deformation estimation. Given a calibrated geometry of the system, the reprojection error is parameterized by the depth and then described with local intensity dissimilarity between a stereo pair in considering spatial deformation. Afterward, a correlation adjustment model is formulated to estimate the depth parameter by minimizing the error. As a solving strategy, we show the Gauss-Newton linearization of the proposed model and its initialization. 3D displacement estimation based on depth information is also presented. Experiments, including rigid translation and bending deformation measurements, are conducted to verify the performance of the proposed method. Results show that the proposed method is accurate yet precise in 3D deformation estimations. Other underlying developments are underway.

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References

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Year
Author
Publication

S. Baker and I. Matthews, “Lucas-kanade 20 years on: A unifying framework,” Int. J. Comput. Vis. 56(3), 221–255 (2004).
[Crossref]
Y. Su, Q. Zhang, Z. Gao, and X. Xu, “Noise-induced bias for convolution-based interpolation in digital image correlation,” Opt. Express 24(2), 1175–1195 (2016).
[Crossref]
G. Bomarito, J. Hochhalter, T. Ruggles, and A. Cannon, “Increasing accuracy and precision of digital image correlation through pattern optimization,” Opt. Lasers Eng. 91, 73–85 (2017).
[Crossref]
Z. Chen, X. Shao, X. Xu, and X. He, “Optimized digital speckle patterns for digital image correlation by consideration of both accuracy and efficiency,” Appl. Opt. 57(4), 884–893 (2018).
[Crossref]
B. Pan, K. Li, and W. Tong, “Fast, robust and accurate digital image correlation calculation without redundant computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]
Y. Gao, T. Cheng, Y. Su, X. Xu, Y. Zhang, and Q. Zhang, “High-efficiency and high-accuracy digital image correlation for three-dimensional measurement,” Opt. Lasers Eng. 65, 73–80 (2015).
[Crossref]
X. Shao, X. Dai, and X. He, “Noise robustness and parallel computation of the inverse compositional gauss–newton algorithm in digital image correlation,” Opt. Lasers Eng. 71, 9–19 (2015).
[Crossref]
J.-J. Orteu, “3-d computer vision in experimental mechanics,” Opt. Lasers Eng. 47(3-4), 282–291 (2009).
[Crossref]
M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, “Strain field measurements on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res. 86A(2), 569 (2008).
[Crossref]
Z. Chen, X. Shao, X. He, J. Wu, X. Xu, and J. Zhang, “Noninvasive, three-dimensional full-field body sensor for surface deformation monitoring of human body in vivo,” J. Biomed. Opt. 22(9), 1–10 (2017).
[Crossref]
Z. Hu, T. Xu, H. Luo, R. Z. Gan, and H. Lu, “Measurement of thickness and profile of a transparent material using fluorescent stereo microscopy,” Opt. Express 24(26), 29822–29829 (2016).
[Crossref]
M. Malesa, K. Malowany, U. Tomczak, B. Siwek, M. Kujawinska, and A. Sieminska-Lewandowska, “Application of 3d digital image correlation in maintenance and process control in industry,” Comput. Ind. 64(9), 1301–1315 (2013).
[Crossref]
J.-E. Dufour, B. Beaubier, F. Hild, and S. Roux, “Cad-based displacement measurements with stereo-dic,” Exp. Mech. 55(9), 1657–1668 (2015).
[Crossref]
X. Tan, Y. Kang, and E. A. Patterson, “Experimental investigation on surface deformation of soft half plane indented by rigid wedge,” Appl. Math. Mech. 37(10), 1349–1360 (2016).
[Crossref]
P. R. Gradl, “Digital image correlation techniques applied to large scale rocket engine testing,” in 52nd AIAA/SAE/ASEE Joint Propulsion Conference, (AIAA, 2016), p. 4977.
L. Ngeljaratan and M. A. Moustafa, “System identification of large-scale bridges using target-tracking digital image correlation,” Front. Built Environ. 5, 85 (2019).
[Crossref]
F. Chen, X. Chen, X. Xie, X. Feng, and L. Yang, “Full-field 3d measurement using multi-camera digital image correlation system,” Opt. Lasers Eng. 51(9), 1044–1052 (2013).
[Crossref]
D. Solav, K. M. Moerman, A. M. Jaeger, K. Genovese, and H. M. Herr, “Multidic: An open-source toolbox for multi-view 3d digital image correlation,” IEEE Access 6, 30520–30535 (2018).
[Crossref]
M. E. Mohammed, X. Shao, and X. He, “Portable device for the local three-dimensional deformation measurement using a single camera,” Sci. China Technol. Sci. 61(1), 51–60 (2018).
[Crossref]
T. Yuan, X. Dai, X. Shao, Z. Zu, X. Cheng, F. Yang, and X. He, “Dual-biprism-based digital image correlation for defect detection of pipelines,” Opt. Eng. 58(1), 1–13 (2019).
[Crossref]
B. Chen and B. Pan, “Calibration-free single camera stereo-digital image correlation for small-scale underwater deformation measurement,” Opt. Express 27(8), 10509–10523 (2019).
[Crossref]
Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22(11), 1330–1334 (2000).
[Crossref]
M. A. Sutton, J.-J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts,Theory and Applications (Springer, 2009), 1st ed.
X. Shao, M. M. Eisa, Z. Chen, S. Dong, and X. He, “Self-calibration single-lens 3d video extensometer for high-accuracy and real-time strain measurement,” Opt. Express 24(26), 30124–30138 (2016).
[Crossref]
Z. Su, L. Lu, S. Dong, F. Yang, and X. He, “Auto-calibration and real-time external parameter correction for stereo digital image correlation,” Opt. Lasers Eng. 121, 46–53 (2019).
[Crossref]
W. Tong, “Formulation of lucas-kanade digital image correlation algorithms for non-contact deformation measurements: A review,” Strain 49(4), 313–334 (2013).
[Crossref]
P. Reu, “A study of the influence of calibration uncertainty on the global uncertainty for digital image correlation using a monte carlo approach,” Exp. Mech. 53(9), 1661–1680 (2013).
[Crossref]
R. Balcaen, P. L. Reu, P. Lava, and D. Debruyne, “Stereo-dic uncertainty quantification based on simulated images,” Exp. Mech. 57(6), 939–951 (2017).
[Crossref]
Y.-Q. Wang, M. A. Sutton, X.-D. Ke, H. W. Schreier, P. L. Reu, and T. J. Miller, “On error assessment in stereo-based deformation measurements,” Exp. Mech. 51(4), 405–422 (2011).
[Crossref]
C. Zhu, S. Yu, C. Liu, P. Jiang, X. Shao, and X. He, “Error estimation of 3d reconstruction in 3d digital image correlation,” Meas. Sci. Technol. 30(2), 025204 (2019).
[Crossref]
L. Yu and G. Lubineau, “Modeling of systematic errors in stereo-digital image correlation due to camera self-heating,” Sci. Rep. 9(1), 6567 (2019).
[Crossref]
Z. Su, L. Lu, X. He, F. Yang, and D. Zhang, “Recursive-iterative digital image correlation based on salient features,” Opt. Eng. 59(3), 1–13 (2020).
[Crossref]
R. I. Hartley and P. Sturm, “Triangulation,” Comput. Vis. Image Underst. 68(2), 146–157 (1997).
[Crossref]
B. Pan, H. Xie, Z. Guo, and T. Hua, “Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation,” Opt. Eng. 46(3), 033601 (2007).
[Crossref]

2020 (1)

Z. Su, L. Lu, X. He, F. Yang, and D. Zhang, “Recursive-iterative digital image correlation based on salient features,” Opt. Eng. 59(3), 1–13 (2020).
[Crossref]

2019 (6)

C. Zhu, S. Yu, C. Liu, P. Jiang, X. Shao, and X. He, “Error estimation of 3d reconstruction in 3d digital image correlation,” Meas. Sci. Technol. 30(2), 025204 (2019).
[Crossref]

L. Yu and G. Lubineau, “Modeling of systematic errors in stereo-digital image correlation due to camera self-heating,” Sci. Rep. 9(1), 6567 (2019).
[Crossref]

T. Yuan, X. Dai, X. Shao, Z. Zu, X. Cheng, F. Yang, and X. He, “Dual-biprism-based digital image correlation for defect detection of pipelines,” Opt. Eng. 58(1), 1–13 (2019).
[Crossref]

B. Chen and B. Pan, “Calibration-free single camera stereo-digital image correlation for small-scale underwater deformation measurement,” Opt. Express 27(8), 10509–10523 (2019).
[Crossref]

Z. Su, L. Lu, S. Dong, F. Yang, and X. He, “Auto-calibration and real-time external parameter correction for stereo digital image correlation,” Opt. Lasers Eng. 121, 46–53 (2019).
[Crossref]

L. Ngeljaratan and M. A. Moustafa, “System identification of large-scale bridges using target-tracking digital image correlation,” Front. Built Environ. 5, 85 (2019).
[Crossref]

2018 (3)

D. Solav, K. M. Moerman, A. M. Jaeger, K. Genovese, and H. M. Herr, “Multidic: An open-source toolbox for multi-view 3d digital image correlation,” IEEE Access 6, 30520–30535 (2018).
[Crossref]

M. E. Mohammed, X. Shao, and X. He, “Portable device for the local three-dimensional deformation measurement using a single camera,” Sci. China Technol. Sci. 61(1), 51–60 (2018).
[Crossref]

Z. Chen, X. Shao, X. Xu, and X. He, “Optimized digital speckle patterns for digital image correlation by consideration of both accuracy and efficiency,” Appl. Opt. 57(4), 884–893 (2018).
[Crossref]

2017 (3)

Z. Chen, X. Shao, X. He, J. Wu, X. Xu, and J. Zhang, “Noninvasive, three-dimensional full-field body sensor for surface deformation monitoring of human body in vivo,” J. Biomed. Opt. 22(9), 1–10 (2017).
[Crossref]

G. Bomarito, J. Hochhalter, T. Ruggles, and A. Cannon, “Increasing accuracy and precision of digital image correlation through pattern optimization,” Opt. Lasers Eng. 91, 73–85 (2017).
[Crossref]

R. Balcaen, P. L. Reu, P. Lava, and D. Debruyne, “Stereo-dic uncertainty quantification based on simulated images,” Exp. Mech. 57(6), 939–951 (2017).
[Crossref]

2016 (4)

X. Tan, Y. Kang, and E. A. Patterson, “Experimental investigation on surface deformation of soft half plane indented by rigid wedge,” Appl. Math. Mech. 37(10), 1349–1360 (2016).
[Crossref]

X. Shao, M. M. Eisa, Z. Chen, S. Dong, and X. He, “Self-calibration single-lens 3d video extensometer for high-accuracy and real-time strain measurement,” Opt. Express 24(26), 30124–30138 (2016).
[Crossref]

Z. Hu, T. Xu, H. Luo, R. Z. Gan, and H. Lu, “Measurement of thickness and profile of a transparent material using fluorescent stereo microscopy,” Opt. Express 24(26), 29822–29829 (2016).
[Crossref]

Y. Su, Q. Zhang, Z. Gao, and X. Xu, “Noise-induced bias for convolution-based interpolation in digital image correlation,” Opt. Express 24(2), 1175–1195 (2016).
[Crossref]

2015 (3)

Y. Gao, T. Cheng, Y. Su, X. Xu, Y. Zhang, and Q. Zhang, “High-efficiency and high-accuracy digital image correlation for three-dimensional measurement,” Opt. Lasers Eng. 65, 73–80 (2015).
[Crossref]

X. Shao, X. Dai, and X. He, “Noise robustness and parallel computation of the inverse compositional gauss–newton algorithm in digital image correlation,” Opt. Lasers Eng. 71, 9–19 (2015).
[Crossref]

J.-E. Dufour, B. Beaubier, F. Hild, and S. Roux, “Cad-based displacement measurements with stereo-dic,” Exp. Mech. 55(9), 1657–1668 (2015).
[Crossref]

2013 (5)

M. Malesa, K. Malowany, U. Tomczak, B. Siwek, M. Kujawinska, and A. Sieminska-Lewandowska, “Application of 3d digital image correlation in maintenance and process control in industry,” Comput. Ind. 64(9), 1301–1315 (2013).
[Crossref]

F. Chen, X. Chen, X. Xie, X. Feng, and L. Yang, “Full-field 3d measurement using multi-camera digital image correlation system,” Opt. Lasers Eng. 51(9), 1044–1052 (2013).
[Crossref]

B. Pan, K. Li, and W. Tong, “Fast, robust and accurate digital image correlation calculation without redundant computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]

W. Tong, “Formulation of lucas-kanade digital image correlation algorithms for non-contact deformation measurements: A review,” Strain 49(4), 313–334 (2013).
[Crossref]

P. Reu, “A study of the influence of calibration uncertainty on the global uncertainty for digital image correlation using a monte carlo approach,” Exp. Mech. 53(9), 1661–1680 (2013).
[Crossref]

2011 (1)

Y.-Q. Wang, M. A. Sutton, X.-D. Ke, H. W. Schreier, P. L. Reu, and T. J. Miller, “On error assessment in stereo-based deformation measurements,” Exp. Mech. 51(4), 405–422 (2011).
[Crossref]

2009 (1)

J.-J. Orteu, “3-d computer vision in experimental mechanics,” Opt. Lasers Eng. 47(3-4), 282–291 (2009).
[Crossref]

2008 (1)

M. Sutton, X. Ke, S. Lessner, M. Goldbach, M. Yost, F. Zhao, and H. Schreier, “Strain field measurements on mouse carotid arteries using microscopic three-dimensional digital image correlation,” J. Biomed. Mater. Res. 86A(2), 569 (2008).
[Crossref]

2007 (1)

B. Pan, H. Xie, Z. Guo, and T. Hua, “Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation,” Opt. Eng. 46(3), 033601 (2007).
[Crossref]

2004 (1)

S. Baker and I. Matthews, “Lucas-kanade 20 years on: A unifying framework,” Int. J. Comput. Vis. 56(3), 221–255 (2004).
[Crossref]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22(11), 1330–1334 (2000).
[Crossref]

1997 (1)

R. I. Hartley and P. Sturm, “Triangulation,” Comput. Vis. Image Underst. 68(2), 146–157 (1997).
[Crossref]

Baker, S.

S. Baker and I. Matthews, “Lucas-kanade 20 years on: A unifying framework,” Int. J. Comput. Vis. 56(3), 221–255 (2004).
[Crossref]

Balcaen, R.

R. Balcaen, P. L. Reu, P. Lava, and D. Debruyne, “Stereo-dic uncertainty quantification based on simulated images,” Exp. Mech. 57(6), 939–951 (2017).
[Crossref]

Beaubier, B.

J.-E. Dufour, B. Beaubier, F. Hild, and S. Roux, “Cad-based displacement measurements with stereo-dic,” Exp. Mech. 55(9), 1657–1668 (2015).
[Crossref]

Bomarito, G.

Cannon, A.

Chen, B.

B. Chen and B. Pan, “Calibration-free single camera stereo-digital image correlation for small-scale underwater deformation measurement,” Opt. Express 27(8), 10509–10523 (2019).
[Crossref]

Chen, F.

F. Chen, X. Chen, X. Xie, X. Feng, and L. Yang, “Full-field 3d measurement using multi-camera digital image correlation system,” Opt. Lasers Eng. 51(9), 1044–1052 (2013).
[Crossref]

Chen, X.

F. Chen, X. Chen, X. Xie, X. Feng, and L. Yang, “Full-field 3d measurement using multi-camera digital image correlation system,” Opt. Lasers Eng. 51(9), 1044–1052 (2013).
[Crossref]

Chen, Z.

Cheng, T.

Cheng, X.

T. Yuan, X. Dai, X. Shao, Z. Zu, X. Cheng, F. Yang, and X. He, “Dual-biprism-based digital image correlation for defect detection of pipelines,” Opt. Eng. 58(1), 1–13 (2019).
[Crossref]

Dai, X.

T. Yuan, X. Dai, X. Shao, Z. Zu, X. Cheng, F. Yang, and X. He, “Dual-biprism-based digital image correlation for defect detection of pipelines,” Opt. Eng. 58(1), 1–13 (2019).
[Crossref]

Debruyne, D.

R. Balcaen, P. L. Reu, P. Lava, and D. Debruyne, “Stereo-dic uncertainty quantification based on simulated images,” Exp. Mech. 57(6), 939–951 (2017).
[Crossref]

Dong, S.

Z. Su, L. Lu, S. Dong, F. Yang, and X. He, “Auto-calibration and real-time external parameter correction for stereo digital image correlation,” Opt. Lasers Eng. 121, 46–53 (2019).
[Crossref]

Dufour, J.-E.

J.-E. Dufour, B. Beaubier, F. Hild, and S. Roux, “Cad-based displacement measurements with stereo-dic,” Exp. Mech. 55(9), 1657–1668 (2015).
[Crossref]

Eisa, M. M.

Feng, X.

F. Chen, X. Chen, X. Xie, X. Feng, and L. Yang, “Full-field 3d measurement using multi-camera digital image correlation system,” Opt. Lasers Eng. 51(9), 1044–1052 (2013).
[Crossref]

Gan, R. Z.

Gao, Y.

Gao, Z.

Y. Su, Q. Zhang, Z. Gao, and X. Xu, “Noise-induced bias for convolution-based interpolation in digital image correlation,” Opt. Express 24(2), 1175–1195 (2016).
[Crossref]

Genovese, K.

D. Solav, K. M. Moerman, A. M. Jaeger, K. Genovese, and H. M. Herr, “Multidic: An open-source toolbox for multi-view 3d digital image correlation,” IEEE Access 6, 30520–30535 (2018).
[Crossref]

Goldbach, M.

Gradl, P. R.

P. R. Gradl, “Digital image correlation techniques applied to large scale rocket engine testing,” in 52nd AIAA/SAE/ASEE Joint Propulsion Conference, (AIAA, 2016), p. 4977.

Guo, Z.

Hartley, R. I.

R. I. Hartley and P. Sturm, “Triangulation,” Comput. Vis. Image Underst. 68(2), 146–157 (1997).
[Crossref]

He, X.

Z. Su, L. Lu, X. He, F. Yang, and D. Zhang, “Recursive-iterative digital image correlation based on salient features,” Opt. Eng. 59(3), 1–13 (2020).
[Crossref]

C. Zhu, S. Yu, C. Liu, P. Jiang, X. Shao, and X. He, “Error estimation of 3d reconstruction in 3d digital image correlation,” Meas. Sci. Technol. 30(2), 025204 (2019).
[Crossref]

T. Yuan, X. Dai, X. Shao, Z. Zu, X. Cheng, F. Yang, and X. He, “Dual-biprism-based digital image correlation for defect detection of pipelines,” Opt. Eng. 58(1), 1–13 (2019).
[Crossref]

Z. Su, L. Lu, S. Dong, F. Yang, and X. He, “Auto-calibration and real-time external parameter correction for stereo digital image correlation,” Opt. Lasers Eng. 121, 46–53 (2019).
[Crossref]

M. E. Mohammed, X. Shao, and X. He, “Portable device for the local three-dimensional deformation measurement using a single camera,” Sci. China Technol. Sci. 61(1), 51–60 (2018).
[Crossref]

Herr, H. M.

D. Solav, K. M. Moerman, A. M. Jaeger, K. Genovese, and H. M. Herr, “Multidic: An open-source toolbox for multi-view 3d digital image correlation,” IEEE Access 6, 30520–30535 (2018).
[Crossref]

Hild, F.

J.-E. Dufour, B. Beaubier, F. Hild, and S. Roux, “Cad-based displacement measurements with stereo-dic,” Exp. Mech. 55(9), 1657–1668 (2015).
[Crossref]

Hochhalter, J.

Hu, Z.

Hua, T.

Jaeger, A. M.

D. Solav, K. M. Moerman, A. M. Jaeger, K. Genovese, and H. M. Herr, “Multidic: An open-source toolbox for multi-view 3d digital image correlation,” IEEE Access 6, 30520–30535 (2018).
[Crossref]

Jiang, P.

C. Zhu, S. Yu, C. Liu, P. Jiang, X. Shao, and X. He, “Error estimation of 3d reconstruction in 3d digital image correlation,” Meas. Sci. Technol. 30(2), 025204 (2019).
[Crossref]

Kang, Y.

X. Tan, Y. Kang, and E. A. Patterson, “Experimental investigation on surface deformation of soft half plane indented by rigid wedge,” Appl. Math. Mech. 37(10), 1349–1360 (2016).
[Crossref]

Ke, X.

Ke, X.-D.

Y.-Q. Wang, M. A. Sutton, X.-D. Ke, H. W. Schreier, P. L. Reu, and T. J. Miller, “On error assessment in stereo-based deformation measurements,” Exp. Mech. 51(4), 405–422 (2011).
[Crossref]

Kujawinska, M.

Lava, P.

R. Balcaen, P. L. Reu, P. Lava, and D. Debruyne, “Stereo-dic uncertainty quantification based on simulated images,” Exp. Mech. 57(6), 939–951 (2017).
[Crossref]

Lessner, S.

Li, K.

B. Pan, K. Li, and W. Tong, “Fast, robust and accurate digital image correlation calculation without redundant computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]

Liu, C.

C. Zhu, S. Yu, C. Liu, P. Jiang, X. Shao, and X. He, “Error estimation of 3d reconstruction in 3d digital image correlation,” Meas. Sci. Technol. 30(2), 025204 (2019).
[Crossref]

Lu, H.

Lu, L.

Z. Su, L. Lu, X. He, F. Yang, and D. Zhang, “Recursive-iterative digital image correlation based on salient features,” Opt. Eng. 59(3), 1–13 (2020).
[Crossref]

Z. Su, L. Lu, S. Dong, F. Yang, and X. He, “Auto-calibration and real-time external parameter correction for stereo digital image correlation,” Opt. Lasers Eng. 121, 46–53 (2019).
[Crossref]

Lubineau, G.

L. Yu and G. Lubineau, “Modeling of systematic errors in stereo-digital image correlation due to camera self-heating,” Sci. Rep. 9(1), 6567 (2019).
[Crossref]

Luo, H.

Malesa, M.

Malowany, K.

Matthews, I.

S. Baker and I. Matthews, “Lucas-kanade 20 years on: A unifying framework,” Int. J. Comput. Vis. 56(3), 221–255 (2004).
[Crossref]

Miller, T. J.

Y.-Q. Wang, M. A. Sutton, X.-D. Ke, H. W. Schreier, P. L. Reu, and T. J. Miller, “On error assessment in stereo-based deformation measurements,” Exp. Mech. 51(4), 405–422 (2011).
[Crossref]

Moerman, K. M.

D. Solav, K. M. Moerman, A. M. Jaeger, K. Genovese, and H. M. Herr, “Multidic: An open-source toolbox for multi-view 3d digital image correlation,” IEEE Access 6, 30520–30535 (2018).
[Crossref]

Mohammed, M. E.

M. E. Mohammed, X. Shao, and X. He, “Portable device for the local three-dimensional deformation measurement using a single camera,” Sci. China Technol. Sci. 61(1), 51–60 (2018).
[Crossref]

Moustafa, M. A.

L. Ngeljaratan and M. A. Moustafa, “System identification of large-scale bridges using target-tracking digital image correlation,” Front. Built Environ. 5, 85 (2019).
[Crossref]

Ngeljaratan, L.

L. Ngeljaratan and M. A. Moustafa, “System identification of large-scale bridges using target-tracking digital image correlation,” Front. Built Environ. 5, 85 (2019).
[Crossref]

Orteu, J.-J.

J.-J. Orteu, “3-d computer vision in experimental mechanics,” Opt. Lasers Eng. 47(3-4), 282–291 (2009).
[Crossref]

M. A. Sutton, J.-J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts,Theory and Applications (Springer, 2009), 1st ed.

Pan, B.

B. Chen and B. Pan, “Calibration-free single camera stereo-digital image correlation for small-scale underwater deformation measurement,” Opt. Express 27(8), 10509–10523 (2019).
[Crossref]

B. Pan, K. Li, and W. Tong, “Fast, robust and accurate digital image correlation calculation without redundant computations,” Exp. Mech. 53(7), 1277–1289 (2013).
[Crossref]

Patterson, E. A.

X. Tan, Y. Kang, and E. A. Patterson, “Experimental investigation on surface deformation of soft half plane indented by rigid wedge,” Appl. Math. Mech. 37(10), 1349–1360 (2016).
[Crossref]

Reu, P.

P. Reu, “A study of the influence of calibration uncertainty on the global uncertainty for digital image correlation using a monte carlo approach,” Exp. Mech. 53(9), 1661–1680 (2013).
[Crossref]

Reu, P. L.

R. Balcaen, P. L. Reu, P. Lava, and D. Debruyne, “Stereo-dic uncertainty quantification based on simulated images,” Exp. Mech. 57(6), 939–951 (2017).
[Crossref]

Y.-Q. Wang, M. A. Sutton, X.-D. Ke, H. W. Schreier, P. L. Reu, and T. J. Miller, “On error assessment in stereo-based deformation measurements,” Exp. Mech. 51(4), 405–422 (2011).
[Crossref]

Roux, S.

J.-E. Dufour, B. Beaubier, F. Hild, and S. Roux, “Cad-based displacement measurements with stereo-dic,” Exp. Mech. 55(9), 1657–1668 (2015).
[Crossref]

Ruggles, T.

Schreier, H.

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T. Yuan, X. Dai, X. Shao, Z. Zu, X. Cheng, F. Yang, and X. He, “Dual-biprism-based digital image correlation for defect detection of pipelines,” Opt. Eng. 58(1), 1–13 (2019).
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B. Chen and B. Pan, “Calibration-free single camera stereo-digital image correlation for small-scale underwater deformation measurement,” Opt. Express 27(8), 10509–10523 (2019).
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Fig. 1. The geometry and schematic illustration of the GC-CA framework, where the object coordinate frame X-Y-Z is aligned and attached to the reference frame

$\mathbf {C}$

. Because of epipolar geometry constraint, the projection

$\mathbf {x}{'}(d)\in \mathbb {R}^2$

of object point

$\mathbf {X}(d)\in \mathbb {R}^3$

produced by adjusting the depth

$d$

should move along a straight line; meanwhile, the deformation parameter vector

$\mathbf {p}$

is also updated to warp the subset

$\Omega (\mathbf {x}')$

surrounds

$\mathbf {x}{'}(d)$

to match against the one

$\Omega (\mathbf {x})$

centered at

$\mathbf {x}$

Download Full Size | PPT Slide | PDF

Fig. 2. 3D displacement estimation pipeline with the proposed GC-CA algorithm. There are two feasible initialization flows for depth computing presented: sequential and parallel initialization. The former allowed for cases with large out-of-plane deformation because the initial guess comes from the previous deformation state, while the latter is suitable for small out-of-plane deformation since the depth estimation after deformation uses the depth information evaluated at begin.

Download Full Size | PPT Slide | PDF

Fig. 3. (a) Experimental setup for rigid body translation and (b) a pair of recorded speckle images with a defined ROI.

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Fig. 4. (a) 3D shape of the planar specimen reconstructed by the proposed GC-CA framework; (b) Depth distribution along the horizontal line at

$Y = 0$

mm, where the embedded curve shows the distance from the fitting line for each depth.

Download Full Size | PPT Slide | PDF

Fig. 5. Measured mean translations (a) and measured mean strains Exx and Eyy (b) by the proposed GC-CA and stereo-DIC, respectively.

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Fig. 6. (a) Experimental setup for 3D deformation measurement and (b) a pair of recorded speckle images with the defined virtual strainmeter.

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Fig. 7. (a) Static strain errors evaluated for the proposed GC-CA; (b) Comparison of strains measured by the proposed GC-CA with those of stereo-DIC and the ground-truth, where the difference curves show respectively the absolute errors of the GC-CA and stereo-DIC relative to the ground-truth.

Download Full Size | PPT Slide | PDF

Tables (1)

Table 1. Pre-calibrated internal and external parameters.

View Table

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

x = K^{- 1} [\begin{matrix} x \\ 1 \end{matrix}],

K = [\begin{array}{ccc} f_{x} & 0 & c_{x} \\ 0 & f_{y} & c_{y} \\ 0 & 0 & 1 \end{array}] \in R^{3 \times 3}

X (d) = x d .

[x^{'} (d), 1]^{T} = K^{'} ⟨ R X (d) + T ⟩,

C (d, p) = \frac{1}{2} \sum_{η \in Ω} {[f (x + T (η; Δ p)) - g (x^{'} (d) + T (η; p))]}^{2},

T (η; p) = [\begin{array}{cc} 1 + u_{x} & u_{y} \\ v_{x} & 1 + v_{y} \end{array}] [\begin{matrix} η_{x} \\ η_{y} \end{matrix}],

L (Δ d, Δ p) = \frac{1}{2} \sum_{η \in Ω} {[ϵ (d, p) + \frac{\partial ϵ (d, p)}{\partial d} Δ d + \frac{\partial ϵ (d, p)}{\partial p} Δ p]}^{2},

ϵ (d, p) = f (x + η) - g (x^{'} (d) + T (η; p))

\frac{\partial ϵ (d, p)}{\partial d} = - \nabla g \frac{\partial x^{'}}{\partial d}

\frac{\partial ϵ (d, p)}{\partial p} = \nabla f \frac{\partial T}{\partial p}

\frac{\partial T}{\partial p} = [\begin{array}{cccc} η_{x} & η_{y} & 0 & 0 \\ 0 & 0 & η_{x} & η_{y} \end{array}]

H [\begin{matrix} Δ d \\ Δ p \end{matrix}] = \sum_{η \in Ω} [\begin{matrix} - \nabla g \frac{\partial x^{'}}{\partial d} \\ {(\nabla f \frac{\partial T}{\partial p})}^{T} \end{matrix}] ϵ,

H = \sum_{η \in Ω} [\begin{array}{cc} {(\nabla g \frac{\partial x^{'}}{\partial d})}^{2} & - \nabla g \frac{\partial x^{'}}{\partial d} \nabla f \frac{\partial T}{\partial p} \\ - \nabla g \frac{\partial x^{'}}{\partial d} {(\nabla f \frac{\partial T}{\partial p})}^{T} & {(\nabla f \frac{\partial T}{\partial p})}^{T} \nabla f \frac{\partial T}{\partial p} \end{array}] .

{\begin{matrix} d \leftarrow d + Δ d \\ T (p) \leftarrow T (p) \circ T^{- 1} (Δ p) \end{matrix}

U = X (d) - X (d_{0}) = K^{- 1} [\begin{matrix} Δ d x_{0} + d u \\ Δ d \end{matrix}]

Parameter	Reference camera	Matching camera
$f_{x}, f_{y}$	10079.50, 10078.30	10096.50, 10101.90
$c_{x}, c_{y}$	1025.37, 1015.24	1047.87, 1003.47
$κ_{1}, κ_{2}$	-0.27, 2.24	0.28, -2.36
$r (^{\circ})$	$(- 1.56, 24.66, 0.75)$
$t (mm)$	$(201.67, - 16.67, 62.26)$