Abstract

This paper presents a novel method for absolute three-dimensional (3D) shape measurement that does not require conventional temporal phase unwrapping. Our proposed method uses a known object (i.e., a ping-pong ball) to provide cues for absolute phase unwrapping. During the measurement, the ping-pong ball is positioned to be close to the nearest point from the scene to the camera. We first segment ping-pong ball and spatially unwrap its phase, and then determine the integer multiple of 2π to be added such that the recovered shape matches its actual geometry. The nearest point of the ball provides zmin to generate the minimum phase Φmin that is then used to unwrap phase of the entire scene pixel by pixel. Experiments demonstrated that only three phase-shifted fringe patterns are required to measure absolute shapes of objects moving along depth z direction.

© 2017 Optical Society of America

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References

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  1. S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
    [Crossref]
  2. D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley and Sons, 2007).
    [Crossref]
  3. D. C. Ghiglia and M. D. Pritt, eds., Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (John Wiley and Sons, 1998).
  4. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42, 245–261 (2004).
    [Crossref]
  5. M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50, 6214–6224 (2011).
    [Crossref] [PubMed]
  6. Y.-Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [Crossref] [PubMed]
  7. Y.-Y. Cheng and J. C. Wyant, “Multiple-wavelength phase shifting interferometry,” Appl. Opt. 24, 804–807 (1985).
    [Crossref]
  8. D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
    [Crossref]
  9. G. Sansoni, M. Carocci, and R. Rodella, “Three-dimensional vision based on a combination of gray-code and phase-shift light projection: Analysis and compensation of the systematic errors,” Appl. Opt. 38, 6565–6573 (1999).
    [Crossref]
  10. S. Zhang, “Flexible 3d shape measurement using projector defocusing: Extended measurement range,” Opt. Lett. 35, 931–933 (2010).
  11. K. Zhong, Z. Li, Y. Shi, and C. Wang, “Analysis of solving the point correspondence problem by trifocal tensor for real-time phase measurement profilometry,” Proc. SPIE,  8493, 849311 (2012).
    [Crossref]
  12. Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
    [Crossref] [PubMed]
  13. K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
    [Crossref]
  14. C. Brauer-Burchardt, P. Kuhmstedt, and G. Notni, “Phase unwrapping using geometric constraints for high-speed fringe projection based 3d measurements,” Proc. SPIE,  8789, 878906 (2013).
    [Crossref]
  15. R. Ishiyama, S. Sakamoto, J. Tajima, T. Okatani, and K. Deguchi, “Absolute phase measurements using geometric constraints between multiple cameras and projectors,” Appl. Opt. 46, 3528–3538 (2007).
    [Crossref] [PubMed]
  16. C. Brauer-Burchardt, P. Kuhmstedt, M. Heinze, P. Kuhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3d measuring systems,” Lect. Notes Comput. Sci. 6979, 265–274 (2011).
    [Crossref]
  17. Y. R. Huddart, J. D. R. Valera, N. J. Weston, and A. J. Moore, “Absolute phase measurement in fringe projection using multiple perspectives,” Opt. Express 21, 21119–21130 (2013).
    [Crossref] [PubMed]
  18. W. Lohry, V. Chen, and S. Zhang, “Absolute three-dimensional shape measurement using coded fringe patterns without phase unwrapping or projector calibration,” Opt. Express 22, 1287–1301 (2014).
    [Crossref] [PubMed]
  19. Y. An, J.-S. Hyun, and S. Zhang, “Pixel-wise absolute phase unwrapping using geometric constraints of structured light system,” Opt. Express 24, 18445–18459 (2016).
    [Crossref] [PubMed]
  20. S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
    [Crossref]
  21. Y. An, Z. Liu, and S. Zhang, “Evaluation of pixel-wise geometric constraint-based phase unwrapping method for low signal-to-noise-ratio (snr) phase,” Adv. Opti. Technol. 5, 423–432 (2016).
  22. S. Zhang, X. Li, and S.-T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46, 50–57 (2007).
    [Crossref]
  23. B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured light system with an out-of-focus projector,” Appl. Opt. 53, 3415–3426 (2014).
    [Crossref] [PubMed]
  24. J.-S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55, 4395–4401 (2016).
    [Crossref] [PubMed]

2016 (3)

2014 (2)

2013 (4)

Y. R. Huddart, J. D. R. Valera, N. J. Weston, and A. J. Moore, “Absolute phase measurement in fringe projection using multiple perspectives,” Opt. Express 21, 21119–21130 (2013).
[Crossref] [PubMed]

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

C. Brauer-Burchardt, P. Kuhmstedt, and G. Notni, “Phase unwrapping using geometric constraints for high-speed fringe projection based 3d measurements,” Proc. SPIE,  8789, 878906 (2013).
[Crossref]

2012 (1)

K. Zhong, Z. Li, Y. Shi, and C. Wang, “Analysis of solving the point correspondence problem by trifocal tensor for real-time phase measurement profilometry,” Proc. SPIE,  8493, 849311 (2012).
[Crossref]

2011 (2)

C. Brauer-Burchardt, P. Kuhmstedt, M. Heinze, P. Kuhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3d measuring systems,” Lect. Notes Comput. Sci. 6979, 265–274 (2011).
[Crossref]

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50, 6214–6224 (2011).
[Crossref] [PubMed]

2010 (2)

S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
[Crossref]

S. Zhang, “Flexible 3d shape measurement using projector defocusing: Extended measurement range,” Opt. Lett. 35, 931–933 (2010).

2007 (2)

2006 (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

2004 (1)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42, 245–261 (2004).
[Crossref]

2003 (1)

D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
[Crossref]

1999 (1)

1985 (1)

1984 (1)

An, Y.

Y. An, Z. Liu, and S. Zhang, “Evaluation of pixel-wise geometric constraint-based phase unwrapping method for low signal-to-noise-ratio (snr) phase,” Adv. Opti. Technol. 5, 423–432 (2016).

Y. An, J.-S. Hyun, and S. Zhang, “Pixel-wise absolute phase unwrapping using geometric constraints of structured light system,” Opt. Express 24, 18445–18459 (2016).
[Crossref] [PubMed]

Asundi, A.

Brauer-Burchardt, C.

C. Brauer-Burchardt, P. Kuhmstedt, and G. Notni, “Phase unwrapping using geometric constraints for high-speed fringe projection based 3d measurements,” Proc. SPIE,  8789, 878906 (2013).
[Crossref]

C. Brauer-Burchardt, P. Kuhmstedt, M. Heinze, P. Kuhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3d measuring systems,” Lect. Notes Comput. Sci. 6979, 265–274 (2011).
[Crossref]

Carocci, M.

Chen, V.

Chen, W.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42, 245–261 (2004).
[Crossref]

Cheng, Y.-Y.

Deguchi, K.

Heinze, M.

C. Brauer-Burchardt, P. Kuhmstedt, M. Heinze, P. Kuhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3d measuring systems,” Lect. Notes Comput. Sci. 6979, 265–274 (2011).
[Crossref]

Huang, L.

Huang, P. S.

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

Huddart, Y. R.

Hyun, J.-S.

Ishiyama, R.

Jones, J. D. C.

D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
[Crossref]

Karpinsky, N.

Kemao, Q.

Kuhmstedt, P.

C. Brauer-Burchardt, P. Kuhmstedt, and G. Notni, “Phase unwrapping using geometric constraints for high-speed fringe projection based 3d measurements,” Proc. SPIE,  8789, 878906 (2013).
[Crossref]

C. Brauer-Burchardt, P. Kuhmstedt, M. Heinze, P. Kuhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3d measuring systems,” Lect. Notes Comput. Sci. 6979, 265–274 (2011).
[Crossref]

C. Brauer-Burchardt, P. Kuhmstedt, M. Heinze, P. Kuhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3d measuring systems,” Lect. Notes Comput. Sci. 6979, 265–274 (2011).
[Crossref]

Lei, Y.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

Li, B.

Li, X.

Li, Y.

Li, Z.

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

K. Zhong, Z. Li, Y. Shi, and C. Wang, “Analysis of solving the point correspondence problem by trifocal tensor for real-time phase measurement profilometry,” Proc. SPIE,  8493, 849311 (2012).
[Crossref]

Liu, Z.

Y. An, Z. Liu, and S. Zhang, “Evaluation of pixel-wise geometric constraint-based phase unwrapping method for low signal-to-noise-ratio (snr) phase,” Adv. Opti. Technol. 5, 423–432 (2016).

Lohry, W.

Moore, A. J.

Notni, G.

C. Brauer-Burchardt, P. Kuhmstedt, and G. Notni, “Phase unwrapping using geometric constraints for high-speed fringe projection based 3d measurements,” Proc. SPIE,  8789, 878906 (2013).
[Crossref]

C. Brauer-Burchardt, P. Kuhmstedt, M. Heinze, P. Kuhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3d measuring systems,” Lect. Notes Comput. Sci. 6979, 265–274 (2011).
[Crossref]

Okatani, T.

Rodella, R.

Sakamoto, S.

Sansoni, G.

Shi, Y.

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

K. Zhong, Z. Li, Y. Shi, and C. Wang, “Analysis of solving the point correspondence problem by trifocal tensor for real-time phase measurement profilometry,” Proc. SPIE,  8493, 849311 (2012).
[Crossref]

Su, X.

Tajima, J.

Towers, C. E.

D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
[Crossref]

Towers, D. P.

D. P. Towers, J. D. C. Jones, and C. E. Towers, “Optimum frequency selection in multi-frequency interferometry,” Opt. Lett. 28, 1–3 (2003).
[Crossref]

Valera, J. D. R.

Wang, C.

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

K. Zhong, Z. Li, Y. Shi, and C. Wang, “Analysis of solving the point correspondence problem by trifocal tensor for real-time phase measurement profilometry,” Proc. SPIE,  8493, 849311 (2012).
[Crossref]

Weston, N. J.

Wyant, J. C.

Yau, S.-T.

Zhang, Q.

Zhang, S.

J.-S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55, 4395–4401 (2016).
[Crossref] [PubMed]

Y. An, J.-S. Hyun, and S. Zhang, “Pixel-wise absolute phase unwrapping using geometric constraints of structured light system,” Opt. Express 24, 18445–18459 (2016).
[Crossref] [PubMed]

Y. An, Z. Liu, and S. Zhang, “Evaluation of pixel-wise geometric constraint-based phase unwrapping method for low signal-to-noise-ratio (snr) phase,” Adv. Opti. Technol. 5, 423–432 (2016).

B. Li, N. Karpinsky, and S. Zhang, “Novel calibration method for structured light system with an out-of-focus projector,” Appl. Opt. 53, 3415–3426 (2014).
[Crossref] [PubMed]

W. Lohry, V. Chen, and S. Zhang, “Absolute three-dimensional shape measurement using coded fringe patterns without phase unwrapping or projector calibration,” Opt. Express 22, 1287–1301 (2014).
[Crossref] [PubMed]

S. Zhang, “Flexible 3d shape measurement using projector defocusing: Extended measurement range,” Opt. Lett. 35, 931–933 (2010).

S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
[Crossref]

S. Zhang, X. Li, and S.-T. Yau, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46, 50–57 (2007).
[Crossref]

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

Zhao, M.

Zhong, K.

Z. Li, K. Zhong, Y. Li, X. Zhou, and Y. Shi, “Multiview phase shifting: a full-resolution and high-speed 3d measurement framework for arbitrary shape dynamic objects,” Opt. Lett. 38, 1389–1391 (2013).
[Crossref] [PubMed]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

K. Zhong, Z. Li, Y. Shi, and C. Wang, “Analysis of solving the point correspondence problem by trifocal tensor for real-time phase measurement profilometry,” Proc. SPIE,  8493, 849311 (2012).
[Crossref]

Zhou, X.

Adv. Opti. Technol. (1)

Y. An, Z. Liu, and S. Zhang, “Evaluation of pixel-wise geometric constraint-based phase unwrapping method for low signal-to-noise-ratio (snr) phase,” Adv. Opti. Technol. 5, 423–432 (2016).

Appl. Opt. (8)

Lect. Notes Comput. Sci. (1)

C. Brauer-Burchardt, P. Kuhmstedt, M. Heinze, P. Kuhmstedt, and G. Notni, “Using geometric constraints to solve the point correspondence problem in fringe projection based 3d measuring systems,” Lect. Notes Comput. Sci. 6979, 265–274 (2011).
[Crossref]

Opt. Eng. (1)

S. Zhang and P. S. Huang, “Novel method for structured light system calibration,” Opt. Eng. 45, 083601 (2006).
[Crossref]

Opt. Express (3)

Opt. Laser Eng. (3)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Laser Eng. 42, 245–261 (2004).
[Crossref]

K. Zhong, Z. Li, Y. Shi, C. Wang, and Y. Lei, “Fast phase measurement profilometry for arbitrary shape objects without phase unwrapping,” Opt. Laser Eng. 51, 1213–1222 (2013).
[Crossref]

S. Zhang, “Recent progresses on real-time 3-d shape measurement using digital fringe projection techniques,” Opt. Laser Eng. 48, 149–158 (2010).
[Crossref]

Opt. Lett. (3)

Proc. SPIE (2)

C. Brauer-Burchardt, P. Kuhmstedt, and G. Notni, “Phase unwrapping using geometric constraints for high-speed fringe projection based 3d measurements,” Proc. SPIE,  8789, 878906 (2013).
[Crossref]

K. Zhong, Z. Li, Y. Shi, and C. Wang, “Analysis of solving the point correspondence problem by trifocal tensor for real-time phase measurement profilometry,” Proc. SPIE,  8493, 849311 (2012).
[Crossref]

Other (2)

D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley and Sons, 2007).
[Crossref]

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

Supplementary Material (2)

NameDescription
» Visualization 1: MP4 (2150 KB)      Visualization 1
» Visualization 2: MP4 (9910 KB)      Visualization 2

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Figures (13)

Fig. 1
Fig. 1 Concept of phase unwrapping using Φmin [19]. (a) Red dashed window shows camera captured area when the virtual plane is at z = zmin and the solid blue window shows the mapped region the virtual plane is at z > zmin; (b) corresponding Φmin and Φ on the projector; (c) cross sections of Φmin and Φ and the wrapped phase maps for the case of only one single 2π discontinuous.
Fig. 2
Fig. 2 Our proposed absolute phase unwrapping pipeline. Three phase-shifted fringe patterns are used to obtain wrapped phase map ϕ(x, y) and texture image It (x, y). The ping-pong ball is segmented from the texture image and its phase map is extracted from the wrapped phase map ϕ(x, y). Since the spatially unwrapped phase map of the ping-pong ball is shifted by 2k0π from absolute phase, an optimization algorithm is employed to determine k0 such that reconstructed 3D geometry matches the actual geometry of the ping-pong ball. The reconstructed ping-pong ball is then used to extract zmin for Φmin computation. The entire phase map (excluding the sphere) is unwrapped pixel by pixel by referring to Φmin map. The final unwrapped phase map can be used to reconstruct 3D geometry directly.
Fig. 3
Fig. 3 Measurement result of a single sphere. (a) One of there phase-shifted fringe patterns; (b) wrapped phase; (c) spatially unwrapped phase.
Fig. 4
Fig. 4 3D reconstruction examples with different number of 2π offsets for the spatially unwrapped phase map shown in Fig. 3(c). Sphere in red is the ideal sphere with a radius of 20 mm. (a) 3D result when k = 15; (b) 3D result when k = 16; (c) 3D result when k = 17; (d) one cross section of reconstructed sphere and the ideal sphere for (a); (e) one cross section of reconstructed sphere and the ideal sphere for (b); (f) one cross section of reconstructed sphere and the ideal sphere for (c).
Fig. 5
Fig. 5 Changes of fitted sphere radius with different number k of 2π added to the spatially unwrapped phase map for 3D reconstruction.
Fig. 6
Fig. 6 Comparing results between our proposed method and the conventional temporal phase unwrapping method. (a) Unwrapped phase from our method; (b) 3D reconstructed geometry from our method; (c) unwrapped phase from conventional temporal phase unwrapping method; (d) 3D reconstructed geometry from conventional temporal phase unwrapping method.
Fig. 7
Fig. 7 Cross sections of the results from our proposed method and the conventional temporal phase unwrapping method. (a) Unwrapped phase maps; (b) 3D shapes.
Fig. 8
Fig. 8 Measurement results of multiple isolated known size ping-pong balls. (a) One of three phase-shifted fringe patterns; (b) 3D reconstruction from our method; (c) 3D reconstruction from a conventional temporal phase unwrapping method.
Fig. 9
Fig. 9 Measurement of two isolated complex sculptures using a known-size ping-pong ball. (a) One of the three phase-shifted fringe patterns; (b) texture image; (c) wrapped phase map; (d) segmented ping-pong ball; (e) wrapped phase map of the ping-pong ball; (f) spatial unwrapped phase map of the ping-pong ball; (g) unwrapped phase after our proposed optimization algorithm; (h) 3D absolute shape of the ping-pong ball.
Fig. 10
Fig. 10 Comparing results between our proposed method and the conventional temporal phase unwrapping method. (a) Unwrapped phase map from our method; (b) 3D reconstruction using phase map shown in (a); (c) unwrapped phase map from conventional temporal phase unwrapping method; (d) 3D reconstruction from the phase map shown in (c).
Fig. 11
Fig. 11 Measurement result of two isolated objects with large depth differences. (a) One of the fringe images; (b) segmented image and 3D reconstruction for the near objects; (c) segmented image and 3D reconstruction for the far object.
Fig. 12
Fig. 12 3D result of the entire scene. (a) 3D result by combining result for Figs. 11(b) and 11(c); (b) 3D reconstruction from the gray-coding method; (c) two different cross sections of the 3D results.
Fig. 13
Fig. 13 Measurement result of moving object along depth direction (associated with Visualization 1 and Visualization 2). (a) Result from our proposed method; (b) result from enhanced two-frequency phase unwrapping method.

Equations (14)

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

I 1 ( x , y ) = I t ( x , y ) + I ( x , y ) cos ( ϕ 2 π / 3 ) ,
I 2 ( x , y ) = I t ( x , y ) + I ( x , y ) cos ( ϕ ) ,
I 3 ( x , y ) = I t ( x , y ) + I ( x , y ) cos ( ϕ + 2 π / 3 ) ,
I t ( x , y ) = [ I 1 + I 2 + I 3 ] / 3 ,
ϕ ( x , y ) = tan 1 [ 3 ( I 1 I 3 ) 2 I 2 I 1 I 3 ] ,
Φ ( x , y ) = k ( x , y ) × 2 π + ϕ ( x , y ) .
s c [ u c v c 1 ] t = P c [ x w y w z w 1 ] t ,
s p [ u p v p 1 ] t = P p [ x w y w z w 1 ] t
Φ m i n ( u c , v c ) = f ( z m i n ; T , P c , P p ) .
k ( x , y ) = c e i l [ Φ m i n ϕ 2 π ] .
Δ z m a x = z m a x z m i n = Δ T s / tan θ ,
Φ b a ( x , y ) = Φ b r ( x , y ) + k 0 × 2 π .
0 k 0 N ,
k arg min | S o ( x , y ) S k ( x , y ) | ,

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