Abstract

Fringe projection profilometry has become one of the most popular 3D information acquisition techniques being developed over the past three decades. However, the general and practical issues on valid point detection, including object segmentation, error correction and noisy point removal, have not been studied thoroughly. Furthermore, existing valid point detection techniques require multiple case-dependent thresholds which increase processing inconvenience. In this paper, we proposed a new valid point detection framework, which includes the k-means clustering for automatic background segmentation, unwrapping error correction based on theoretical analysis, and noisy point detection in both temporal and spatial directions with automatic threshold setting. Experimental results are given to validate the proposed framework.

© 2015 Optical Society of America

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Opt. Lett. 41(21) 4951-4954 (2016)

References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  10. Y. Hung, L. Lin, H. Shang, and B. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39(1), 143–149 (2000).
  11. H. Liu, W. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringeprofilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1), 65–80 (2003).
    [Crossref]
  12. S. Zhang and S. T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14(7), 2644–2649 (2006).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  14. D. Moreno and G. Taubin, “Simple, Accurate, and Robust Projector-Camera calibration,” 3D Imaging, Modeling, Processing, Visualization and Transmission (3DIMPVT), 2012 Second International Conference on, 464–471 (2012).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  18. L. Huang and A. K. Asundi, “Phase invalidity identification framework with the temporal phase unwrapping methods,” Meas. Sci. Technol. 22(3), 035304 (2011).
    [Crossref]
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    [Crossref] [PubMed]
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  22. Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).
  23. R. E. Walpole, R. H. Myers, S. L. Myers, and K. Ye, Probability and Statistics for Engineers and Scientists, 8th edition (Person Prentice Hall, 2007).
  24. N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Sys., Man., Cyber. 9(1), 62–66 (1979).
    [Crossref]

2014 (1)

2011 (1)

L. Huang and A. K. Asundi, “Phase invalidity identification framework with the temporal phase unwrapping methods,” Meas. Sci. Technol. 22(3), 035304 (2011).
[Crossref]

2010 (4)

F. Chen, X. Su, and L. Xiang, “Analysis and identification of phase error in phase measuring profilometry,” Opt. Express 18(11), 11300–11307 (2010).
[Crossref] [PubMed]

L. Huang, P. S. Chua, and A. Asundi, “Least-squares calibration method for fringe projection profilometry considering camera lens distortion,” Appl. Opt. 49(9), 1539–1548 (2010).
[Crossref] [PubMed]

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Z. Wang, D. A. Nguyen, and J. C. Bames, “Some practical considerations for fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

2009 (4)

2006 (1)

2004 (1)

2003 (2)

H. Liu, W. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringeprofilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1), 65–80 (2003).
[Crossref]

A. Baldi, “Phase unwrapping by region growing,” Appl. Opt. 42(14), 2498–2505 (2003).
[Crossref] [PubMed]

2001 (1)

S. Su and X. Lian, “Phase unwrapping algorithm based on fringe frequency analysis in Fourier-transform profilometry,” Opt. Eng. 40(4), 637–643 (2001).
[Crossref]

2000 (1)

Y. Hung, L. Lin, H. Shang, and B. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39(1), 143–149 (2000).

1997 (2)

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997).
[Crossref] [PubMed]

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrappingand a spatial light modulator-based fringe projector,” Opt. Eng. 36(2), 610–615 (1997).
[Crossref]

1984 (1)

1979 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Sys., Man., Cyber. 9(1), 62–66 (1979).
[Crossref]

Asundi, A.

Asundi, A. K.

L. Huang and A. K. Asundi, “Phase invalidity identification framework with the temporal phase unwrapping methods,” Meas. Sci. Technol. 22(3), 035304 (2011).
[Crossref]

Baldi, A.

Bames, J. C.

Z. Wang, D. A. Nguyen, and J. C. Bames, “Some practical considerations for fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Cai, L. Z.

Chang, Y.

Chen, F.

Chen, M.

Chua, P. S.

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Guo, H.

Guo, J. P.

Hahn, J.

Halioua, M.

He, H.

Huang, L.

Hung, Y.

Y. Hung, L. Lin, H. Shang, and B. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39(1), 143–149 (2000).

Huntley, J. M.

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrappingand a spatial light modulator-based fringe projector,” Opt. Eng. 36(2), 610–615 (1997).
[Crossref]

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997).
[Crossref] [PubMed]

Kemao, Q.

Kim, E. H.

Kim, H.

Lee, B.

Li, A. M.

Li, Z.

Lian, X.

S. Su and X. Lian, “Phase unwrapping algorithm based on fringe frequency analysis in Fourier-transform profilometry,” Opt. Eng. 40(4), 637–643 (2001).
[Crossref]

Lin, L.

Y. Hung, L. Lin, H. Shang, and B. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39(1), 143–149 (2000).

Liu, H.

H. Liu, W. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringeprofilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1), 65–80 (2003).
[Crossref]

Liu, H. C.

Meng, X. F.

Nguyen, D. A.

Z. Wang, D. A. Nguyen, and J. C. Bames, “Some practical considerations for fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Otsu, N.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Sys., Man., Cyber. 9(1), 62–66 (1979).
[Crossref]

Pan, B.

Park, B.

Y. Hung, L. Lin, H. Shang, and B. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39(1), 143–149 (2000).

Peng, X.

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Reichard, K.

H. Liu, W. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringeprofilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1), 65–80 (2003).
[Crossref]

Saldner, H. O.

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrappingand a spatial light modulator-based fringe projector,” Opt. Eng. 36(2), 610–615 (1997).
[Crossref]

H. O. Saldner and J. M. Huntley, “Temporal phase unwrapping: application to surface profiling of discontinuous objects,” Appl. Opt. 36(13), 2770–2775 (1997).
[Crossref] [PubMed]

Shang, H.

Y. Hung, L. Lin, H. Shang, and B. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39(1), 143–149 (2000).

Song, L.

Srinivasan, V.

Su, S.

S. Su and X. Lian, “Phase unwrapping algorithm based on fringe frequency analysis in Fourier-transform profilometry,” Opt. Eng. 40(4), 637–643 (2001).
[Crossref]

Su, W.

H. Liu, W. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringeprofilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1), 65–80 (2003).
[Crossref]

Su, X.

Wang, P.

Wang, Y. R.

Wang, Z.

Z. Wang, D. A. Nguyen, and J. C. Bames, “Some practical considerations for fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Xi, J.

Xiang, L.

Xing, G.

Yau, S. T.

Yin, S.

H. Liu, W. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringeprofilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1), 65–80 (2003).
[Crossref]

Zhang, S.

S. Zhang, “Phase unwrapping error reduction frameworkfor a multiple-wavelength phase-shifting algorithm,” Opt. Eng. 48(10), 105601 (2009).
[Crossref]

S. Zhang and S. T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14(7), 2644–2649 (2006).
[Crossref] [PubMed]

Appl. Opt. (5)

IEEE Trans. Sys., Man., Cyber. (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Sys., Man., Cyber. 9(1), 62–66 (1979).
[Crossref]

Meas. Sci. Technol. (1)

L. Huang and A. K. Asundi, “Phase invalidity identification framework with the temporal phase unwrapping methods,” Meas. Sci. Technol. 22(3), 035304 (2011).
[Crossref]

Opt. Commun. (1)

H. Liu, W. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringeprofilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1), 65–80 (2003).
[Crossref]

Opt. Eng. (4)

S. Zhang, “Phase unwrapping error reduction frameworkfor a multiple-wavelength phase-shifting algorithm,” Opt. Eng. 48(10), 105601 (2009).
[Crossref]

Y. Hung, L. Lin, H. Shang, and B. Park, “Practical three-dimensional computer vision techniques for full-field surface measurement,” Opt. Eng. 39(1), 143–149 (2000).

H. O. Saldner and J. M. Huntley, “Profilometry using temporal phase unwrappingand a spatial light modulator-based fringe projector,” Opt. Eng. 36(2), 610–615 (1997).
[Crossref]

S. Su and X. Lian, “Phase unwrapping algorithm based on fringe frequency analysis in Fourier-transform profilometry,” Opt. Eng. 40(4), 637–643 (2001).
[Crossref]

Opt. Express (4)

Opt. Lasers Eng. (2)

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Z. Wang, D. A. Nguyen, and J. C. Bames, “Some practical considerations for fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[Crossref]

Opt. Lett. (2)

Other (4)

D. Moreno and G. Taubin, “Simple, Accurate, and Robust Projector-Camera calibration,” 3D Imaging, Modeling, Processing, Visualization and Transmission (3DIMPVT), 2012 Second International Conference on, 464–471 (2012).
[Crossref]

B. S. Everitt, S. Landau, M. Leese, and D. Stahl, Cluster Analysis, 5th edition (Wiley, 2011).

Q. Kemao, Windowed Fringe Pattern Analysis (SPIE, 2013).

R. E. Walpole, R. H. Myers, S. L. Myers, and K. Ye, Probability and Statistics for Engineers and Scientists, 8th edition (Person Prentice Hall, 2007).

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Figures (7)

Fig. 1
Fig. 1 Proposed valid point detection flowchart.
Fig. 2
Fig. 2 Measured modulation and phases.(a) The calculated modulation; (b) the calculated wrapped phase; (c) the unwrapped phase; (d) the manually separated object phase as the ground true.
Fig. 3
Fig. 3 Separated object phases and errors. (a) The separated object phase using a threshold of 8; (b) the point differences between Fig. 2(d) and Fig. 3(a); (c) the separated object phase using the proposed k-means clustering; (d) the point differences between Fig. 2(d) and Fig. 3(c).
Fig. 4
Fig. 4 Phase Correction. (a) The corrected phase; (b) the wrapped phase, the continuous phase before and after correction at the region highlighted by the red rectangle in Fig. 4(a).
Fig. 5
Fig. 5 Reconstructed model.(a) The reconstructed model before noisy point detection; (b) the model after noisy point detection; (c) the detected noisy points.
Fig. 6
Fig. 6 Front-view results(a) from Zhang’s framework, (b) from the modified Zhang’s framework, (c) from Huang et al.’s framework, (d) from the modified Huang et al.’s framework, and (e) from the proposed framework.
Fig. 7
Fig. 7 Top view results(a) from Zhang’s framework, (b) from modified Zhang’s framework,(c) from Huang et al.’s framework, (d) from modified Huang et al.’s framework, and (e) from the proposed framework.

Equations (29)

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f ˜ l,t ( u p , v p )=127+127cos[ Φ ˜ l ( u p , v p )+ 2tπ T ],l=0,1,...,L1,t=0,1,...,T1,
Φ ˜ l ( u p , v p )=h Φ ˜ l1 ( u p , v p ), Φ ˜ 0 ( u p , v p )= 2π u p m [ 0,2π ),l=1,2,...L1, u p =0,1,...m1,
f l,t ( u c , v c )= a l ( u c , v c )+ b l ( u c , v c )cos[ Φ l ( u c , v c )+ 2tπ T ],l=0,1,...,L1,t=0,1,...,T1,
Φ l ( u c , v c )h Φ l1 ( u c , v c ), Φ 0 [ 0,2π ),l=1,2,...L1.
φ l =arctan2( f l,3 f l,1 , f l,0 f l,2 )[ 0,2π ).
Φ l = φ l +2 λ l π, Φ o = φ o ,
λ l =round( h Φ l1 φ l 2π ),
Φ L1 ( u c , v c )= Φ ˜ L1 ( u p , v p )= h L1 Φ ˜ 0 ( u p , v p )= h L1 2π u p m ,
s c [ u c , v c ,1 ] T = M c [ X,Y,Z,1 ] T s p [ u p , v p ,1 ] T = M p [ X,Y,Z,1 ] T ,
M [ X Y Z ] T =R,
M=[ M c ( 0,0 ) M c ( 2,0 ) u c M c ( 0,1 ) M c ( 2,1 ) u c M c ( 0,2 ) M c ( 2,2 ) u c M c ( 1,0 ) M c ( 2,0 ) v c M c ( 1,1 ) M c ( 2,1 ) v c M c ( 1,2 ) M c ( 2,2 ) v c M p ( 0,0 ) M p ( 2,0 ) u p M p ( 0,1 ) M p ( 2,1 ) u p M p ( 0,2 ) M p ( 2,2 ) u p ],
R=[ M c ( 2,3 ) u c M c ( 0,3 ) M c ( 2,3 ) v c M c ( 1,3 ) M p ( 2,3 ) u p M p ( 0,3 ) ].
b ¯ = 1 L l=0 L1 [ 2 T ( t=0 T1 f l,t sin 2tπ T ) 2 + ( t=0 T1 f l,t cos 2tπ T ) 2 ] .
p c { object, b ¯ t b background, b ¯ < t b .
i=1 k b ¯ S i | b ¯ c i | 2 minimum.
{ c 1 =mean( b ¯ | b ¯ > c 2 ) c 2 =mean( b ¯ ) c 3 =mean( b ¯ | b ¯ < c 2 ) .
( φ l ) n =arctan2[ sin( Φ l )+ n l,3 n l,1 2 b l ,cos( Φ l )+ n l,0 n l,2 2 b l ][ 0,2π ).
( φ l ) n = φ l +Δ φ l + ρ l 2π
ρ l ={ 0, Δ φ l φ l <2πΔ φ l 1, φ l <Δ φ l 1, φ l 2πΔ φ l ,
Δ φ l cos( Φ l )( n l,3 n l,1 )sin( Φ l )( n l,0 n l,2 ) 2 b l ,
( λ 1 ) n =round[ h( φ 0 +Δ φ 0 + ρ 0 2π )( φ 1 +Δ φ 1 + ρ 1 2π ) 2π ] =round[ h φ 0 φ 1 +( hΔ φ 0 Δ φ 1 ) 2π ]+h ρ 0 ρ 1 = λ 1 +h ρ 0 ρ 1 .
( Φ 1 ) n = ( φ 1 ) n + ( λ 1 ) n 2π= φ 1 +Δ φ 1 + λ 1 2π+h ρ 0 2π.
Φ L1 ( x,y+1 )={ Φ L1 ( x,y+1 ) | Φ 0 ( x,y+1 ) Φ 0 ( x,y ) |<3π/2 Φ L1 ( x,y+1 )2π h L1 Φ 0 ( x,y+1 ) Φ 0 ( x,y )>3π/2 Φ L1 ( x,y+1 )+2π h L1 Φ 0 ( x,y+1 ) Φ 0 ( x,y )<3π/2 .
Φ f = l=0 L1 Φ l h l / l=0 L1 h 2l ,
RMSE= l=0 L1 ( Φ l h l Φ f ) 2 L .
| Φ xx |< t 2nd .
t RMSE = α 1 t Otsu ,
d ε,η = ( X u c +ε, v c +η X u c , v c ) 2 + ( Y u c +ε, v c +η Y u c , v c ) 2 + ( Z u c +ε, v c +η Z u c , v c ) 2 .
t d = α 2 mean ( ε,η ) S 1 ( d ε,η )

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