Abstract

In this paper, a generalized reference-plane-based calibration method is proposed in optical triangular profilometry by exploring projection ray tracing method and image ray tracing method. The pin-hole camera model is used to model the camera and the projector, and parallel planes model is used to model the reference and test planes. The camera, projector, and planes can be in arbitrary positions and arbitrary directions. The reciprocal of the height and the reciprocal of the phase shift (or pixel position vertical distance) are in linear relationship. Experiments are conducted to verify the proposed method.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  16. O. Faugeras, “Three-Dimensional Computer Vision: A Geometric Viewpoint,” (MIT Press, 1993).
  17. C. Steger, “An Unbiased Detector of Curvilinear Structures,” IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (1998).
    [CrossRef]
  18. P. S. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45(21), 5086–5091 (2006).
    [CrossRef] [PubMed]
  19. J. Meneses, T. Gharbi, and P. Humbert, “Phase-unwrapping algorithm for images with high noise content based on a local histogram,” Appl. Opt. 44(7), 1207–1215 (2005).
    [CrossRef] [PubMed]

2009

2007

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A, Pure Appl. Opt. 9(6), S66–S75 (2007).
[CrossRef]

H. Du and Z. Wang, “Three-dimensional shape measurement with an arbitrarily arranged fringe projection profilometry system,” Opt. Lett. 32(16), 2438–2440 (2007).
[CrossRef] [PubMed]

2006

2005

2004

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 467–471 (2004).

2000

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

1999

1998

C. Steger, “An Unbiased Detector of Curvilinear Structures,” IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (1998).
[CrossRef]

1994

W. S. Zhou and X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41(1), 89–94 (1994).
[CrossRef]

Asundi, A.

Bi, H.

Bothe, T.

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 467–471 (2004).

Burton, D. R.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A, Pure Appl. Opt. 9(6), S66–S75 (2007).
[CrossRef]

Chen, L.

Chen, M.

Cui, S.

Du, H.

Gharbi, T.

Guo, H.

He, H.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[CrossRef]

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[CrossRef]

P. S. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45(21), 5086–5091 (2006).
[CrossRef] [PubMed]

Humbert, P.

Juptner, W. P.

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 467–471 (2004).

Karout, S. A.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A, Pure Appl. Opt. 9(6), S66–S75 (2007).
[CrossRef]

Lalor, M. J.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A, Pure Appl. Opt. 9(6), S66–S75 (2007).
[CrossRef]

Meneses, J.

Park, S.

Quan, C.

Rajoub, B. A.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A, Pure Appl. Opt. 9(6), S66–S75 (2007).
[CrossRef]

Saenz, R. L.

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 467–471 (2004).

Steger, C.

C. Steger, “An Unbiased Detector of Curvilinear Structures,” IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (1998).
[CrossRef]

Su, X. Y.

W. S. Zhou and X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41(1), 89–94 (1994).
[CrossRef]

Tay, C. J.

Wang, W.

Wang, Z.

Wensen, Z.

Xie, H.

Xie, Y.

Yu, Y.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[CrossRef]

Zhang, S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[CrossRef]

P. S. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45(21), 5086–5091 (2006).
[CrossRef] [PubMed]

Zhang, Z.

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

Zheng, P.

Zhou, W. S.

W. S. Zhou and X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41(1), 89–94 (1994).
[CrossRef]

Zhu, X.

Appl. Opt.

IEEE Trans. Pattern Anal. Mach. Intell.

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

C. Steger, “An Unbiased Detector of Curvilinear Structures,” IEEE Trans. Pattern Anal. Mach. Intell. 20(2), 113–125 (1998).
[CrossRef]

J. Mod. Opt.

W. S. Zhou and X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt. 41(1), 89–94 (1994).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

B. A. Rajoub, M. J. Lalor, D. R. Burton, and S. A. Karout, “A new model for measuring object shape using non-collimated fringe-pattern projections,” J. Opt. A, Pure Appl. Opt. 9(6), S66–S75 (2007).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

H. Guo, H. He, Y. Yu, and M. Chen, “Least-squares calibration method for fringe projection profilometry,” Opt. Eng. 44(3), 033603 (2005).
[CrossRef]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45(8), 083601 (2006).
[CrossRef]

R. L. Saenz, T. Bothe, and W. P. Juptner, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43, 467–471 (2004).

Opt. Express

Opt. Lett.

Other

J. Heikkila, and O. Silven, “Calibration Procedure for short focal length off-the-shelf CCD cameras,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Vienna, Austria, 1996), pp. 166–170.

O. Faugeras, “Three-Dimensional Computer Vision: A Geometric Viewpoint,” (MIT Press, 1993).

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Figures (5)

Fig. 1
Fig. 1

Schematics of the system setup.

Fig. 2
Fig. 2

Line stripe pattern of the projectors image and camera image. (a) A line stripe where v p = v p g i v e n on the projector image. (b) An image of the reference plane. (c) An image of the test plane. (d) The combination of two images.

Fig. 3
Fig. 3

Experiments result for the line stripe pattern profilometry. (a) Camera image of the reference plane. (b) Camera image of one of test planes. (c) The combination image of the extracted test and reference lines. (d) Plot of parameter p 1 and variable u c . (e) Measuring result of a given block. (f) Error of (e).

Fig. 4
Fig. 4

The measured result of the given plane. (a) Measured result. (b) The error of the measured result

Fig. 5
Fig. 5

Measured result of face. (a) 2D show of the face, gray value represented the height dedicated by the color bar on the right side of the Fig. 5(b) 3D mesh grid of the measured face.

Equations (31)

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a x + b y + c z + d r e f = 0.
a x + b y + c z + d i = 0.
v s = [ a , b , c ] T .
h i = ( d i d r e f ) / a 2 + b 2 + c 2 .
X p = R p X 1 + t p .
s p [ u p v p 1 ] T = P p X p .
s p [ u p v p 1 ] T = P p ( R p X 1 + T p ) .
s c [ u c v c 1 ] T = P c ( R c X 1 + T c ) .
s p [ u p v p 1 ] T = M p X 1 + t b p .
s c [ u c v c 1 ] T = M c X 1 + t b c .
A X 1 = B .
v s T X 1 + d i = 0.
d i = v s T X 1 .
d i = a 1 v c + a 2 u c + a 3 + a 4 v p v c + a 5 v p u c + a 6 v p b 1 v c + b 2 u c + b 3 + b 4 v p v c + b 5 v p u c + b 6 v p .
d i = k c 1 u c + k c 2 v c + c 4 u c + c 5 + c 1 .
d r e f = k c 1 u c + k c 2 v c r e f + c 4 u c + c 5 + c 1 .
h i = k n 1 u c + k n 2 v c + c 4 u c + c 5 k n 1 u c + k n 2 v c r e f + c 4 u c + c 5 .
1 h i = ( v c r e f + c 4 u c + c 5 ) 2 k n 1 u c + k n 2 1 v c v c r e f v c r e f + c 4 u c + c 5 k n 1 u c + k n 2 .
1 h i = k c 1 u c + k c 2 ( d r e f c 1 ) 2 a 2 + b 2 + c 2 1 v c v c r e f 1 ( d r e f c 1 ) a 2 + b 2 + c 2 .
y = p 1 ( u c , v c ) x + p 2 .
p 1 ( u c , v c ) = k b 1 u c + k b 2 .
h ( u c , v c ) = { ( k b 1 u c + k b 2 ) ( v c v c r e f ) 1 + p 2 } 1 .
p 1 ( u c , v c , v p ) = k p 1 a v p + k p 1 b ( v p + k p 0 ) 2 u c + k p 2 a v p + k p 2 b ( v p + k p 0 ) 2 .
p 2 ( u c , v c , v p ) = ( k p a v p + k p b ) / ( v p + k p 0 ) .
v p = ϕ / 2 π .
v c 1 = k r c 1 v p 1 + k r c 0 + k r c 2 .
h = { p 1 ( u c , v c , v p ) ( v c v c r e f ) 1 + p 2 ( u c , v c , v p ) } 1
d i = t 1 + t 2 v p + t 3 .
1 h i = 1 d r e f t 1 t 2 ( d r e f t 1 ) 2 1 v p v p r e f .
h i = { p 1 ( u c , v c ) ( v p i v p r e f ) 1 + p 2 ( u c , v c ) } 1 .
u d = u + 2 P 1 u v + P 2 ( r 2 + 2 u 2 ) + K 1 u r 2 + K 2 u r 4 + K 3 u r 6 v d = v + 2 P 2 u v + P 1 ( r 2 + 2 v 2 ) + K 1 v r 2 + K 2 v r 4 + K 3 v r 6 .

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