Abstract

We propose a new three-step phase-shifting algorithm, which is much faster than the traditional three-step algorithm. We achieve the speed advantage by using a simple intensity ratio function to replace the arctangent function in the traditional algorithm. The phase error caused by this new algorithm is compensated for by use of a lookup table. Our experimental results show that both the new algorithm and the traditional algorithm generate similar results, but the new algorithm is 3.4 times faster. By implementing this new algorithm in a high-resolution, real-time three-dimensional shape measurement system, we were able to achieve a measurement speed of 40 frames per second at a resolution of 532×500 pixels, all with an ordinary personal computer.

© 2006 Optical Society of America

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References

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  1. D.Malacara, ed., Optical Shop Testing (Wiley, 1992).
  2. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  3. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, "Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path," Appl. Opt. 41, 7437-7444 (2002).
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. P. Huang, S. Zhang, and F.-P. Chiang, "Trapezoidal phase-shifting method for 3-D shape Measurement," in Two- and Three-Dimensional Vision Systems for Inspection, Control, and Metrology II, K. G. Harding, ed., Proc. SPIE 5606, 142-152 (2004).
    [CrossRef]
  7. D.-S. Wan and D.-T. Lin, "Ronchi test and a new phase reduction algorithm," Appl. Opt. 29, 3255-3265 (1990).
    [CrossRef] [PubMed]
  8. P. S. Huang, C. Zhang, and F. P. Chiang, "High-speed 3-D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003).
    [CrossRef]
  9. S. Zhang and P. Huang, "High-resolution, real-time 3-D shape acquisition," presented at the IEEE Computer Vision and Pattern Recognition Workshop (CVPRW'04), Washington, D.C., 27 June-2 July 2004.
  10. S. Zhang, "High-resolution, real-time 3D shape measurement," Ph.D. thesis (State University of New York at Stony Brook, 2005).
  11. C. Zhang, P. S. Huang, and F.-P. Chiang, "Microscopic phase-shifting profilometry based on digital micromirror device technology," Appl. Opt. 41, 5896-5904 (2002).
    [CrossRef] [PubMed]
  12. B. Carrihill and R. Hummel, "Experiments with the intensity ratio depth sensor," Comput. Vis. Graph. Image Process. 32, 337-358 (1985).
    [CrossRef]
  13. T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "Reconstruction of realistic 3D surface model and 3D animation from range images obtained by real time 3D measurement system," in Proceedings of the International Conference on Pattern Recognition 2000 (IEEE, 2000), pp. 594-598.
    [CrossRef]
  14. T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "High speed 3-D measurement system using incoherent light source for human performance analysis," in XIXth Congress of the International Society for Photogrammetry and Remote Sensing, K.J. B. M.Molenaar, ed. (ISPRS, 2000), pp. 16-23.
  15. G. Chazan and N. Kiryati, "Pyramidal intensity-ratio depth sensor," Tech. Rep. 121 (Israel Institute of Technology, 1995).

2004 (1)

P. Huang, S. Zhang, and F.-P. Chiang, "Trapezoidal phase-shifting method for 3-D shape Measurement," in Two- and Three-Dimensional Vision Systems for Inspection, Control, and Metrology II, K. G. Harding, ed., Proc. SPIE 5606, 142-152 (2004).
[CrossRef]

2003 (1)

P. S. Huang, C. Zhang, and F. P. Chiang, "High-speed 3-D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003).
[CrossRef]

2002 (3)

1998 (1)

1990 (1)

1985 (1)

B. Carrihill and R. Hummel, "Experiments with the intensity ratio depth sensor," Comput. Vis. Graph. Image Process. 32, 337-358 (1985).
[CrossRef]

Araki, K.

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "Reconstruction of realistic 3D surface model and 3D animation from range images obtained by real time 3D measurement system," in Proceedings of the International Conference on Pattern Recognition 2000 (IEEE, 2000), pp. 594-598.
[CrossRef]

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "High speed 3-D measurement system using incoherent light source for human performance analysis," in XIXth Congress of the International Society for Photogrammetry and Remote Sensing, K.J. B. M.Molenaar, ed. (ISPRS, 2000), pp. 16-23.

Asundi, A.

Burton, D. R.

Carrihill, B.

B. Carrihill and R. Hummel, "Experiments with the intensity ratio depth sensor," Comput. Vis. Graph. Image Process. 32, 337-358 (1985).
[CrossRef]

Chazan, G.

G. Chazan and N. Kiryati, "Pyramidal intensity-ratio depth sensor," Tech. Rep. 121 (Israel Institute of Technology, 1995).

Chiang, F. P.

P. S. Huang, C. Zhang, and F. P. Chiang, "High-speed 3-D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003).
[CrossRef]

Chiang, F.-P.

P. Huang, S. Zhang, and F.-P. Chiang, "Trapezoidal phase-shifting method for 3-D shape Measurement," in Two- and Three-Dimensional Vision Systems for Inspection, Control, and Metrology II, K. G. Harding, ed., Proc. SPIE 5606, 142-152 (2004).
[CrossRef]

C. Zhang, P. S. Huang, and F.-P. Chiang, "Microscopic phase-shifting profilometry based on digital micromirror device technology," Appl. Opt. 41, 5896-5904 (2002).
[CrossRef] [PubMed]

Gdeisat, M. A.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Herráez, M. A.

Hirose, M.

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "Reconstruction of realistic 3D surface model and 3D animation from range images obtained by real time 3D measurement system," in Proceedings of the International Conference on Pattern Recognition 2000 (IEEE, 2000), pp. 594-598.
[CrossRef]

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "High speed 3-D measurement system using incoherent light source for human performance analysis," in XIXth Congress of the International Society for Photogrammetry and Remote Sensing, K.J. B. M.Molenaar, ed. (ISPRS, 2000), pp. 16-23.

Huang, P.

P. Huang, S. Zhang, and F.-P. Chiang, "Trapezoidal phase-shifting method for 3-D shape Measurement," in Two- and Three-Dimensional Vision Systems for Inspection, Control, and Metrology II, K. G. Harding, ed., Proc. SPIE 5606, 142-152 (2004).
[CrossRef]

S. Zhang and P. Huang, "High-resolution, real-time 3-D shape acquisition," presented at the IEEE Computer Vision and Pattern Recognition Workshop (CVPRW'04), Washington, D.C., 27 June-2 July 2004.

Huang, P. S.

P. S. Huang, C. Zhang, and F. P. Chiang, "High-speed 3-D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003).
[CrossRef]

C. Zhang, P. S. Huang, and F.-P. Chiang, "Microscopic phase-shifting profilometry based on digital micromirror device technology," Appl. Opt. 41, 5896-5904 (2002).
[CrossRef] [PubMed]

Hummel, R.

B. Carrihill and R. Hummel, "Experiments with the intensity ratio depth sensor," Comput. Vis. Graph. Image Process. 32, 337-358 (1985).
[CrossRef]

Kiryati, N.

G. Chazan and N. Kiryati, "Pyramidal intensity-ratio depth sensor," Tech. Rep. 121 (Israel Institute of Technology, 1995).

Kuroda, K.

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "High speed 3-D measurement system using incoherent light source for human performance analysis," in XIXth Congress of the International Society for Photogrammetry and Remote Sensing, K.J. B. M.Molenaar, ed. (ISPRS, 2000), pp. 16-23.

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "Reconstruction of realistic 3D surface model and 3D animation from range images obtained by real time 3D measurement system," in Proceedings of the International Conference on Pattern Recognition 2000 (IEEE, 2000), pp. 594-598.
[CrossRef]

Lalor, M. J.

Lin, D.-T.

Miyasaka, T.

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "High speed 3-D measurement system using incoherent light source for human performance analysis," in XIXth Congress of the International Society for Photogrammetry and Remote Sensing, K.J. B. M.Molenaar, ed. (ISPRS, 2000), pp. 16-23.

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "Reconstruction of realistic 3D surface model and 3D animation from range images obtained by real time 3D measurement system," in Proceedings of the International Conference on Pattern Recognition 2000 (IEEE, 2000), pp. 594-598.
[CrossRef]

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Wan, D.-S.

Zhang, C.

P. S. Huang, C. Zhang, and F. P. Chiang, "High-speed 3-D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003).
[CrossRef]

C. Zhang, P. S. Huang, and F.-P. Chiang, "Microscopic phase-shifting profilometry based on digital micromirror device technology," Appl. Opt. 41, 5896-5904 (2002).
[CrossRef] [PubMed]

Zhang, S.

P. Huang, S. Zhang, and F.-P. Chiang, "Trapezoidal phase-shifting method for 3-D shape Measurement," in Two- and Three-Dimensional Vision Systems for Inspection, Control, and Metrology II, K. G. Harding, ed., Proc. SPIE 5606, 142-152 (2004).
[CrossRef]

S. Zhang, "High-resolution, real-time 3D shape measurement," Ph.D. thesis (State University of New York at Stony Brook, 2005).

S. Zhang and P. Huang, "High-resolution, real-time 3-D shape acquisition," presented at the IEEE Computer Vision and Pattern Recognition Workshop (CVPRW'04), Washington, D.C., 27 June-2 July 2004.

Zhou, W.

Appl. Opt. (5)

Comput. Vis. Graph. Image Process. (1)

B. Carrihill and R. Hummel, "Experiments with the intensity ratio depth sensor," Comput. Vis. Graph. Image Process. 32, 337-358 (1985).
[CrossRef]

Opt. Eng. (1)

P. S. Huang, C. Zhang, and F. P. Chiang, "High-speed 3-D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003).
[CrossRef]

Proc. SPIE (1)

P. Huang, S. Zhang, and F.-P. Chiang, "Trapezoidal phase-shifting method for 3-D shape Measurement," in Two- and Three-Dimensional Vision Systems for Inspection, Control, and Metrology II, K. G. Harding, ed., Proc. SPIE 5606, 142-152 (2004).
[CrossRef]

Other (7)

S. Zhang and P. Huang, "High-resolution, real-time 3-D shape acquisition," presented at the IEEE Computer Vision and Pattern Recognition Workshop (CVPRW'04), Washington, D.C., 27 June-2 July 2004.

S. Zhang, "High-resolution, real-time 3D shape measurement," Ph.D. thesis (State University of New York at Stony Brook, 2005).

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "Reconstruction of realistic 3D surface model and 3D animation from range images obtained by real time 3D measurement system," in Proceedings of the International Conference on Pattern Recognition 2000 (IEEE, 2000), pp. 594-598.
[CrossRef]

T. Miyasaka, K. Kuroda, M. Hirose, and K. Araki, "High speed 3-D measurement system using incoherent light source for human performance analysis," in XIXth Congress of the International Society for Photogrammetry and Remote Sensing, K.J. B. M.Molenaar, ed. (ISPRS, 2000), pp. 16-23.

G. Chazan and N. Kiryati, "Pyramidal intensity-ratio depth sensor," Tech. Rep. 121 (Israel Institute of Technology, 1995).

D.Malacara, ed., Optical Shop Testing (Wiley, 1992).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

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Figures (8)

Fig. 1
Fig. 1

Cross sections of the three phase-shifted sinusoidal fringe patterns. (a) I 1(α = −120°). (b) I 2(α = 0°). (c) I 3(α = 120°).

Fig. 2
Fig. 2

Cross sections of the intensity ratio image and the phase image. (a) Intensity ratio. (b) Phase.

Fig. 3
Fig. 3

(Color online) Nonlinearity error caused by the use of the fast three-step algorithm. (a) Intensity ratio in the region N = 1. (b) Nonlinearity error.

Fig. 4
Fig. 4

Fringe images of a flat board captured by an 8-bit B∕W CCD camera. (a) Fringe image I 1(α = −120°). (b) Fringe image I 2(α = 0°). (c) Fringe image I 3(α = 120°).

Fig. 5
Fig. 5

(Color online) Intensity ratio error (×π/3 for phase error). (a) With the traditional three-step algorithm. (b) With the fast three-step algorithm before error compensation. (c) With the fast three-step algorithm after error compensation.

Fig. 6
Fig. 6

(Color online) Measurement results of a Lincoln head sculpture. (a) Fringe image I 1(α = −120°). (b) Fringe image I 2(α = 0°). (c) Fringe image I 3(α = 120°). (d) 2D photo. (e) 3D shape by the traditional three-step algorithm. (f) 3D shape by the fast three-step algorithm.

Fig. 7
Fig. 7

(Color online) Experimental setup for real-time 3D shape acquisition, reconstruction, and display.

Fig. 8
Fig. 8

(Color online) Real-time measurement of human facial expressions.

Equations (12)

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I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) α ] ,
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) ] ,
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) + α ] ,
ϕ ( x , y ) = arctan ( 3 I 1 I 3 2 I 2 I 1 I 3 ) .
r ( x , y ) = I med ( x , y ) I min ( x , y ) I max ( x , y ) I min ( x , y ) ,
ϕ ( x , y ) = π 3 [ 2 × round ( N 1 2 ) + ( 1 ) N 1 r ( x , y ) ] ,
r ( ϕ ) = I 1 I 3 I 2 I 3 = 1 2 + 3 2 tan ( ϕ π 6 ) .
r ( ϕ ) = ϕ π / 3 + Δ r ( ϕ ) ,
Δ r ( ϕ ) = r ( ϕ ) ϕ π / 3 = 1 2 + 3 2 tan ( ϕ π 6 ) ϕ π / 3 .
ϕ = π 6 ± cos 1 ( 3 π / 6 ) ,
Δ r ( ϕ ) max = Δ r ( ϕ ) | ϕ = ϕ 1 = 0.0186 ,
Δ r ( ϕ ) min = Δ r ( ϕ ) | ϕ = ϕ 2 = 0.0186.

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