Abstract

A multilevel quality-guided phase unwrapping algorithm for real-time 3D shape measurement is presented. The quality map is generated from the gradient of the phase map. Multilevel thresholds are used to unwrap the phase level by level. Within the data points in each level, a fast scan-line algorithm is employed. The processing time of this algorithm is approximately 18.3  ms for an image size of 640×480 pixels in an ordinary computer. We demonstrate that this algorithm can be implemented into our real-time 3D shape measurement system for real-time 3D reconstruction. Experiments show that this algorithm improves the previous scan-line phase unwrapping algorithm significantly although it reduces its processing speed slightly.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999).
    [CrossRef]
  2. P. S. Huang, C. Zhang, and F.-P. Chiang, "High-speed 3D shape measurement based on digital fringe projection," Opt. Eng. 42, 163-168 (2003).
    [CrossRef]
  3. L. Kinell, "Spatiotemporal approach for real-time absolute shape measurements by use of projected fringes," Appl. Opt. 43, 3018-3027 (2004).
    [CrossRef] [PubMed]
  4. J. Pan, P. S. Huang, and F.-P. Chiang, "Color phase-shifting technique for three-dimensional shape measurement," Opt. Eng. 45 , 013602-1-9 (2006).
  5. S. Zhang and P. S. Huang, "High-resolution, real-time 3D shape measurement," Opt. Eng., to be published; http://math.harvard.edu/∼songzhang/publications/realtime.pdf.
  6. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  7. J. M. Huntley, "Noise-immune phase unwrapping algorithm," Appl. Opt. 28, 3268-3270 (1989).
    [CrossRef] [PubMed]
  8. R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Two-dimensional phase unwrapping," Radio Sci. 23, 713-720 (1988).
    [CrossRef]
  9. R. Cusack, J. M. Huntley, and H. T. Goldrein, "Improved noise-immune phase unwrapping algorithm," Appl. Opt. 34, 781-789 (1995).
    [CrossRef] [PubMed]
  10. J. R. Buchland, J. M. Huntley, and S. R. E. Turner, "Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm," Appl. Opt. 34, 5100-5108 (1995).
    [CrossRef]
  11. M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, "Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping," Appl. Opt. 45, 2711-2722 (2006).
    [CrossRef] [PubMed]
  12. T. J. Flynn, "Two-dimensional phase unwrapping with minimum weighted discontinuity," J. Opt. Soc. Am. A 14, 2692-2701 (1997).
    [CrossRef]
  13. A. Baldi, "Phase unwrapping by region growing," Appl. Opt. 42, 2498-2505 (2003).
    [CrossRef] [PubMed]
  14. K. M. Hung and T. Yamada, "Phase unwrapping by regions using least-squares approach," Opt. Eng. 37, 2965-2970 (1998).
    [CrossRef]
  15. M. A. Merráez, J. G. Boticario, M. J. Labor, and D. R. Burton, "Agglomerative clustering-based approach for two-dimensional phase unwrapping," Appl. Opt. 44, 1129-1140 (2005).
    [CrossRef]
  16. J.-J. Chyou, S.-J. Chen, and Y.-K. Chen, "Two-dimensional phase unwrapping with a multichannel least-mean-square algorithm," Appl. Opt. 43, 5655-5661 (2004).
    [CrossRef] [PubMed]
  17. J. M. Huntley and H. O. Saldner, "Temporal phase-unwrapping algorithm for automated interferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
    [CrossRef] [PubMed]
  18. H. O. Saldner and J. M. Huntley, "Temporal phase unwrapping: application to surface profiling of discontinuous objects," Appl. Opt. 36, 2770-2775 (1997).
    [CrossRef] [PubMed]
  19. D. J. Bone, "Fourier fringe analysis: the two-dimensional phase unwrapping problem," Appl. Opt. 30, 3627-3632 (1991).
    [CrossRef] [PubMed]
  20. J. A. Quiroga, A. Gonzalez-Cano, and E. Bernabeu, "Phase-unwrapping algorithm based on an adaptive criterion," Appl. Opt. 34, 2560-2563 (1995).
    [CrossRef] [PubMed]
  21. M. D. Pritt, "Phase-unwrapping by means of multigrid techniques for interferometric SAR," IEEE Trans. Geosci. Remote Sens. 34, 728-738 (1996).
    [CrossRef]
  22. B. Ströbel, "Processing of interferometric phase maps as complex-valued phasor images," Appl. Opt. 35, 2192-2198 (1996).
    [CrossRef] [PubMed]
  23. J.-L. Li, X.-Y. Su, and J.-T. Li, "Phase unwrapping algorithm based on reliability and edge detection," Opt. Eng. 36, 1685-1690 (1997).
    [CrossRef]
  24. 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).
    [CrossRef] [PubMed]
  25. C. Quan, C. J. Tay, L. Chen, and Y. Fu, "Spatial-fringe-modulation-based quality map for phase unwrapping," Appl. Opt. 42, 7060-7065 (2003).
    [CrossRef] [PubMed]
  26. S. Zhang and S.-T. Yau, "High-resolution, real-time absolute coordinate measurement based on the phase-shifting method," Opt. Express 14, 2644-2649 (2006).
    [CrossRef] [PubMed]
  27. S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
    [CrossRef]
  28. P. S. Huang and S. Zhang, "Fast three-step phase-shifting algorithm," Appl. Opt. 45, 5086-5091 (2006).
    [CrossRef] [PubMed]

2006 (5)

2005 (1)

2004 (2)

2003 (3)

2002 (1)

1999 (1)

P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999).
[CrossRef]

1998 (1)

K. M. Hung and T. Yamada, "Phase unwrapping by regions using least-squares approach," Opt. Eng. 37, 2965-2970 (1998).
[CrossRef]

1997 (3)

1996 (2)

B. Ströbel, "Processing of interferometric phase maps as complex-valued phasor images," Appl. Opt. 35, 2192-2198 (1996).
[CrossRef] [PubMed]

M. D. Pritt, "Phase-unwrapping by means of multigrid techniques for interferometric SAR," IEEE Trans. Geosci. Remote Sens. 34, 728-738 (1996).
[CrossRef]

1995 (3)

1993 (1)

1991 (1)

1989 (1)

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Two-dimensional phase unwrapping," Radio Sci. 23, 713-720 (1988).
[CrossRef]

Baldi, A.

Beauregard, D. A.

Bernabeu, E.

Bone, D. J.

Boticario, J. G.

Buchland, J. R.

Burton, D. R.

Chen, L.

Chen, S.-J.

Chen, Y.-K.

Chiang, F. P.

P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999).
[CrossRef]

Chiang, F.-P.

J. Pan, P. S. Huang, and F.-P. Chiang, "Color phase-shifting technique for three-dimensional shape measurement," Opt. Eng. 45 , 013602-1-9 (2006).

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

Chyou, J.-J.

Cusack, R.

Flynn, T. J.

Fu, Y.

Gdeisat, M. A.

Ghiglia, D. C.

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

Goldrein, H. T.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Two-dimensional phase unwrapping," Radio Sci. 23, 713-720 (1988).
[CrossRef]

Gonzalez-Cano, A.

Graves, M. J.

Herráez, M. A.

Hu, Q.

P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999).
[CrossRef]

Huang, P. S.

J. Pan, P. S. Huang, and F.-P. Chiang, "Color phase-shifting technique for three-dimensional shape measurement," Opt. Eng. 45 , 013602-1-9 (2006).

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
[CrossRef]

P. S. Huang and S. Zhang, "Fast three-step phase-shifting algorithm," Appl. Opt. 45, 5086-5091 (2006).
[CrossRef] [PubMed]

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

P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999).
[CrossRef]

S. Zhang and P. S. Huang, "High-resolution, real-time 3D shape measurement," Opt. Eng., to be published; http://math.harvard.edu/∼songzhang/publications/realtime.pdf.

Hung, K. M.

K. M. Hung and T. Yamada, "Phase unwrapping by regions using least-squares approach," Opt. Eng. 37, 2965-2970 (1998).
[CrossRef]

Huntley, J. M.

Jin, F.

P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999).
[CrossRef]

Kinell, L.

Labor, M. J.

Lalor, M. J.

Li, J.-L.

J.-L. Li, X.-Y. Su, and J.-T. Li, "Phase unwrapping algorithm based on reliability and edge detection," Opt. Eng. 36, 1685-1690 (1997).
[CrossRef]

Li, J.-T.

J.-L. Li, X.-Y. Su, and J.-T. Li, "Phase unwrapping algorithm based on reliability and edge detection," Opt. Eng. 36, 1685-1690 (1997).
[CrossRef]

Merráez, M. A.

Pan, J.

J. Pan, P. S. Huang, and F.-P. Chiang, "Color phase-shifting technique for three-dimensional shape measurement," Opt. Eng. 45 , 013602-1-9 (2006).

Pritt, M. D.

M. D. Pritt, "Phase-unwrapping by means of multigrid techniques for interferometric SAR," IEEE Trans. Geosci. Remote Sens. 34, 728-738 (1996).
[CrossRef]

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

Quan, C.

Quiroga, J. A.

Ruiz, P. D.

Saldner, H. O.

Salfity, M. F.

Ströbel, B.

Su, X.-Y.

J.-L. Li, X.-Y. Su, and J.-T. Li, "Phase unwrapping algorithm based on reliability and edge detection," Opt. Eng. 36, 1685-1690 (1997).
[CrossRef]

Tay, C. J.

Turner, S. R. E.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Two-dimensional phase unwrapping," Radio Sci. 23, 713-720 (1988).
[CrossRef]

Yamada, T.

K. M. Hung and T. Yamada, "Phase unwrapping by regions using least-squares approach," Opt. Eng. 37, 2965-2970 (1998).
[CrossRef]

Yau, S.-T.

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Two-dimensional phase unwrapping," Radio Sci. 23, 713-720 (1988).
[CrossRef]

Zhang, C.

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

Zhang, S.

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
[CrossRef]

S. Zhang and S.-T. Yau, "High-resolution, real-time absolute coordinate measurement based on the phase-shifting method," Opt. Express 14, 2644-2649 (2006).
[CrossRef] [PubMed]

P. S. Huang and S. Zhang, "Fast three-step phase-shifting algorithm," Appl. Opt. 45, 5086-5091 (2006).
[CrossRef] [PubMed]

S. Zhang and P. S. Huang, "High-resolution, real-time 3D shape measurement," Opt. Eng., to be published; http://math.harvard.edu/∼songzhang/publications/realtime.pdf.

Appl. Opt. (16)

L. Kinell, "Spatiotemporal approach for real-time absolute shape measurements by use of projected fringes," Appl. Opt. 43, 3018-3027 (2004).
[CrossRef] [PubMed]

J. M. Huntley, "Noise-immune phase unwrapping algorithm," Appl. Opt. 28, 3268-3270 (1989).
[CrossRef] [PubMed]

R. Cusack, J. M. Huntley, and H. T. Goldrein, "Improved noise-immune phase unwrapping algorithm," Appl. Opt. 34, 781-789 (1995).
[CrossRef] [PubMed]

J. R. Buchland, J. M. Huntley, and S. R. E. Turner, "Unwrapping noisy phase maps by use of a minimum-cost-matching algorithm," Appl. Opt. 34, 5100-5108 (1995).
[CrossRef]

M. F. Salfity, P. D. Ruiz, J. M. Huntley, M. J. Graves, R. Cusack, and D. A. Beauregard, "Branch cut surface placement for unwrapping of undersampled three-dimensional phase data: application to magnetic resonance imaging arterial flow mapping," Appl. Opt. 45, 2711-2722 (2006).
[CrossRef] [PubMed]

M. A. Merráez, J. G. Boticario, M. J. Labor, and D. R. Burton, "Agglomerative clustering-based approach for two-dimensional phase unwrapping," Appl. Opt. 44, 1129-1140 (2005).
[CrossRef]

J.-J. Chyou, S.-J. Chen, and Y.-K. Chen, "Two-dimensional phase unwrapping with a multichannel least-mean-square algorithm," Appl. Opt. 43, 5655-5661 (2004).
[CrossRef] [PubMed]

J. M. Huntley and H. O. Saldner, "Temporal phase-unwrapping algorithm for automated interferogram analysis," Appl. Opt. 32, 3047-3052 (1993).
[CrossRef] [PubMed]

H. O. Saldner and J. M. Huntley, "Temporal phase unwrapping: application to surface profiling of discontinuous objects," Appl. Opt. 36, 2770-2775 (1997).
[CrossRef] [PubMed]

D. J. Bone, "Fourier fringe analysis: the two-dimensional phase unwrapping problem," Appl. Opt. 30, 3627-3632 (1991).
[CrossRef] [PubMed]

J. A. Quiroga, A. Gonzalez-Cano, and E. Bernabeu, "Phase-unwrapping algorithm based on an adaptive criterion," Appl. Opt. 34, 2560-2563 (1995).
[CrossRef] [PubMed]

A. Baldi, "Phase unwrapping by region growing," Appl. Opt. 42, 2498-2505 (2003).
[CrossRef] [PubMed]

B. Ströbel, "Processing of interferometric phase maps as complex-valued phasor images," Appl. Opt. 35, 2192-2198 (1996).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

C. Quan, C. J. Tay, L. Chen, and Y. Fu, "Spatial-fringe-modulation-based quality map for phase unwrapping," Appl. Opt. 42, 7060-7065 (2003).
[CrossRef] [PubMed]

P. S. Huang and S. Zhang, "Fast three-step phase-shifting algorithm," Appl. Opt. 45, 5086-5091 (2006).
[CrossRef] [PubMed]

IEEE Trans. Geosci. Remote Sens. (1)

M. D. Pritt, "Phase-unwrapping by means of multigrid techniques for interferometric SAR," IEEE Trans. Geosci. Remote Sens. 34, 728-738 (1996).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (5)

P. S. Huang, Q. Hu, F. Jin, and F. P. Chiang, "Color-encoded digital fringe projection technique for high-speed three-dimensional surface contouring," Opt. Eng. 38, 1065-1071 (1999).
[CrossRef]

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

S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Opt. Eng. 45, 083601-1-8 (2006).
[CrossRef]

J.-L. Li, X.-Y. Su, and J.-T. Li, "Phase unwrapping algorithm based on reliability and edge detection," Opt. Eng. 36, 1685-1690 (1997).
[CrossRef]

K. M. Hung and T. Yamada, "Phase unwrapping by regions using least-squares approach," Opt. Eng. 37, 2965-2970 (1998).
[CrossRef]

Opt. Eng. 45 (1)

J. Pan, P. S. Huang, and F.-P. Chiang, "Color phase-shifting technique for three-dimensional shape measurement," Opt. Eng. 45 , 013602-1-9 (2006).

Opt. Express (1)

Radio Sci. (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Two-dimensional phase unwrapping," Radio Sci. 23, 713-720 (1988).
[CrossRef]

Other (2)

S. Zhang and P. S. Huang, "High-resolution, real-time 3D shape measurement," Opt. Eng., to be published; http://math.harvard.edu/∼songzhang/publications/realtime.pdf.

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic of the scan-line phase unwrapping algorithm.

Fig. 2
Fig. 2

Example of the data for testing our phase unwrapping algorithm. (a) I 1 ( 2 π / 3 ) , (b) I2(0), (c) I 3 ( 2 π / 3 ) , (d) wrapped phase map, (e) data modulation quality map with the white being 1.0 in value, (f) good data points after removing the background by using a threshold of gamma map (0.25), white denotes the good points and black denotes the background points.

Fig. 3
Fig. 3

Quality map and the threshold value for each level. (a) Patch of interest, the largest good connected patch; the white points are the patch of interest. (b) Quality map. (c) Histograph of the quality map. The solid line shows the mean value that determines the first threshold for the first level. The dashed line shows the threshold used for the second level. (Standard deviation δ, 0.036; mean value, 0.039.)

Fig. 4
Fig. 4

(Color online) Unwrapping points after each step. The phase unwrapping starts from level 1 with the highest quality data points and unwraps these points using the scan-line algorithm, then continues to data points on a lower level until finished. (a) Unwrapping points represented as white after the first level as the first step. (b) Unwrapping points after the second step. (c) Unwrapping points when it finishes. (d) Unwrapped geometry after the first step. (e) Unwrapped geometry after the second step. (f) The final results.

Fig. 5
Fig. 5

(Color online) Three-dimensional reconstruction results using different phase unwrapping algorithms. (a) 3D result using fastest scan-line phase unwrapping algorithm. (b) 3D result using variance quality-guided phase unwrapping algorithm. (c) 3D result using multilevel quality-guided phase unwrapping algorithm. (d) Difference map between (b) and (c), black denotes the same and white denotes different. (e) Difference map between (a) and (b), black denotes the same and white denotes different.

Fig. 6
Fig. 6

(Color online) Three-dimensional shape reconstruction results for different phase unwrapping algorithms. (a) 3D result using fastest scan-line phase unwrapping algorithm. (b) 3D result using variance quality-guided phase unwrapping algorithm. (c) 3D result using multilevel quality-guided phase unwrapping algorithm. (d) Difference map between (b) and (c), black denotes the same and white denotes different. (e) Difference map between (a) and (b), black denotes the same and white denotes different.

Fig. 7
Fig. 7

(Color online) Real-time 3D reconstruction using the proposed phase unwrapping algorithm.

Tables (2)

Tables Icon

Table 1 Comparison of Phase Unwrapping Time of Different Algorithms a

Tables Icon

Table 2 Comparison of Phase Unwrapping Algorithms

Equations (8)

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

I i ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) + δ i ] ,
γ ( x , y ) = I ( x , y ) / I ( x , y )
ϕ ( x , y ) = tan - 1 { 3 I 1 I 3 2 I 2 I 1 I 3 } ,
γ ( x , y ) = 3 ( I 1 I 3 ) 2 + ( 2 I 2 I 1 I 3 ) 2 I 1 + I 2 + I 3 ,
Q ( i , j ) = max { Δ i , j x , Δ i , j y }   with   Q ( i , j ) [ 0 , 1 ) ,
Δ i , j x = max { | W { ψ ( i , j ) ψ ( i , j 1 ) } | , | W { ψ ( i , j + 1 ) ψ ( i , j ) } | } ,
Δ i , j y = max { | W { ψ ( i , j ) ψ ( i 1 , j ) } | , | W { ψ ( i + 1 , j ) ψ ( i , j ) } | } ,
Z m , n = ( ψ ( i , j ) x ψ ( i , j ) ¯ x ) 2 + ( ψ ( i , j ) y ψ ( i , j ) ¯ y ) 2 k 2 ,

Metrics