Abstract

In this article an analysis of two-dimensional (2D) digital image correlation (DIC) data captured over a long period of time is presented, where the case of a 2D DIC setup is not fixed in the same position between consecutive measurements. An implementation of the data merging procedure is described and a proof of concept is provided using example measurements for both: a numerical model and a physical model. An evaluation of the accuracy of the method and main sources of errors are also presented. The developed method can be used for long-term monitoring of different kinds of objects, which is particularly important for the use of DIC technique in application, e.g., building engineering, building control, or power engineering.

© 2012 Optical Society of America

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References

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  1. M. Sutton, J.-J. Orteau, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).
  2. B. Pan, “Recent progress in digital image correlation,” Exp. Mech. 51, 1223–1235 (2011).
    [CrossRef]
  3. T. Nam Nguyen, J. M. Huntley, R. L. Burguete, and C. Russel Coggrave, “Shape and displacement measurement of discontinuous surfaces by combining fringe projection and digital image correlation,” Opt. Eng. 50, 101505 (2011).
    [CrossRef]
  4. M. Malesa, M. Kujawinska, D. Szczepanek, A. Swiercz, and P. Kolakowski, “Monitoring of civil engineering structures using Digital Image Correlation technique,” in Proceedings of 14th International Conference on Experimental Mechanics (EPJ Web of Conferences, 2010), Vol. 6, p. 31014.
  5. A. Piekarczuk, M. Malesa, M. Kujawinska, and K. Malowany, “Application of hybrid FEM-DIC for assessment of low cost building structures,” Exp. Mech. 52, 1297–1311 (2012).
    [CrossRef]
  6. M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
    [CrossRef]
  7. J. M. Dulieu-Barton, D. Khennouf, A. R. Chambers, F. Lennard, and D. Eastop, “Long term condition monitoring of tapestries using image correlation,” in Proceedings of the SEM Annual Conference (SEM, 2010), Vol. 14, pp. 331–338.
  8. R. Jiang, D. V. Jauregui, and K. R. White, “Close-range photogrammetry applications in bridge measurement: literature review,” Meas. Sci. Technol. 41, 823–834 (2008).
    [CrossRef]
  9. W. Linder, Digital Photogrammetry: A Practical Course (Springer, 2009).
  10. G. Bradski, and A. Kaebler, Learning OpenCV: Computer Vision with the OpenCV Library (O’Reilly, 2008).
  11. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).
  12. R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 291153–1160 (1981).
    [CrossRef]
  13. J.-Y. Bouguet, “Camera calibration toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc .
  14. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).
  15. M. A. Fischler, and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
    [CrossRef]
  16. Blender Foundation, http://www.blender.org/ .

2012 (1)

A. Piekarczuk, M. Malesa, M. Kujawinska, and K. Malowany, “Application of hybrid FEM-DIC for assessment of low cost building structures,” Exp. Mech. 52, 1297–1311 (2012).
[CrossRef]

2011 (3)

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

B. Pan, “Recent progress in digital image correlation,” Exp. Mech. 51, 1223–1235 (2011).
[CrossRef]

T. Nam Nguyen, J. M. Huntley, R. L. Burguete, and C. Russel Coggrave, “Shape and displacement measurement of discontinuous surfaces by combining fringe projection and digital image correlation,” Opt. Eng. 50, 101505 (2011).
[CrossRef]

2008 (1)

R. Jiang, D. V. Jauregui, and K. R. White, “Close-range photogrammetry applications in bridge measurement: literature review,” Meas. Sci. Technol. 41, 823–834 (2008).
[CrossRef]

1981 (2)

R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 291153–1160 (1981).
[CrossRef]

M. A. Fischler, and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
[CrossRef]

Bolles, R. C.

M. A. Fischler, and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
[CrossRef]

Bradski, G.

G. Bradski, and A. Kaebler, Learning OpenCV: Computer Vision with the OpenCV Library (O’Reilly, 2008).

Burguete, R. L.

T. Nam Nguyen, J. M. Huntley, R. L. Burguete, and C. Russel Coggrave, “Shape and displacement measurement of discontinuous surfaces by combining fringe projection and digital image correlation,” Opt. Eng. 50, 101505 (2011).
[CrossRef]

Chambers, A. R.

J. M. Dulieu-Barton, D. Khennouf, A. R. Chambers, F. Lennard, and D. Eastop, “Long term condition monitoring of tapestries using image correlation,” in Proceedings of the SEM Annual Conference (SEM, 2010), Vol. 14, pp. 331–338.

Dulieu-Barton, J. M.

J. M. Dulieu-Barton, D. Khennouf, A. R. Chambers, F. Lennard, and D. Eastop, “Long term condition monitoring of tapestries using image correlation,” in Proceedings of the SEM Annual Conference (SEM, 2010), Vol. 14, pp. 331–338.

Eastop, D.

J. M. Dulieu-Barton, D. Khennouf, A. R. Chambers, F. Lennard, and D. Eastop, “Long term condition monitoring of tapestries using image correlation,” in Proceedings of the SEM Annual Conference (SEM, 2010), Vol. 14, pp. 331–338.

Fischler, M. A.

M. A. Fischler, and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

Huntley, J. M.

T. Nam Nguyen, J. M. Huntley, R. L. Burguete, and C. Russel Coggrave, “Shape and displacement measurement of discontinuous surfaces by combining fringe projection and digital image correlation,” Opt. Eng. 50, 101505 (2011).
[CrossRef]

Jauregui, D. V.

R. Jiang, D. V. Jauregui, and K. R. White, “Close-range photogrammetry applications in bridge measurement: literature review,” Meas. Sci. Technol. 41, 823–834 (2008).
[CrossRef]

Jiang, R.

R. Jiang, D. V. Jauregui, and K. R. White, “Close-range photogrammetry applications in bridge measurement: literature review,” Meas. Sci. Technol. 41, 823–834 (2008).
[CrossRef]

Kaebler, A.

G. Bradski, and A. Kaebler, Learning OpenCV: Computer Vision with the OpenCV Library (O’Reilly, 2008).

Keys, R. G.

R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 291153–1160 (1981).
[CrossRef]

Khennouf, D.

J. M. Dulieu-Barton, D. Khennouf, A. R. Chambers, F. Lennard, and D. Eastop, “Long term condition monitoring of tapestries using image correlation,” in Proceedings of the SEM Annual Conference (SEM, 2010), Vol. 14, pp. 331–338.

Kolakowski, P.

M. Malesa, M. Kujawinska, D. Szczepanek, A. Swiercz, and P. Kolakowski, “Monitoring of civil engineering structures using Digital Image Correlation technique,” in Proceedings of 14th International Conference on Experimental Mechanics (EPJ Web of Conferences, 2010), Vol. 6, p. 31014.

Kujawinska, M.

A. Piekarczuk, M. Malesa, M. Kujawinska, and K. Malowany, “Application of hybrid FEM-DIC for assessment of low cost building structures,” Exp. Mech. 52, 1297–1311 (2012).
[CrossRef]

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

M. Malesa, M. Kujawinska, D. Szczepanek, A. Swiercz, and P. Kolakowski, “Monitoring of civil engineering structures using Digital Image Correlation technique,” in Proceedings of 14th International Conference on Experimental Mechanics (EPJ Web of Conferences, 2010), Vol. 6, p. 31014.

Kwiatkowska, E.

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

Lennard, F.

J. M. Dulieu-Barton, D. Khennouf, A. R. Chambers, F. Lennard, and D. Eastop, “Long term condition monitoring of tapestries using image correlation,” in Proceedings of the SEM Annual Conference (SEM, 2010), Vol. 14, pp. 331–338.

Linder, W.

W. Linder, Digital Photogrammetry: A Practical Course (Springer, 2009).

Malesa, M.

A. Piekarczuk, M. Malesa, M. Kujawinska, and K. Malowany, “Application of hybrid FEM-DIC for assessment of low cost building structures,” Exp. Mech. 52, 1297–1311 (2012).
[CrossRef]

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

M. Malesa, M. Kujawinska, D. Szczepanek, A. Swiercz, and P. Kolakowski, “Monitoring of civil engineering structures using Digital Image Correlation technique,” in Proceedings of 14th International Conference on Experimental Mechanics (EPJ Web of Conferences, 2010), Vol. 6, p. 31014.

Malowany, K.

A. Piekarczuk, M. Malesa, M. Kujawinska, and K. Malowany, “Application of hybrid FEM-DIC for assessment of low cost building structures,” Exp. Mech. 52, 1297–1311 (2012).
[CrossRef]

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

Nam Nguyen, T.

T. Nam Nguyen, J. M. Huntley, R. L. Burguete, and C. Russel Coggrave, “Shape and displacement measurement of discontinuous surfaces by combining fringe projection and digital image correlation,” Opt. Eng. 50, 101505 (2011).
[CrossRef]

Orteau, J.-J.

M. Sutton, J.-J. Orteau, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

Pan, B.

B. Pan, “Recent progress in digital image correlation,” Exp. Mech. 51, 1223–1235 (2011).
[CrossRef]

Piekarczuk, A.

A. Piekarczuk, M. Malesa, M. Kujawinska, and K. Malowany, “Application of hybrid FEM-DIC for assessment of low cost building structures,” Exp. Mech. 52, 1297–1311 (2012).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Rouba, B.

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

Russel Coggrave, C.

T. Nam Nguyen, J. M. Huntley, R. L. Burguete, and C. Russel Coggrave, “Shape and displacement measurement of discontinuous surfaces by combining fringe projection and digital image correlation,” Opt. Eng. 50, 101505 (2011).
[CrossRef]

Schreier, H.

M. Sutton, J.-J. Orteau, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

Sutton, M.

M. Sutton, J.-J. Orteau, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

Swiercz, A.

M. Malesa, M. Kujawinska, D. Szczepanek, A. Swiercz, and P. Kolakowski, “Monitoring of civil engineering structures using Digital Image Correlation technique,” in Proceedings of 14th International Conference on Experimental Mechanics (EPJ Web of Conferences, 2010), Vol. 6, p. 31014.

Szczepanek, D.

M. Malesa, M. Kujawinska, D. Szczepanek, A. Swiercz, and P. Kolakowski, “Monitoring of civil engineering structures using Digital Image Correlation technique,” in Proceedings of 14th International Conference on Experimental Mechanics (EPJ Web of Conferences, 2010), Vol. 6, p. 31014.

Targowski, P.

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Tyminska-Widmer, L.

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

White, K. R.

R. Jiang, D. V. Jauregui, and K. R. White, “Close-range photogrammetry applications in bridge measurement: literature review,” Meas. Sci. Technol. 41, 823–834 (2008).
[CrossRef]

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

Commun. ACM (1)

M. A. Fischler, and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Commun. ACM 24, 381–395 (1981).
[CrossRef]

Exp. Mech. (2)

B. Pan, “Recent progress in digital image correlation,” Exp. Mech. 51, 1223–1235 (2011).
[CrossRef]

A. Piekarczuk, M. Malesa, M. Kujawinska, and K. Malowany, “Application of hybrid FEM-DIC for assessment of low cost building structures,” Exp. Mech. 52, 1297–1311 (2012).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

R. G. Keys, “Cubic convolution interpolation for digital image processing,” IEEE Trans. Acoust. Speech Signal Process. 291153–1160 (1981).
[CrossRef]

Meas. Sci. Technol. (1)

R. Jiang, D. V. Jauregui, and K. R. White, “Close-range photogrammetry applications in bridge measurement: literature review,” Meas. Sci. Technol. 41, 823–834 (2008).
[CrossRef]

Opt. Eng. (1)

T. Nam Nguyen, J. M. Huntley, R. L. Burguete, and C. Russel Coggrave, “Shape and displacement measurement of discontinuous surfaces by combining fringe projection and digital image correlation,” Opt. Eng. 50, 101505 (2011).
[CrossRef]

Proc. SPIE (1)

M. Malesa, K. Malowany, L. Tyminska-Widmer, E. Kwiatkowska, M. Kujawinska, B. Rouba, and P. Targowski, “Application of digital image correlation (DIC) for tracking of canvas painting deformations,” Proc. SPIE 8084, 80840L (2011).
[CrossRef]

Other (9)

J. M. Dulieu-Barton, D. Khennouf, A. R. Chambers, F. Lennard, and D. Eastop, “Long term condition monitoring of tapestries using image correlation,” in Proceedings of the SEM Annual Conference (SEM, 2010), Vol. 14, pp. 331–338.

M. Malesa, M. Kujawinska, D. Szczepanek, A. Swiercz, and P. Kolakowski, “Monitoring of civil engineering structures using Digital Image Correlation technique,” in Proceedings of 14th International Conference on Experimental Mechanics (EPJ Web of Conferences, 2010), Vol. 6, p. 31014.

W. Linder, Digital Photogrammetry: A Practical Course (Springer, 2009).

G. Bradski, and A. Kaebler, Learning OpenCV: Computer Vision with the OpenCV Library (O’Reilly, 2008).

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2003).

J.-Y. Bouguet, “Camera calibration toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc .

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University, 2007).

Blender Foundation, http://www.blender.org/ .

M. Sutton, J.-J. Orteau, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

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Figures (18)

Fig. 1.
Fig. 1.

Flow-chart of 2D DIC aided with the merging data procedure.

Fig. 2.
Fig. 2.

Scheme of two-stage data merging procedure.

Fig. 3.
Fig. 3.

Data merging procedure.

Fig. 4.
Fig. 4.

Example of a merging data CA.

Fig. 5.
Fig. 5.

Arrangement used for validation of the numerical setup generated in Blender.

Fig. 6.
Fig. 6.

Exemplary U displacement map with overlaid points of analysis.

Fig. 7.
Fig. 7.

Results of the numerical evaluation of the data merging procedure. First row, errors introduced by rotating the camera; second row, errors introduced by translating the camera.

Fig. 8.
Fig. 8.

(a) Errors introduced by incoplanarity of a measured object and a CA. (b) Effect of modification of homography matrix.

Fig. 9.
Fig. 9.

Distribution of error within AOI: (a) U displacement measurement: RMS=0.0139 and (b) V displacement measurement: RMS=0.0255. Data merging procedure has been applied to images acquired when camera was translated in x axis by 1 mm.

Fig. 10.
Fig. 10.

Distribution of error within AOI: (a) U displacement measurement: RMS=0.0139 and (b) V displacement measurement: RMS=0.0255. Data merging procedure has been applied to images acquired when camera was translated and rotated in all directions simultaneously.

Fig. 11.
Fig. 11.

Errors of the merging procedure: (a) with masked part of CA and (b) with the whole CA.

Fig. 12.
Fig. 12.

Photo of the setup used for experimental validation of merging procedure.

Fig. 13.
Fig. 13.

Position of the CAs markers overlaid on original (a) reference image and (b) image to be merged.

Fig. 14.
Fig. 14.

(a) Reference image. (b) Image to be merged before transformation. (c) Transformed image.

Fig. 15.
Fig. 15.

Example U displacement map with overlaid points of analysis.

Fig. 16.
Fig. 16.

Results of the numerical evaluation of the data merging procedure. First row, errors introduced by rotating the camera; second row, errors introduced by translating the camera.

Fig. 17.
Fig. 17.

Distribution of errors obtained when camera was rotated around “z” axis: (a) U displacement, RMS=0.2224 and (b) V displacement, RMS=0.0216.

Fig. 18.
Fig. 18.

Distribution of errors obtained when all transformations were applied simultaneously: (a) U displacement, RMS=0.2848 and (b) V displacement, RMS=0.0673.

Tables (3)

Tables Icon

Table 1. Transformation Components Introduced to the Camera for the Last Test

Tables Icon

Table 2. Example Coordinates of CAs’ Markers (Green Labels in Fig. 13)

Tables Icon

Table 3. Transformation Components Introduced to the Camera for the Last Test

Equations (24)

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

Pref=sHPimg,
H=sMW=sM[Rt],
[xrefyref1]=sM[r11r12r13t1r21r22r23t2r31r32r33t3][ximgyimg01]=sM[r11r12t1r21r22t2r31r32t3][ximgyimg1].
[xrefyref1]=s[fx0cx0fycy001][r11r12r13t1r21r22r23t2r31r32r33t3][ximgyimgzimg1],
W=1/sM1H=[r11r12t1r21r22t2r31r32t3].
r3=r1×r2.
[xrefyref1]=s[fx0cx0fycy001][r11r12r13t1r21r22r23t2r31r32r33t3][ximgyimgzimg1]=s[fx0cx0fycy001][r11*ximg+r12*yimg+r13*zimg+t1r21*ximg+r22*yimg+r23*zimg+t2r31*ximg+r32*yimg+r33*zimg+t3].
W=[r11r12t1r21r22t2r31r32t3]=[r11r12r13*zimg+t1r21r22r23*zimg+t2r31r32r33*zimg+t3].
H=sMW=sM[r11r21t1r12r22t2r13r23t3].
Pref=HrefQvirtualPimg=HimgQvirtualQvirtual=Himg1PimgPref=HrefHimg1Pimg.
δUPi=|nUnnmUrefmm|,
Himg=[0.168.27440.958.270.09176.15001],
Href=[0.168.27427.278.270.09175.06000.99].
Wimg=[0.0180.99344.380.9990.01752.150.0070.055711.40],
Wref=[0.0180.99246.040.9990.01752.280.0080.054711.41].
Wimg[r3]=Wimg[r1]*Wimg[r2]=[0.0550.0060.993],
Wref[r3]=Wref[r1]*Wref[r2]=[0.0540.0070.993].
WimgExt=[0.0180.9930.05544.380.9990.0170.00652.150.0070.0550.993711.40],
WrefExt=[0.0180.9920.05446.040.9990.0170.00752.280.0080.0540.993711.41].
Wimg=[0.0180.99343.910.9990.01752.100.0070.055702.96],
Wref=[0.071.1945.580.070.1252.220.997.66702.97].
Himg1=[0.0020.1221.400.120.00253.08001.02],
Href=[0.168.27421.168.270.09167.96000.99].
H=[1013.96010.98001].

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