Abstract

We propose a multiscale approach to determine the displacement field by digital image correlation. The displacement field is first estimated on a coarse resolution image and progressively finer details are introduced in the analysis as the displacement is more and more securely and accurately determined. Such a scheme has been developed to increase the robustness, accuracy, and reliability of the image-matching algorithm. The procedure is used on two different types of examples. The first one deals with a representative image that is deformed precisely and purposefully to assess the intrinsic performances. In particular, the maximum measurable strain is determined. The second case deals with a series of pictures taken during compression experiments on mineral-wool samples. The different steps of the procedure are analyzed and their respective role is assessed. Both reflection and transmission images are tested.

© 2002 Optical Society of America

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  1. L. Hesselink, “Digital image processing in flow visualization,” Annu. Rev. Fluid Mech. 20, 421–485 (1988).
    [CrossRef]
  2. R. J. Adrian, “Particle imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
    [CrossRef]
  3. C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
    [CrossRef]
  4. N. A. Fomin, Speckle Photography for Fluid Mechanical Measurements (Springer, Berlin, 1998).
  5. M. Raffel, C. E. Willert, J. Kompenhans, Particle Image Velocimetry, a practical guide, (Springer, Berlin, 1998).
  6. M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1, 133–139 (1983).
    [CrossRef]
  7. M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in Two-Dimensional and Three-Dimensional Computer Vision,” in Photomechanics, P. K. Rastogi, ed. (Springer, Berlin, 2000), pp. 323–372.
  8. P. T. Tokumaru, P. E. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
    [CrossRef]
  9. S. Roux, F. Hild, Y. Berthaud, “Correlation image velocimetry: A spectral approach,” Appl. Opt. 41, 108–115 (2002).
    [CrossRef] [PubMed]
  10. T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
    [CrossRef]
  11. D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
    [CrossRef] [PubMed]
  12. Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proc. Colloque national MECAMAT, Cachan, Mécanismes et mécanique des grandes déformations, (1996), pp. 77–80.
  13. F. P. Chiang, Q. Wang, F. Lehman, “New developments in full-field strain measurements using speckles,” in Non-Traditional Methods of Sensing Stress, Strain and Damage in Materials and Structures (ASTM, Philadelphia, 1997), STP 1318, pp. 156–169.
  14. D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. 25, 251–262 (1991).
  15. C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
    [CrossRef]
  16. L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A. Solids 20, 169–187 (2001).
    [CrossRef]
  17. G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, Bellingham, Wash., 1998).
  18. B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
    [CrossRef]
  19. A. Mitiche, P. Bouthemy, “Computation and analysis of image motion: A synopsis of current problems and methods,” Int. J. Comput. Vision 19, 29–55 (1996).
    [CrossRef]
  20. P. J. Hubert, Robust Statistics (Wiley, New York, 1981).
  21. M. Black, “Robust Incremental Optical Flow,” Ph.D. dissertation (Yale University, New Haven, Conn., 1992).
  22. J.-M. Odobez, P. Bouthemy, “Robust multiresolution estimation of parametric motion models,” J. Visual Commun. Image Represent. 6, 348–365 (1995).
    [CrossRef]
  23. D. Bogen, D. Rahdert, “A strain energy approach to regularization in displacement field fits of elastically deforming bodies,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 629–635 (1996).
    [CrossRef]
  24. B. Wagne, S. Roux, F. Hild, “Spectral approach to displacement evaluation from image analysis,” Eur. Phys. J. 17, 247–252 (2002).
  25. L. C. Gui, W. Merzkirch, “A comparative study of the MQD method and several correlation-based PIV evaluation algorithms,” Exp. Fluids 28, 36–44 (2000).
    [CrossRef]
  26. R. Hill, “Aspects of invariance in solid mechanics,” Adv. Appl. Mech. 18, 1–75 (1978).
  27. R. D. Keane, R. J. Adrian, “Optimization of particle image velocimeters. Part I: Double pulsed systems,” Meas. Sci. Technol. 1, 1202–1215 (1990).
    [CrossRef]
  28. Matlab, Matlab 5.3, the Language of Technical Computing, version 5.3 (the MathWorks inc., http://www.mathworks.com , 1999).
  29. J.-N. Périé, S. Calloch, C. Cluzel, F. Hild, “Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model,” Exp. Mech. (in press) (2002).
  30. J. Bolinder, On the accuracy of digital particle image velocimetry system, Technical Report, Lund Institute of Technology, ISSN 0282–1990 (1999).
  31. D. P. Hart, “Super-resolution PIV by recursive local correlation,” J. Visual Commun. Image Represent. 10, 1–10 (1990).
  32. When a number Ξ is written as Ξ ± ξ, ξ corresponds to the standard error.
  33. Y. Marco, L. Chevalier, M. Chaouche, “X-Ray stuy of induced cristallisation and orientation in PET under biaxial loading: Application to blow-moulding process,” in Proc. 5th International ESAFORM Conference on Material Forming, M. Pietryk, Z. Mitura, J. Kaczmar, eds., (Akapit, Krakow (Poland), 2002), pp. 227–230.

2002 (2)

S. Roux, F. Hild, Y. Berthaud, “Correlation image velocimetry: A spectral approach,” Appl. Opt. 41, 108–115 (2002).
[CrossRef] [PubMed]

B. Wagne, S. Roux, F. Hild, “Spectral approach to displacement evaluation from image analysis,” Eur. Phys. J. 17, 247–252 (2002).

2001 (1)

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A. Solids 20, 169–187 (2001).
[CrossRef]

2000 (1)

L. C. Gui, W. Merzkirch, “A comparative study of the MQD method and several correlation-based PIV evaluation algorithms,” Exp. Fluids 28, 36–44 (2000).
[CrossRef]

1996 (3)

A. Mitiche, P. Bouthemy, “Computation and analysis of image motion: A synopsis of current problems and methods,” Int. J. Comput. Vision 19, 29–55 (1996).
[CrossRef]

Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proc. Colloque national MECAMAT, Cachan, Mécanismes et mécanique des grandes déformations, (1996), pp. 77–80.

D. Bogen, D. Rahdert, “A strain energy approach to regularization in displacement field fits of elastically deforming bodies,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 629–635 (1996).
[CrossRef]

1995 (2)

P. T. Tokumaru, P. E. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
[CrossRef]

J.-M. Odobez, P. Bouthemy, “Robust multiresolution estimation of parametric motion models,” J. Visual Commun. Image Represent. 6, 348–365 (1995).
[CrossRef]

1993 (1)

1992 (1)

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

1991 (3)

R. J. Adrian, “Particle imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. 25, 251–262 (1991).

1990 (2)

R. D. Keane, R. J. Adrian, “Optimization of particle image velocimeters. Part I: Double pulsed systems,” Meas. Sci. Technol. 1, 1202–1215 (1990).
[CrossRef]

D. P. Hart, “Super-resolution PIV by recursive local correlation,” J. Visual Commun. Image Represent. 10, 1–10 (1990).

1988 (1)

L. Hesselink, “Digital image processing in flow visualization,” Annu. Rev. Fluid Mech. 20, 421–485 (1988).
[CrossRef]

1985 (1)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[CrossRef]

1983 (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1, 133–139 (1983).
[CrossRef]

1981 (1)

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

1978 (1)

R. Hill, “Aspects of invariance in solid mechanics,” Adv. Appl. Mech. 18, 1–75 (1978).

Adrian, R. J.

R. J. Adrian, “Particle imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

R. D. Keane, R. J. Adrian, “Optimization of particle image velocimeters. Part I: Double pulsed systems,” Meas. Sci. Technol. 1, 1202–1215 (1990).
[CrossRef]

Berthaud, Y.

S. Roux, F. Hild, Y. Berthaud, “Correlation image velocimetry: A spectral approach,” Appl. Opt. 41, 108–115 (2002).
[CrossRef] [PubMed]

Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proc. Colloque national MECAMAT, Cachan, Mécanismes et mécanique des grandes déformations, (1996), pp. 77–80.

Black, M.

M. Black, “Robust Incremental Optical Flow,” Ph.D. dissertation (Yale University, New Haven, Conn., 1992).

Bogen, D.

D. Bogen, D. Rahdert, “A strain energy approach to regularization in displacement field fits of elastically deforming bodies,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 629–635 (1996).
[CrossRef]

Bolinder, J.

J. Bolinder, On the accuracy of digital particle image velocimetry system, Technical Report, Lund Institute of Technology, ISSN 0282–1990 (1999).

Bouthemy, P.

A. Mitiche, P. Bouthemy, “Computation and analysis of image motion: A synopsis of current problems and methods,” Int. J. Comput. Vision 19, 29–55 (1996).
[CrossRef]

J.-M. Odobez, P. Bouthemy, “Robust multiresolution estimation of parametric motion models,” J. Visual Commun. Image Represent. 6, 348–365 (1995).
[CrossRef]

Calloch, S.

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A. Solids 20, 169–187 (2001).
[CrossRef]

J.-N. Périé, S. Calloch, C. Cluzel, F. Hild, “Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model,” Exp. Mech. (in press) (2002).

Chao, Y. J.

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in Two-Dimensional and Three-Dimensional Computer Vision,” in Photomechanics, P. K. Rastogi, ed. (Springer, Berlin, 2000), pp. 323–372.

Chaouche, M.

Y. Marco, L. Chevalier, M. Chaouche, “X-Ray stuy of induced cristallisation and orientation in PET under biaxial loading: Application to blow-moulding process,” in Proc. 5th International ESAFORM Conference on Material Forming, M. Pietryk, Z. Mitura, J. Kaczmar, eds., (Akapit, Krakow (Poland), 2002), pp. 227–230.

Chen, D. J.

Chevalier, L.

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A. Solids 20, 169–187 (2001).
[CrossRef]

Y. Marco, L. Chevalier, M. Chaouche, “X-Ray stuy of induced cristallisation and orientation in PET under biaxial loading: Application to blow-moulding process,” in Proc. 5th International ESAFORM Conference on Material Forming, M. Pietryk, Z. Mitura, J. Kaczmar, eds., (Akapit, Krakow (Poland), 2002), pp. 227–230.

Chiang, F. P.

D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
[CrossRef] [PubMed]

F. P. Chiang, Q. Wang, F. Lehman, “New developments in full-field strain measurements using speckles,” in Non-Traditional Methods of Sensing Stress, Strain and Damage in Materials and Structures (ASTM, Philadelphia, 1997), STP 1318, pp. 156–169.

Choi, D.

D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. 25, 251–262 (1991).

Chu, T. C.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[CrossRef]

Cluzel, C.

J.-N. Périé, S. Calloch, C. Cluzel, F. Hild, “Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model,” Exp. Mech. (in press) (2002).

Dahnoun, A.

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Dimotakis, P. E.

P. T. Tokumaru, P. E. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
[CrossRef]

Don, H. S.

Fomin, N. A.

N. A. Fomin, Speckle Photography for Fluid Mechanical Measurements (Springer, Berlin, 1998).

G’Sell, C.

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Gharib, M.

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

Gui, L. C.

L. C. Gui, W. Merzkirch, “A comparative study of the MQD method and several correlation-based PIV evaluation algorithms,” Exp. Fluids 28, 36–44 (2000).
[CrossRef]

Hanna, R.

D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. 25, 251–262 (1991).

Hart, D. P.

D. P. Hart, “Super-resolution PIV by recursive local correlation,” J. Visual Commun. Image Represent. 10, 1–10 (1990).

Helm, J. D.

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in Two-Dimensional and Three-Dimensional Computer Vision,” in Photomechanics, P. K. Rastogi, ed. (Springer, Berlin, 2000), pp. 323–372.

Hesselink, L.

L. Hesselink, “Digital image processing in flow visualization,” Annu. Rev. Fluid Mech. 20, 421–485 (1988).
[CrossRef]

Hild, F.

S. Roux, F. Hild, Y. Berthaud, “Correlation image velocimetry: A spectral approach,” Appl. Opt. 41, 108–115 (2002).
[CrossRef] [PubMed]

B. Wagne, S. Roux, F. Hild, “Spectral approach to displacement evaluation from image analysis,” Eur. Phys. J. 17, 247–252 (2002).

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A. Solids 20, 169–187 (2001).
[CrossRef]

J.-N. Périé, S. Calloch, C. Cluzel, F. Hild, “Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model,” Exp. Mech. (in press) (2002).

Hill, R.

R. Hill, “Aspects of invariance in solid mechanics,” Adv. Appl. Mech. 18, 1–75 (1978).

Hiver, J.-M.

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, Bellingham, Wash., 1998).

Horn, B. K. P.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

Hubert, P. J.

P. J. Hubert, Robust Statistics (Wiley, New York, 1981).

Keane, R. D.

R. D. Keane, R. J. Adrian, “Optimization of particle image velocimeters. Part I: Double pulsed systems,” Meas. Sci. Technol. 1, 1202–1215 (1990).
[CrossRef]

Kompenhans, J.

M. Raffel, C. E. Willert, J. Kompenhans, Particle Image Velocimetry, a practical guide, (Springer, Berlin, 1998).

Lehman, F.

F. P. Chiang, Q. Wang, F. Lehman, “New developments in full-field strain measurements using speckles,” in Non-Traditional Methods of Sensing Stress, Strain and Damage in Materials and Structures (ASTM, Philadelphia, 1997), STP 1318, pp. 156–169.

Marco, Y.

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A. Solids 20, 169–187 (2001).
[CrossRef]

Y. Marco, L. Chevalier, M. Chaouche, “X-Ray stuy of induced cristallisation and orientation in PET under biaxial loading: Application to blow-moulding process,” in Proc. 5th International ESAFORM Conference on Material Forming, M. Pietryk, Z. Mitura, J. Kaczmar, eds., (Akapit, Krakow (Poland), 2002), pp. 227–230.

McNeill, S. R.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1, 133–139 (1983).
[CrossRef]

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in Two-Dimensional and Three-Dimensional Computer Vision,” in Photomechanics, P. K. Rastogi, ed. (Springer, Berlin, 2000), pp. 323–372.

Merzkirch, W.

L. C. Gui, W. Merzkirch, “A comparative study of the MQD method and several correlation-based PIV evaluation algorithms,” Exp. Fluids 28, 36–44 (2000).
[CrossRef]

Mitiche, A.

A. Mitiche, P. Bouthemy, “Computation and analysis of image motion: A synopsis of current problems and methods,” Int. J. Comput. Vision 19, 29–55 (1996).
[CrossRef]

Odobez, J.-M.

J.-M. Odobez, P. Bouthemy, “Robust multiresolution estimation of parametric motion models,” J. Visual Commun. Image Represent. 6, 348–365 (1995).
[CrossRef]

Périé, J.-N.

J.-N. Périé, S. Calloch, C. Cluzel, F. Hild, “Analysis of a multiaxial test on a C/C composite by using digital image correlation and a damage model,” Exp. Mech. (in press) (2002).

Peters, W. H.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1, 133–139 (1983).
[CrossRef]

Petters, W. H.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[CrossRef]

Raffel, M.

M. Raffel, C. E. Willert, J. Kompenhans, Particle Image Velocimetry, a practical guide, (Springer, Berlin, 1998).

Rahdert, D.

D. Bogen, D. Rahdert, “A strain energy approach to regularization in displacement field fits of elastically deforming bodies,” IEEE Trans. Pattern Anal. Mach. Intell. 18, 629–635 (1996).
[CrossRef]

Ranson, W. F.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1, 133–139 (1983).
[CrossRef]

Roux, S.

S. Roux, F. Hild, Y. Berthaud, “Correlation image velocimetry: A spectral approach,” Appl. Opt. 41, 108–115 (2002).
[CrossRef] [PubMed]

B. Wagne, S. Roux, F. Hild, “Spectral approach to displacement evaluation from image analysis,” Eur. Phys. J. 17, 247–252 (2002).

Scholz, J.

Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proc. Colloque national MECAMAT, Cachan, Mécanismes et mécanique des grandes déformations, (1996), pp. 77–80.

Schunck, B. G.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

Souahi, A.

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Sutton, M. A.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1, 133–139 (1983).
[CrossRef]

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in Two-Dimensional and Three-Dimensional Computer Vision,” in Photomechanics, P. K. Rastogi, ed. (Springer, Berlin, 2000), pp. 323–372.

Tan, Y. S.

Thesing, J.

Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proc. Colloque national MECAMAT, Cachan, Mécanismes et mécanique des grandes déformations, (1996), pp. 77–80.

Thorpe, J. L.

D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. 25, 251–262 (1991).

Tokumaru, P. T.

P. T. Tokumaru, P. E. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
[CrossRef]

Wagne, B.

B. Wagne, S. Roux, F. Hild, “Spectral approach to displacement evaluation from image analysis,” Eur. Phys. J. 17, 247–252 (2002).

Wang, Q.

F. P. Chiang, Q. Wang, F. Lehman, “New developments in full-field strain measurements using speckles,” in Non-Traditional Methods of Sensing Stress, Strain and Damage in Materials and Structures (ASTM, Philadelphia, 1997), STP 1318, pp. 156–169.

Willert, C. E.

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

M. Raffel, C. E. Willert, J. Kompenhans, Particle Image Velocimetry, a practical guide, (Springer, Berlin, 1998).

Wolters, W. J.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1, 133–139 (1983).
[CrossRef]

Adv. Appl. Mech. (1)

R. Hill, “Aspects of invariance in solid mechanics,” Adv. Appl. Mech. 18, 1–75 (1978).

Annu. Rev. Fluid Mech. (2)

L. Hesselink, “Digital image processing in flow visualization,” Annu. Rev. Fluid Mech. 20, 421–485 (1988).
[CrossRef]

R. J. Adrian, “Particle imaging techniques for experimental fluid mechanics,” Annu. Rev. Fluid Mech. 23, 261–304 (1991).
[CrossRef]

Appl. Opt. (2)

Artif. Intell. (1)

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

Eur. J. Mech. A. Solids (1)

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A. Solids 20, 169–187 (2001).
[CrossRef]

Eur. Phys. J. (1)

B. Wagne, S. Roux, F. Hild, “Spectral approach to displacement evaluation from image analysis,” Eur. Phys. J. 17, 247–252 (2002).

Exp. Fluids (3)

L. C. Gui, W. Merzkirch, “A comparative study of the MQD method and several correlation-based PIV evaluation algorithms,” Exp. Fluids 28, 36–44 (2000).
[CrossRef]

P. T. Tokumaru, P. E. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
[CrossRef]

C. E. Willert, M. Gharib, “Digital particle image velocimetry,” Exp. Fluids 10, 181–193 (1991).
[CrossRef]

Exp. Mech. (1)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
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When a number Ξ is written as Ξ ± ξ, ξ corresponds to the standard error.

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Figures (12)

Fig. 1
Fig. 1

(a) Initial and (b) artificially deformed (E yy = 0.05) images of a stone-wool sample. The region of interest (ROIref) and two zones of interest (ZOIref and ZOIdef) are depicted. Four centers of ZOIs are shown on the reference picture (δ: separation between neighboring ZOIs).

Fig. 2
Fig. 2

Flowchart of the principal steps in a conventional correlation algorithm.

Fig. 3
Fig. 3

Standard deviation of the vertical displacement vs. vertical position y of the ZOI when a strain E yy = 0.05 is prescribed (Fig. 1). A classical digital image correlation procedure is used for different sizes (2 p × 2 p pixels) of the zones of interest (δ = 16 pixels).

Fig. 4
Fig. 4

Different notations used in the multiscale approach. Sub-ROI (scale no. 2) of a reference image and corresponding superimages on scales nos. 3, 4.

Fig. 5
Fig. 5

Flowchart of the principal steps in the multiscale correlation algorithm.

Fig. 6
Fig. 6

Initial (a) and last deformed (b) images of a glass-wool sample. The reference length L 0 and the length variation ΔL are drawn.

Fig. 7
Fig. 7

Vertical displacement (open circles) and corresponding standard deviation (filled circles) vs. vertical position y of the ZOI when a strain E yy = 0.35 is prescribed. The multiscale correlation procedure is used (p = 4, δ = 16 pixels).

Fig. 8
Fig. 8

Average strain vs. iteration number for different sizes (2 p × 2 p pixels) of the zones of interest and shifts δ. The dashed curve corresponds to a simulation in which no iteration is used for a given scale. The arrows show the first time a scale, the level of which is indicated by the numbers close to the arrows, is invoked. A strain E yy = 0.35 is applied.

Fig. 9
Fig. 9

Reference and deformed images of a stone-wool sample. The estimated reference length L 0 is drawn.

Fig. 10
Fig. 10

Reference and deformed meshes of a stone-wool sample predicted by using two strategies of the multiscale approach and corresponding error contours: (a) no image update, (b) with two image updates. The black square depicts one ZOI (p = 5, δ = 32 pixels).

Fig. 11
Fig. 11

(a) Average residual strain vs. standard deviation of a compressed glass-wool sample. (b) Reference and deformed meshes at the end of the sequence (p = 5, δ = 32 pixels).

Fig. 12
Fig. 12

Comparison of reference and deformed meshes at the end of the sequence of a compressed glass-wool sample (p = 5, δ = 32 pixels). Four different options are used in the multiscale approach: (a) no image update, (b) with image update and no iteration, (c) with image update and no limitation on η, and (d) with image update and no test on the local texture fluctuations.

Tables (1)

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Table 1 Average Nominal Strain yy and Corresponding Standard Deviation E¯¯yya

Equations (22)

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

gx=fx-u+bx,
minvg-f.-v2
hv=g  fv-+-+gxfx-vdx,
g  f=FFT-1FFTgFFTf¯,
dx=Fdx0
F=1+u,
Em=12mCm-1when m012lnCwhen m  0+,
=12u+ut.
w¯¯yy=αp+βp255.5-y2,
ZOI˜=ZOI  χ
χI=121-cos4πI2p-1when 0I<2p-2,1when 2p-2I<3×2p-2,121-cos4πI2p-1when 3×2p-2I<2p-1.
ZOIˆ=W ZOI W,
ux0=Ax0+a,
A=Axx00Ayy,
C=A2,
ux1=Ax1+a+Ad01.
ux2=Ax2+a+Ad01+d12.
uxn=Axn+22-na+Ad01+d12.
E1=ΔwmaxN-1δ,
E4=ΔwmaxL4,
unxn=Bnxn+bn,
η=MEANZOIrefMEANROIref-MEANZOIdefMEANROIdef×MEANZOIrefMEANZOIdef1/2

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