Abstract

An improved speckle projection profilometry that combines the projection of computer generated random speckle patterns using an ordinary LCD projector and the two-dimensional digital image correlation technique for in-plane displacements measurement is proposed for accurate out-of-plane shape and displacement measurements. The improved technique employs a simple yet effective calibration technique to determine the linear relationship between the out-of-plane height and the measured in-plane displacements. In addition, the iterative spatial domain cross-correlation algorithm, i.e., the improved Newton–Raphson algorithm using the zero-normalized sum of squared differences correlation criterion and the second-order shape function was employed in image correlation analysis for in-plane displacement determination of the projected speckle patterns, which provides more reliable and accurate matching with a higher correlation coefficient. Experimental results of both a regular cylinder and a human hand demonstrate that the proposed technique is easy to implement and can be applied to a practical out-of-plane shape and displacement measurement with high accuracy.

© 2008 Optical Society of America

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References

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  1. F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10-22 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. H. Du and Z. Y. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. 32, 2438-2440 (2007).
    [CrossRef] [PubMed]
  5. P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech. 33, 123-132(1993).
    [CrossRef]
  6. B. Pan, H. M. Xie, L. H. Yang, and Z. Y. Wang, “Accurate measurement of satellite antenna surface using three-dimensional digital image correlation technique,” Strain 10.1111/j.1475-1305 (2008).
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    [CrossRef] [PubMed]
  8. P. Sriram and S. Hanagud, “Projection-speckle digital-correlation method for surface-displacement measurement,” Exp. Mech. 28, 340-345 (1988).
    [CrossRef]
  9. J. Brillaud and F. Lagattu, “Digital correlation of grainy shadow images for surface profile measurement,” Optik 117, 411-417 (2006).
    [CrossRef]
  10. J. X. Gao, W. Xu, and J. P. Geng, “3D shape reconstruction of teeth by shadow speckle correlation method,” Opt. Las. Eng. 44, 455-465 (2006).
    [CrossRef]
  11. J. X. Gao, W. Xu, and J. P. Geng, “Use of shadow-speckle correlation method for 3D tooth model reconstruction,” Intl. J. Prosthodontics 18, 436-437 (2005).
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    [CrossRef]
  13. M. Sjodahl and P. Synnergren, “Measurement of shape by using projected random patterns and temporal digital speckle photography,” Appl. Opt. 38, 1990-1997 (1999).
    [CrossRef]
  14. H. J. Dai and X. Y. Su, “Shape measurement by digital speckle temporal sequence correlation with digital light projector,” Opt. Las. Eng. 40, 793-800 (2001).
  15. S. R. McNeill, M. A. Sutton, Z. Miao, and J. Ma, “Measurement of surface profile using digital image correlation” Exp. Mech. 37, 13-20 (1997).
    [CrossRef]
  16. H. W. Schreier and M. A. Sutton, “Systematic errors in digital image correlation due to undermatched subset shape functions,” Exp. Mech. 42, 303-310 (2002).
    [CrossRef]
  17. B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615-1621 (2006).
    [CrossRef]
  18. B. Pan, H. M. Xie, Z. Y. Wang, and K. M. Qian, “Study of subset size selection in digital image correlation for speckle patterns,” Opt. Express 16, 7037-7048 (2008).
    [CrossRef] [PubMed]
  19. B. Pan, H. M. Xie, Z. Q. Guo, and T. Hua, “Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation,” Opt. Eng. 46, 033601 (2007).
    [CrossRef]
  20. H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393-400 (2000).
    [CrossRef]
  21. H. A. Bruck, S. R. McNeil, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261-267 (1989).
    [CrossRef]
  22. G. Vendroux and W. G. Knauss, “Submicron deformation field measurements. Part 2. Improved digital image correlation,” Exp. Mech. 38, 86-92 (1998).
    [CrossRef]

2008 (1)

2007 (2)

H. Du and Z. Y. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. 32, 2438-2440 (2007).
[CrossRef] [PubMed]

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

2006 (4)

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

J. Brillaud and F. Lagattu, “Digital correlation of grainy shadow images for surface profile measurement,” Optik 117, 411-417 (2006).
[CrossRef]

J. X. Gao, W. Xu, and J. P. Geng, “3D shape reconstruction of teeth by shadow speckle correlation method,” Opt. Las. Eng. 44, 455-465 (2006).
[CrossRef]

Z. Y. Wang, H. Du, and B. Han, “Out-of-plane shape determination in generalized fringe projection profilometry,” Opt. Express 14, 12122-12133 (2006).
[CrossRef] [PubMed]

2005 (1)

J. X. Gao, W. Xu, and J. P. Geng, “Use of shadow-speckle correlation method for 3D tooth model reconstruction,” Intl. J. Prosthodontics 18, 436-437 (2005).

2002 (1)

H. W. Schreier and M. A. Sutton, “Systematic errors in digital image correlation due to undermatched subset shape functions,” Exp. Mech. 42, 303-310 (2002).
[CrossRef]

2001 (1)

H. J. Dai and X. Y. Su, “Shape measurement by digital speckle temporal sequence correlation with digital light projector,” Opt. Las. Eng. 40, 793-800 (2001).

2000 (2)

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10-22 (2000).
[CrossRef]

H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393-400 (2000).
[CrossRef]

1999 (1)

1998 (2)

G. Vendroux and W. G. Knauss, “Submicron deformation field measurements. Part 2. Improved digital image correlation,” Exp. Mech. 38, 86-92 (1998).
[CrossRef]

M. Sjodahl, “Some recent advances in electronic speckle photography,” Opt. Las. Eng. 29, 125-144 (1998).
[CrossRef]

1997 (1)

S. R. McNeill, M. A. Sutton, Z. Miao, and J. Ma, “Measurement of surface profile using digital image correlation” Exp. Mech. 37, 13-20 (1997).
[CrossRef]

1993 (1)

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech. 33, 123-132(1993).
[CrossRef]

1989 (1)

H. A. Bruck, S. R. McNeil, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261-267 (1989).
[CrossRef]

1988 (1)

P. Sriram and S. Hanagud, “Projection-speckle digital-correlation method for surface-displacement measurement,” Exp. Mech. 28, 340-345 (1988).
[CrossRef]

1986 (1)

1983 (1)

Brillaud, J.

J. Brillaud and F. Lagattu, “Digital correlation of grainy shadow images for surface profile measurement,” Optik 117, 411-417 (2006).
[CrossRef]

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10-22 (2000).
[CrossRef]

Bruck, H. A.

H. A. Bruck, S. R. McNeil, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261-267 (1989).
[CrossRef]

Cary, P. D.

H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393-400 (2000).
[CrossRef]

Chao, Y. J.

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech. 33, 123-132(1993).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10-22 (2000).
[CrossRef]

Dai, F. L.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

Dai, H. J.

H. J. Dai and X. Y. Su, “Shape measurement by digital speckle temporal sequence correlation with digital light projector,” Opt. Las. Eng. 40, 793-800 (2001).

Du, H.

Gao, J. X.

J. X. Gao, W. Xu, and J. P. Geng, “3D shape reconstruction of teeth by shadow speckle correlation method,” Opt. Las. Eng. 44, 455-465 (2006).
[CrossRef]

J. X. Gao, W. Xu, and J. P. Geng, “Use of shadow-speckle correlation method for 3D tooth model reconstruction,” Intl. J. Prosthodontics 18, 436-437 (2005).

Geng, J. P.

J. X. Gao, W. Xu, and J. P. Geng, “3D shape reconstruction of teeth by shadow speckle correlation method,” Opt. Las. Eng. 44, 455-465 (2006).
[CrossRef]

J. X. Gao, W. Xu, and J. P. Geng, “Use of shadow-speckle correlation method for 3D tooth model reconstruction,” Intl. J. Prosthodontics 18, 436-437 (2005).

Gilbert, J. A.

Guo, Z. Q.

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

Han, B.

Hanagud, S.

P. Sriram and S. Hanagud, “Projection-speckle digital-correlation method for surface-displacement measurement,” Exp. Mech. 28, 340-345 (1988).
[CrossRef]

Hua, T.

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

Knauss, W. G.

G. Vendroux and W. G. Knauss, “Submicron deformation field measurements. Part 2. Improved digital image correlation,” Exp. Mech. 38, 86-92 (1998).
[CrossRef]

Lagattu, F.

J. Brillaud and F. Lagattu, “Digital correlation of grainy shadow images for surface profile measurement,” Optik 117, 411-417 (2006).
[CrossRef]

Lu, H.

H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393-400 (2000).
[CrossRef]

Luo, P. F.

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech. 33, 123-132(1993).
[CrossRef]

Ma, J.

S. R. McNeill, M. A. Sutton, Z. Miao, and J. Ma, “Measurement of surface profile using digital image correlation” Exp. Mech. 37, 13-20 (1997).
[CrossRef]

Matthys, D. R.

McNeil, S. R.

H. A. Bruck, S. R. McNeil, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261-267 (1989).
[CrossRef]

McNeill, S. R.

S. R. McNeill, M. A. Sutton, Z. Miao, and J. Ma, “Measurement of surface profile using digital image correlation” Exp. Mech. 37, 13-20 (1997).
[CrossRef]

Miao, Z.

S. R. McNeill, M. A. Sutton, Z. Miao, and J. Ma, “Measurement of surface profile using digital image correlation” Exp. Mech. 37, 13-20 (1997).
[CrossRef]

Mutoh, K.

Pan, B.

B. Pan, H. M. Xie, Z. Y. Wang, and K. M. Qian, “Study of subset size selection in digital image correlation for speckle patterns,” Opt. Express 16, 7037-7048 (2008).
[CrossRef] [PubMed]

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

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

B. Pan, H. M. Xie, L. H. Yang, and Z. Y. Wang, “Accurate measurement of satellite antenna surface using three-dimensional digital image correlation technique,” Strain 10.1111/j.1475-1305 (2008).

Peters, W. H.

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech. 33, 123-132(1993).
[CrossRef]

H. A. Bruck, S. R. McNeil, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261-267 (1989).
[CrossRef]

Petersen, M. E.

Qian, K. M.

Schreier, H. W.

H. W. Schreier and M. A. Sutton, “Systematic errors in digital image correlation due to undermatched subset shape functions,” Exp. Mech. 42, 303-310 (2002).
[CrossRef]

Sjodahl, M.

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10-22 (2000).
[CrossRef]

Sriram, P.

P. Sriram and S. Hanagud, “Projection-speckle digital-correlation method for surface-displacement measurement,” Exp. Mech. 28, 340-345 (1988).
[CrossRef]

Su, X. Y.

H. J. Dai and X. Y. Su, “Shape measurement by digital speckle temporal sequence correlation with digital light projector,” Opt. Las. Eng. 40, 793-800 (2001).

Sutton, M. A.

H. W. Schreier and M. A. Sutton, “Systematic errors in digital image correlation due to undermatched subset shape functions,” Exp. Mech. 42, 303-310 (2002).
[CrossRef]

S. R. McNeill, M. A. Sutton, Z. Miao, and J. Ma, “Measurement of surface profile using digital image correlation” Exp. Mech. 37, 13-20 (1997).
[CrossRef]

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech. 33, 123-132(1993).
[CrossRef]

H. A. Bruck, S. R. McNeil, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261-267 (1989).
[CrossRef]

Synnergren, P.

Taher, M. A.

Takeda, M.

Vendroux, G.

G. Vendroux and W. G. Knauss, “Submicron deformation field measurements. Part 2. Improved digital image correlation,” Exp. Mech. 38, 86-92 (1998).
[CrossRef]

Wang, Z. Y.

Xie, H. M.

B. Pan, H. M. Xie, Z. Y. Wang, and K. M. Qian, “Study of subset size selection in digital image correlation for speckle patterns,” Opt. Express 16, 7037-7048 (2008).
[CrossRef] [PubMed]

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

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

B. Pan, H. M. Xie, L. H. Yang, and Z. Y. Wang, “Accurate measurement of satellite antenna surface using three-dimensional digital image correlation technique,” Strain 10.1111/j.1475-1305 (2008).

Xu, B. Q.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

Xu, W.

J. X. Gao, W. Xu, and J. P. Geng, “3D shape reconstruction of teeth by shadow speckle correlation method,” Opt. Las. Eng. 44, 455-465 (2006).
[CrossRef]

J. X. Gao, W. Xu, and J. P. Geng, “Use of shadow-speckle correlation method for 3D tooth model reconstruction,” Intl. J. Prosthodontics 18, 436-437 (2005).

Yang, L. H.

B. Pan, H. M. Xie, L. H. Yang, and Z. Y. Wang, “Accurate measurement of satellite antenna surface using three-dimensional digital image correlation technique,” Strain 10.1111/j.1475-1305 (2008).

Appl. Opt. (3)

Exp. Mech. (7)

H. Lu and P. D. Cary, “Deformation measurement by digital image correlation: implementation of a second-order displacement gradient,” Exp. Mech. 40, 393-400 (2000).
[CrossRef]

H. A. Bruck, S. R. McNeil, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton-Raphson method of partial differential correction,” Exp. Mech. 29, 261-267 (1989).
[CrossRef]

G. Vendroux and W. G. Knauss, “Submicron deformation field measurements. Part 2. Improved digital image correlation,” Exp. Mech. 38, 86-92 (1998).
[CrossRef]

P. F. Luo, Y. J. Chao, M. A. Sutton, and W. H. Peters, “Accurate measurement of three-dimensional displacement in deformable bodies using computer vision,” Exp. Mech. 33, 123-132(1993).
[CrossRef]

P. Sriram and S. Hanagud, “Projection-speckle digital-correlation method for surface-displacement measurement,” Exp. Mech. 28, 340-345 (1988).
[CrossRef]

S. R. McNeill, M. A. Sutton, Z. Miao, and J. Ma, “Measurement of surface profile using digital image correlation” Exp. Mech. 37, 13-20 (1997).
[CrossRef]

H. W. Schreier and M. A. Sutton, “Systematic errors in digital image correlation due to undermatched subset shape functions,” Exp. Mech. 42, 303-310 (2002).
[CrossRef]

Intl. J. Prosthodontics (1)

J. X. Gao, W. Xu, and J. P. Geng, “Use of shadow-speckle correlation method for 3D tooth model reconstruction,” Intl. J. Prosthodontics 18, 436-437 (2005).

Meas. Sci. Technol. (1)

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615-1621 (2006).
[CrossRef]

Opt. Eng. (2)

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

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10-22 (2000).
[CrossRef]

Opt. Express (2)

Opt. Las. Eng. (3)

M. Sjodahl, “Some recent advances in electronic speckle photography,” Opt. Las. Eng. 29, 125-144 (1998).
[CrossRef]

H. J. Dai and X. Y. Su, “Shape measurement by digital speckle temporal sequence correlation with digital light projector,” Opt. Las. Eng. 40, 793-800 (2001).

J. X. Gao, W. Xu, and J. P. Geng, “3D shape reconstruction of teeth by shadow speckle correlation method,” Opt. Las. Eng. 44, 455-465 (2006).
[CrossRef]

Opt. Lett. (1)

Optik (1)

J. Brillaud and F. Lagattu, “Digital correlation of grainy shadow images for surface profile measurement,” Optik 117, 411-417 (2006).
[CrossRef]

Other (1)

B. Pan, H. M. Xie, L. H. Yang, and Z. Y. Wang, “Accurate measurement of satellite antenna surface using three-dimensional digital image correlation technique,” Strain 10.1111/j.1475-1305 (2008).

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Figures (9)

Fig. 1
Fig. 1

Experimental setup of speckle projection profilometry; random speckle pattern was projected onto the specimen surface by a projector and recorded by a CCD camera from the normal view direction.

Fig. 2
Fig. 2

Schematic geometry of the speckle projection system; the out-of-plane height of point C leads to the in-plane motion of the speckle pattern from B to A.

Fig. 3
Fig. 3

Actual experimental setup of speckle projection profilometry.

Fig. 4
Fig. 4

Projected speckle images on (a) the specimen surface, the yellow rectangular is the calculation area, and (b) the reference plane.

Fig. 5
Fig. 5

Computed v-displacement component.

Fig. 6
Fig. 6

(top) Computed v-displacement and (bottom) the ZNCC correlation coefficient along line A A using a different shape function.

Fig. 7
Fig. 7

Reconstructed 3D profile of the cylinder surface and the gauge object.

Fig. 8
Fig. 8

Side view of the cylinder surface and the gauge object.

Fig. 9
Fig. 9

Profile of a human hand using speckle projection profilometry: (a) contour plot superimposed on the speckle image, (b) 3D plot.

Equations (7)

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

Δ y h ( y ) = d c y l c + d p + y + Δ y l p = ( d c l c + d p l p ) + ( 1 l p 1 l c ) y + 1 l p Δ y ,
h ( y ) = Δ y D 0 + D 1 y + D 2 Δ y ,
h ( y ) = Δ y D 0 .
h ( y ) = k v ,
x = x 0 + Δ x + u + u x Δ x + u y Δ y + 1 2 u x x Δ x 2 + 1 2 u y y Δ y 2 + u x y Δ x Δ y , y = y 0 + Δ y + v + v x Δ x + v y Δ y + 1 2 v x x Δ x 2 + 1 2 v y y Δ y 2 + v x y Δ x Δ y ,
C Z N S S D ( p ) = x = M M y = M M [ f ( x , y ) f m x = M M y = M M [ f ( x , y ) f m ] 2 g ( x , y ) g m x = M M y = M M [ g ( x , y ) g m ] 2 ] 2 = 2 [ 1 x = M M y = M M [ f ( x , y ) f m ] × [ g ( x , y ) g m ] x = M M y = M M [ f ( x , y ) f m ] 2 x = M M y = M M [ g ( x , y ) g m ] 2 ] = 2 [ 1 C Z N C C ( p ) ] .
P = P 0 C ( P 0 ) C ( P 0 ) ,

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