Abstract

Commonly, fringe-projection photogrammetry involves two independent stages: system calibration and measurement. The measurement accuracy largely depends on the calibration procedure. However, the results of system calibration may be unstable in different occasions. In this Letter, we propose a robust self-calibration 3D shape measurement in fringe-projection photogrammetry by combining control and measurement points. The control points with known 3D coordinates are provided on the checkerboard, and the measurement points are identified by absolute phase information in the deformed fringes. The introduction of control points in the nonlinear collinearity equations can be regarded as invariant in the optimization procedure, which enhances the measurement robustness. Compared to the binocular model in fringe-projection technique, moreover, multiple-view ray intersection is utilized to reflect the advantage of photogrammetry in the fringe-projection 3D measurement.

© 2013 Optical Society of America

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References

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  1. T. Luhmann, ISPRS J. Photogramm. Remote Sens. 65, 558 (2010).
    [CrossRef]
  2. W. Schreiber and G. Notni, Opt. Eng. 39, 159 (2000).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. X. Su and W. Chen, Opt. Laser Eng. 42, 245 (2004).
    [CrossRef]
  13. C. Bräuer-Burchardt, Proc. SPIE 5962, 59620J (2005).
    [CrossRef]
  14. M. I. A. Lourakis and A. A. Argyros, ACM Trans. Math. Softw. 36, 1 (2009).
    [CrossRef]

2012 (1)

2010 (2)

T. Luhmann, ISPRS J. Photogramm. Remote Sens. 65, 558 (2010).
[CrossRef]

C. Bräuer-Burchardt, M. Möller, C. Munkelt, P. Kühmstedt, and G. Notni, Proc. SPIE 7830, 783019 (2010).
[CrossRef]

2009 (1)

M. I. A. Lourakis and A. A. Argyros, ACM Trans. Math. Softw. 36, 1 (2009).
[CrossRef]

2006 (2)

S. Zhang and S. T. Yau, Opt. Express 14, 2644 (2006).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
[CrossRef]

2005 (1)

C. Bräuer-Burchardt, Proc. SPIE 5962, 59620J (2005).
[CrossRef]

2004 (2)

X. Su and W. Chen, Opt. Laser Eng. 42, 245 (2004).
[CrossRef]

R. Legarda-Saenz, T. Bothe, and W. P. Jüptner, Opt. Eng. 43, 464 (2004).
[CrossRef]

2000 (3)

Z. Zhang, IEEE Trans. Pattern Anal. Machine Intell. 22, 1330 (2000).
[CrossRef]

W. Schreiber and G. Notni, Opt. Eng. 39, 159 (2000).
[CrossRef]

C. Reich, R. Ritter, and J. Thesing, Opt. Eng. 39, 224(2000).
[CrossRef]

Argyros, A. A.

M. I. A. Lourakis and A. A. Argyros, ACM Trans. Math. Softw. 36, 1 (2009).
[CrossRef]

Atkinson, K. B.

K. B. Atkinson, Close Range Photogrammetry and Machine Vision (Whittles, 1996).

Bothe, T.

R. Legarda-Saenz, T. Bothe, and W. P. Jüptner, Opt. Eng. 43, 464 (2004).
[CrossRef]

Bräuer-Burchardt, C.

C. Bräuer-Burchardt, M. Möller, C. Munkelt, P. Kühmstedt, and G. Notni, Proc. SPIE 7830, 783019 (2010).
[CrossRef]

C. Bräuer-Burchardt, Proc. SPIE 5962, 59620J (2005).
[CrossRef]

Chen, W.

X. Su and W. Chen, Opt. Laser Eng. 42, 245 (2004).
[CrossRef]

Gao, B. Z.

Huang, P. S.

S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
[CrossRef]

Jüptner, W. P.

R. Legarda-Saenz, T. Bothe, and W. P. Jüptner, Opt. Eng. 43, 464 (2004).
[CrossRef]

Kühmstedt, P.

C. Bräuer-Burchardt, M. Möller, C. Munkelt, P. Kühmstedt, and G. Notni, Proc. SPIE 7830, 783019 (2010).
[CrossRef]

Legarda-Saenz, R.

R. Legarda-Saenz, T. Bothe, and W. P. Jüptner, Opt. Eng. 43, 464 (2004).
[CrossRef]

Li, A.

Liu, X.

Lourakis, M. I. A.

M. I. A. Lourakis and A. A. Argyros, ACM Trans. Math. Softw. 36, 1 (2009).
[CrossRef]

Luhmann, T.

T. Luhmann, ISPRS J. Photogramm. Remote Sens. 65, 558 (2010).
[CrossRef]

Madsen, K.

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Technical University of Denmark, 2004).

Möller, M.

C. Bräuer-Burchardt, M. Möller, C. Munkelt, P. Kühmstedt, and G. Notni, Proc. SPIE 7830, 783019 (2010).
[CrossRef]

Munkelt, C.

C. Bräuer-Burchardt, M. Möller, C. Munkelt, P. Kühmstedt, and G. Notni, Proc. SPIE 7830, 783019 (2010).
[CrossRef]

Nielsen, H. B.

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Technical University of Denmark, 2004).

Notni, G.

C. Bräuer-Burchardt, M. Möller, C. Munkelt, P. Kühmstedt, and G. Notni, Proc. SPIE 7830, 783019 (2010).
[CrossRef]

W. Schreiber and G. Notni, Opt. Eng. 39, 159 (2000).
[CrossRef]

Peng, X.

Reich, C.

C. Reich, R. Ritter, and J. Thesing, Opt. Eng. 39, 224(2000).
[CrossRef]

Ritter, R.

C. Reich, R. Ritter, and J. Thesing, Opt. Eng. 39, 224(2000).
[CrossRef]

Schreiber, W.

W. Schreiber and G. Notni, Opt. Eng. 39, 159 (2000).
[CrossRef]

Su, X.

X. Su and W. Chen, Opt. Laser Eng. 42, 245 (2004).
[CrossRef]

Thesing, J.

C. Reich, R. Ritter, and J. Thesing, Opt. Eng. 39, 224(2000).
[CrossRef]

Tingleff, O.

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Technical University of Denmark, 2004).

Yau, S. T.

Yin, Y.

Zhang, S.

S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
[CrossRef]

S. Zhang and S. T. Yau, Opt. Express 14, 2644 (2006).
[CrossRef]

Zhang, Z.

Z. Zhang, IEEE Trans. Pattern Anal. Machine Intell. 22, 1330 (2000).
[CrossRef]

ACM Trans. Math. Softw. (1)

M. I. A. Lourakis and A. A. Argyros, ACM Trans. Math. Softw. 36, 1 (2009).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (1)

Z. Zhang, IEEE Trans. Pattern Anal. Machine Intell. 22, 1330 (2000).
[CrossRef]

ISPRS J. Photogramm. Remote Sens. (1)

T. Luhmann, ISPRS J. Photogramm. Remote Sens. 65, 558 (2010).
[CrossRef]

Opt. Eng. (4)

W. Schreiber and G. Notni, Opt. Eng. 39, 159 (2000).
[CrossRef]

C. Reich, R. Ritter, and J. Thesing, Opt. Eng. 39, 224(2000).
[CrossRef]

S. Zhang and P. S. Huang, Opt. Eng. 45, 083601 (2006).
[CrossRef]

R. Legarda-Saenz, T. Bothe, and W. P. Jüptner, Opt. Eng. 43, 464 (2004).
[CrossRef]

Opt. Express (1)

Opt. Laser Eng. (1)

X. Su and W. Chen, Opt. Laser Eng. 42, 245 (2004).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (2)

C. Bräuer-Burchardt, Proc. SPIE 5962, 59620J (2005).
[CrossRef]

C. Bräuer-Burchardt, M. Möller, C. Munkelt, P. Kühmstedt, and G. Notni, Proc. SPIE 7830, 783019 (2010).
[CrossRef]

Other (2)

K. B. Atkinson, Close Range Photogrammetry and Machine Vision (Whittles, 1996).

K. Madsen, H. B. Nielsen, and O. Tingleff, Methods for Non-Linear Least Squares Problems, 2nd ed. (Technical University of Denmark, 2004).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic diagram of fringe-projection photogrammetry.

Fig. 2.
Fig. 2.

(a) Reprojection error and (b) 3D reconstruction error versus noise when bundle adjustment (BA) is operated with and without control points.

Fig. 3.
Fig. 3.

Reprojection error versus the (a) number of control and (b) measurement points.

Fig. 4.
Fig. 4.

Horizontal and vertical projected fringes captured in one position.

Fig. 5.
Fig. 5.

(a) Final 3D measurement results. (b) Histogram comparison of reprojection errors in self-calibration implemented without and with control points.

Tables (1)

Tables Icon

Table 1. Comparisons of the Self-Calibration Results (Pixels)

Equations (4)

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

{λx^=K[RT]Xx=x^+δ(kc;x^),
{Δcki=R(ξk,Xc)XckΔmki=R(ξk,Xm)Xmk,
{argminf(ξ1,ξ2,ξk,Xm)=k=1Mp=1i[Δckp]2+k=1Mq=1j[Δckq]2subject toξ1,ξ2,ξk,XmR.
[Δξ1,Δξ2,Δξk,ΔXm]=(JTJ+μI)1Jε,

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