Abstract

This paper proposes a novel method to substantially reduce motion-introduced phase error in phase-shifting profilometry. We first estimate the motion of an object from the difference between two subsequent 3D frames. After that, by leveraging the projector’s pinhole model, we can determine the motion-induced phase shift error from the estimated motion. A generic phase-shifting algorithm considering phase shift error is then utilized to compute the phase. Experiments demonstrated that proposed algorithm effectively improved the measurement quality by compensating for the phase shift error introduced by rigid and nonrigid motion for a standard single-projector and single-camera digital fringe projection system.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  7. H. Schreiber and J. H. Bruning, Optical Shop Testing, 3rd ed. (John Wiley & Sons, 2007).
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    [Crossref]
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    [Crossref] [PubMed]

2018 (1)

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

2014 (3)

2013 (1)

2009 (1)

2004 (1)

2000 (1)

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

Bruning, J. H.

H. Schreiber and J. H. Bruning, Optical Shop Testing, 3rd ed. (John Wiley & Sons, 2007).

Chen, Q.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

Feng, S.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

Gao, P.

Geist, E.

Gu, G.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

Guo, C.-S.

Guo, Q.

Han, B.

Harder, I.

Hu, Y.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

Karpinsky, N.

Li, B.

Lindlein, N.

Lu, L.

Mantel, K.

Schreiber, H.

H. Schreiber and J. H. Bruning, Optical Shop Testing, 3rd ed. (John Wiley & Sons, 2007).

Sha, B.

Tao, T.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

Wang, Z.

Xi, J.

Xie, Y.-Y.

Yao, B.

Yu, Y.

Zhang, M.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

Zhang, S.

Zhang, X.-J.

Zhang, Z.

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

Zuo, C.

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

Appl. Opt. (1)

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

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

Opt. Express (1)

Opt. Laser Eng. (1)

S. Feng, C. Zuo, T. Tao, Y. Hu, M. Zhang, Q. Chen, and G. Gu, “Robust dynamic 3-d measurements with motion-compensated phase-shifting profilometry,” Opt. Laser Eng. 103, 127–138 (2018).
[Crossref]

Opt. Lett. (4)

Other (1)

H. Schreiber and J. H. Bruning, Optical Shop Testing, 3rd ed. (John Wiley & Sons, 2007).

Supplementary Material (2)

NameDescription
» Visualization 1       motion artifact reduction
» Visualization 2       motion artefact reduction

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Figures (4)

Fig. 1
Fig. 1 Object motion could introduce nonhomogeous phase shift error.
Fig. 2
Fig. 2 Measurement result of a moving sphere (associated with Visualization 1). (a) 3D results from standard phase-shifting method; (b) 3D result using our proposed phase-shift error compensation method; (c) error map of the result shown in (a) (mean 0.482 mm, standard deviation 0.209 mm); (d) error map of the result shown in (b) (mean 0.032 mm, standard deviation 0.037 mm).
Fig. 3
Fig. 3 Experiment results of an object with complex geometry. (a) the photograph of the object; (b) 3D result without employing motion error compensation while the object is moving; (c) 3D result from proposed method while the object is moving; (d) 3D result while the object is stationary (i.e., ground truth).
Fig. 4
Fig. 4 Experiment results of a dynamically deformable complex object, human facial expression (associated with Visualization 2). (a) 3D result without employing our proposed method; (b) 3D result after employing our proposed phase shift error compensation algorithm; (c) texture mapped 3D result of (a); (d) texture mapped 3D result of (b).

Equations (11)

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I k ( u c , v c ) = I ( u c , v c ) + I ( u c , v c ) cos [ Φ ( u c , v c ) δ k ] ,
[ a 0 ( u c , v c ) a 1 ( u c , v c ) a 2 ( u c , v c ) ] = [ M cos δ k sin δ k cos δ k cos 2 δ k cos δ k sin δ k sin δ k cos δ k sin δ k sin 2 δ k ] 1 [ I k I k cos δ k I k sin δ k ] ,
ϕ ( u c , v c ) = tan 1 [ a 2 ( u c , v c ) a 1 ( u c , v c ) ] .
Φ ( u c , v c ) = ϕ ( u c , v c ) + k ( u c , v c ) × 2 π ,
δ k ¯ ( u c , v c ) = δ k ( u c , v c ) + ϵ k ( u c , v c ) ,
ϵ 1 = Φ 1 ¯ Φ 1 .
ϵ 2 = Φ 2 ¯ Φ 2 .
s p { u p v p 1 } = A p [ R p , t p ] { x w y w z w 1 } = [ P 11 P 12 P 13 P 14 P 21 P 22 P 23 P 24 P 31 P 32 P 33 P 34 ] { x w y w z w 1 }
u p x w = P 11 ( P 32 y w + P 33 z w + P 34 ) P 1 1 ( P 12 y w + P 13 z w + P 14 ) ( P 31 x w + P 32 y w + P 33 z w + P 34 ) 2 .
ϵ ( u c , v c ) = 2 π λ ( u p x w Δ x w + u p y w Δ y w + u p z w Δ z w ) .
Δ x w = x w ¯ x w N ; Δ y w = y w ¯ y w N ; Δ z w = z w ¯ z w N ,

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