Abstract

Fringe-projection-based (FPB) three-dimensional (3D) imaging technique has become one of the most prevalent methods for 3D shape measurement and 3D image acquisition, and an essential component of the technique is the calibration process. This paper presents a framework for hyper-accurate system calibration with flexible setup and inexpensive hardware. Owing to the crucial improvement in the camera calibration technique, an enhanced governing equation for 3D shape determination, and an advanced flexible system calibration technique as well as some practical considerations on accurate fringe phase retrieval, the novel FPB 3D imaging technique can achieve a relative measurement accuracy of 0.010%. The validity and practicality are verified by both simulation and experiments.

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References

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    [CrossRef]
  4. Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
    [CrossRef]
  5. X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
    [CrossRef]
  6. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [CrossRef]
  7. J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceedings European Conference on Computer Vision (1998), pp. 158–174.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  13. T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. 35(12), 1992–1994 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  15. C. Engels, H. Stewenius, and D. Nister, “Bundle adjustment rules,” in Proceedings on Photogrammetric Computer Vision (2006), pp. 266–271.
  16. J. Heikkila, “Moment and curvature preserving technique for accurate ellipse boundary detection,” in Proceedings IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1998), pp. 734–737.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2011 (1)

2010 (5)

2009 (5)

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
[CrossRef]

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[CrossRef]

X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
[CrossRef]

B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
[CrossRef] [PubMed]

L. Xiong and S. Jia, “Phase-error analysis and elimination for nonsinusoidal waveforms in Hilbert transform digital-fringe projection profilometry,” Opt. Lett. 34(15), 2363–2365 (2009).
[CrossRef] [PubMed]

2008 (1)

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[CrossRef]

2007 (1)

2005 (1)

2000 (1)

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

Asundi, A.

Barnes, J.

Z. Wang, D. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[CrossRef]

Chihara, K.

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
[CrossRef]

Chua, P.

Datta, A.

A. Datta, J. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings IEEE International Conference on Computer Vision Workshops (IEEE, 2009), 1201–1208.

Dhome, M.

J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceedings European Conference on Computer Vision (1998), pp. 158–174.

Douxchamps, D.

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
[CrossRef]

Du, H.

Engels, C.

C. Engels, H. Stewenius, and D. Nister, “Bundle adjustment rules,” in Proceedings on Photogrammetric Computer Vision (2006), pp. 266–271.

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of art in structured light patterns for surface profilometry,” Pattern Recogn. 43(8), 2666–2680 (2010).
[CrossRef]

Heikkila, J.

J. Heikkila, “Moment and curvature preserving technique for accurate ellipse boundary detection,” in Proceedings IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1998), pp. 734–737.

Hoang, T.

Huang, L.

Jia, S.

Kanade, T.

A. Datta, J. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings IEEE International Conference on Computer Vision Workshops (IEEE, 2009), 1201–1208.

Kemao, Q.

Kim, J.

A. Datta, J. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings IEEE International Conference on Computer Vision Workshops (IEEE, 2009), 1201–1208.

Lavest, J.

J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceedings European Conference on Computer Vision (1998), pp. 158–174.

Li, Z.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[CrossRef]

Llado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of art in structured light patterns for surface profilometry,” Pattern Recogn. 43(8), 2666–2680 (2010).
[CrossRef]

Luu, L.

Ma, J.

Nguyen, D.

T. Hoang, B. Pan, D. Nguyen, and Z. Wang, “Generic gamma correction for accuracy enhancement in fringe-projection profilometry,” Opt. Lett. 35(12), 1992–1994 (2010).
[CrossRef] [PubMed]

Z. Wang, D. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[CrossRef]

Nister, D.

C. Engels, H. Stewenius, and D. Nister, “Bundle adjustment rules,” in Proceedings on Photogrammetric Computer Vision (2006), pp. 266–271.

Pan, B.

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of art in structured light patterns for surface profilometry,” Pattern Recogn. 43(8), 2666–2680 (2010).
[CrossRef]

Qian, K.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[CrossRef]

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of art in structured light patterns for surface profilometry,” Pattern Recogn. 43(8), 2666–2680 (2010).
[CrossRef]

Shi, Y.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[CrossRef]

Stewenius, H.

C. Engels, H. Stewenius, and D. Nister, “Bundle adjustment rules,” in Proceedings on Photogrammetric Computer Vision (2006), pp. 266–271.

Viala, M.

J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceedings European Conference on Computer Vision (1998), pp. 158–174.

Vo, M.

Wang, C.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[CrossRef]

Wang, Y.

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[CrossRef]

Wang, Z.

Weng, J.

Xie, H.

B. Pan, H. Xie, and Z. Wang, “Equivalence of digital image correlation criteria for pattern matching,” Appl. Opt. 49(28), 5501–5509 (2010).
[CrossRef] [PubMed]

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[CrossRef]

Xiong, L.

Zhang, X.

X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
[CrossRef]

Zhang, Z.

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

Zhong, J.

Zhu, L.

X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Pattern Anal. Mach. Intell. (2)

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

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 376–383 (2009).
[CrossRef]

Meas. Sci. Technol. (1)

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20(6), 062001 (2009).
[CrossRef]

Opt. Eng. (2)

Z. Li, Y. Shi, C. Wang, and Y. Wang, “Accurate calibration method for a structured light system,” Opt. Eng. 47(5), 053604 (2008).
[CrossRef]

X. Zhang and L. Zhu, “Projector calibration from the camera image point of view,” Opt. Eng. 48(11), 117208 (2009).
[CrossRef]

Opt. Lasers Eng. (1)

Z. Wang, D. Nguyen, and J. Barnes, “Some practical considerations in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 218–225 (2010).
[CrossRef]

Opt. Lett. (6)

Pattern Recogn. (1)

J. Salvi, S. Fernandez, T. Pribanic, and X. Llado, “A state of art in structured light patterns for surface profilometry,” Pattern Recogn. 43(8), 2666–2680 (2010).
[CrossRef]

Other (4)

C. Engels, H. Stewenius, and D. Nister, “Bundle adjustment rules,” in Proceedings on Photogrammetric Computer Vision (2006), pp. 266–271.

J. Heikkila, “Moment and curvature preserving technique for accurate ellipse boundary detection,” in Proceedings IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1998), pp. 734–737.

J. Lavest, M. Viala, and M. Dhome, “Do we really need an accurate calibration pattern to achieve a reliable camera calibration?” in Proceedings European Conference on Computer Vision (1998), pp. 158–174.

A. Datta, J. Kim, and T. Kanade, “Accurate camera calibration using iterative refinement of control points,” in Proceedings IEEE International Conference on Computer Vision Workshops (IEEE, 2009), 1201–1208.

Supplementary Material (1)

» Media 1: MOV (3987 KB)     

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Figures (14)

Fig. 1
Fig. 1

The conversion from raw image (left) to frontal image (middle) enables the correlation with the ring templates (right).

Fig. 2
Fig. 2

Representative images of system calibration: calibration board with projection fringes, unwrapped phase map, and out-of-reference-plane height map.

Fig. 3
Fig. 3

Localization errors of the control points obtained by: (a) Heikkila’s method, and (b) the frontal image correlation method.

Fig. 4
Fig. 4

Convergence of the proposed camera calibration scheme.

Fig. 5
Fig. 5

Errors of control point detection with different interpolation methods.

Fig. 6
Fig. 6

Reprojection error of camera calibration with different interpolation methods.

Fig. 7
Fig. 7

Reprojection errors at the control points obtained by: (a) the conventional method, and (b) the frontal image correlation method. The vector scales are different in the figures for clear illustration purpose.

Fig. 8
Fig. 8

Phase retrieval error as a function of: (a) number of images, and (b) gamma pre-encoded values.

Fig. 9
Fig. 9

The effect of pre-encoded gamma values on the captured fringe patterns.

Fig. 10
Fig. 10

3D imaging results of a plate with eight gage blocks.

Fig. 11
Fig. 11

A conch shell and its 3D images observed from five different views.

Fig. 12
Fig. 12

A printed circuit board, the 2D height map, and the 3D rendered surface.

Fig. 13
Fig. 13

A horse sculpture, a 2D height map in color, and the 3D images.

Fig. 14
Fig. 14

A lion toy and its 3D images ( Media 1).

Tables (2)

Tables Icon

Table 1 Retrieved calibration parameters and their accuracy assessment

Tables Icon

Table 2 Actual and measured heights of gage blocks

Equations (16)

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

s { m 1 } = A [ R T ] { M 1 } , A = [ α γ u 0 0 β v 0 0 0 1 ]
x c n ' = ( 1 + a 0 r 2 + a 1 r 4 + a 2 r 6 ) x c n + ( p 0 + r 2 p 2 ) ( r 2 + 2 x c n 2 ) + 2 ( p 1 + r 2 p 3 ) w + s 0 r 2 + s 2 r 4 y c n ' = ( 1 + a 0 r 2 + a 1 r 4 + a 2 r 6 ) y c n + ( p 1 + r 2 p 3 ) ( r 2 + 2 y c n 2 ) + 2 ( p 0 + r 2 p 2 ) w + s 1 r 2 + s 3 r 4 r 2 = x c n 2 + y c n 2 , w = x c n y c n
{ x c n y c n 1 } = A 1 { u v 1 } , { x c n ' y c n ' 1 } = A 1 { u v 1 }
S = i = 1 k j = 1 l | | m i j P ( A , φ , ρ i , T i , M j ) | | 2
C = i = 1 N [ a f ( x i , y i ) + b g ( x i ' , y i ' ) ] 2
x i ' = x i + ξ + s x ( x i x 0 ) y i ' = y i + η + s y ( y i y 0 )
I 0 i ( x , y ) = I c [ 1 + cos ( 2 π f x / W + δ i ) ]
I i ( u , v ) = a ( u , v ) + j = 1 p b j ( u , v ) cos { j [ ϕ ( u , v ) + δ i ] }
ϕ w ( u , v ) = arctan i = 1 N sin ( δ i ) I i ( u , v ) i = 1 N cos ( δ i ) I i ( u , v )
I ^ = I ^ 0 γ 0
I ^ = ( I ^ 0 1 γ p ) γ 0 = I ^ 0 γ 0 / γ p
ϕ i ( u , v ) = ϕ i w ( u , v ) + 2 π I N T [ ϕ i 1 u w ( f i / f i 1 ) ϕ i w 2 π ]
Z = 1 + c 1 ϕ + ( c 2 + c 3 ϕ ) u + ( c 4 + c 5 ϕ ) v d 0 + d 1 ϕ + ( d 2 + d 3 ϕ ) u + ( d 4 + d 5 ϕ ) v
Z = F c F d F c = 1 + c 1 ϕ + ( c 2 + c 3 ϕ ) u + ( c 4 + c 5 ϕ ) v + ( c 6 + c 7 ϕ ) u 2 + ( c 8 + c 9 ϕ ) v 2 + ( c 10 + c 11 ϕ ) u v + ( c 12 + c 13 ϕ ) u 2 v + ( c 14 + c 15 ϕ ) u v 2 + ( c 16 + c 17 ϕ ) u 2 v 2 F d = d 0 + d 1 ϕ + ( d 2 + d 3 ϕ ) u + ( d 4 + d 5 ϕ ) v + ( d 6 + d 7 ϕ ) u 2 + ( d 8 + d 9 ϕ ) v 2 + ( d 10 + d 11 ϕ ) u v + ( d 12 + d 13 ϕ ) u 2 v + ( d 14 + d 15 ϕ ) u v 2 + ( d 16 + d 17 ϕ ) u 2 v 2
Z i j = A X c , i j + B Y c , i j + C Z c , i j + 1 A 2 + B 2 + C 2
S = i = 1 k j = 1 l ( F c F d Z i j ) 2

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