Abstract

Structured light illumination by means of phase shifting patterns is a widely employed method for three-dimensional (3-D) image acquisition that is robust to ambient light and object albedo but may be especially susceptible to sensor and environment noise. In this paper, we study the specific technique of phase measuring profilometry (PMP) and the maximization of a pattern’s signal to noise ratio (SNR). By treating the design of an N-pattern PMP process as placing points in an N-dimensional coding space, we define a pattern’s SNR in terms of a pattern set’s computational length and the number of coded phase periods in the projected patterns. Then, without introducing phase ambiguities, we propose a so-called edge pattern strategy that maximizes the computational length and number of periods. Theoretically, the edge pattern technique improves the SNR by 1.2381 times when using three component patterns and by 15.5421 times when using five patterns. Experimental results further demonstrate the improved SNR of the proposed edge pattern technique such that more accurate 3-D results are achieved using fewer component patterns.

© 2010 Optical Society of America

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References

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  1. J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light system,” Pattern Recogn. 37, 827–849 (2004).
    [Crossref]
  2. S. Y. Chen, Y. F. Li, and J. Zhang, “Vision processing for realtime 3-d data acquisition based on coded structured light,” IEEE Trans. Image Process. 17, 167–176 (2008).
    [Crossref] [PubMed]
  3. T. P. Koninckx and L. V. Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 432–445 (2006).
    [Crossref] [PubMed]
  4. S. Zhang, D. Royer, and S. T. Yau, “High-resolution, real-time-geometry video acquisition system,” in Proceedings of ACM SIGGRAPH 2006 (ACM, SIGGRAPH, 2006), Article 14.
  5. V. Srinivasan, H. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3d diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [Crossref] [PubMed]
  6. D. Skocaj and A. Leonardis, “Range image acquisition of objects with non-uniform albedo using structured light range sensor,” in Proceedings of the 15th International Conference on Pattern Recognition (IEEE, 2000), Vol. 1, pp. 778–781.
    [Crossref]
  7. D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
    [Crossref]
  8. P. Huang, S. Zhang, and F. Chiang, “Trapezoidal phase-shifting method for three-dimensional shape measurement,” Opt. Eng. (Bellingham) 44, 123601 (2005).
    [Crossref]
  9. S. Zhang and S. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase shifting algorithm,” Opt. Eng. (Bellingham) 46, 113603 (2007).
    [Crossref]
  10. P. Jia, J. Kofman, and C. English, “Intensity-ratio error compensation for triangular-pattern phase-shifting profilometry,” J. Opt. Soc. Am. A 24, 3150–3158 (2007).
    [Crossref]
  11. S. Rusinkiewicz, O. Hall-Holt, and M. Levoy, “Real-time 3D model acquisition,” in Proceedings of SIGGRAPH 2006 (ACM SIGGRAPH, 2002), Vol. 21, pp. 438–446.
  12. J. Li, L. G. Hassebrook, and C. Guan, “Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity,” J. Opt. Soc. Am. A 20, 106–115 (2003).
    [Crossref]
  13. C. Guan, L. G. Hassebrook, and D. L. Lau, “Composite structured light pattern for three-dimensional video,” Opt. Express 11, 406–417 (2003).
    [Crossref] [PubMed]
  14. S. Zhang and P. S. Huang, “Phase error compensation for a 3-d shape measurement system based on the phase-shifting method,” Opt. Eng. (Bellingham) 46, 063601 (2007).
    [Crossref]
  15. B. Kamgar-Parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–940 (1989).
    [Crossref]
  16. Y. Y. Schechner, S. K. Nayar, and P. N. Belhumeur, “A theory of multiplexed illumination,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (IEEE, 2003), Vol. 2, pp. 808–815.
    [Crossref]
  17. T. Weise, B. Leibe, and L. V. Gool, “Fast 3D scanning with automatic motion compensation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.
  18. A. K. Wong, P. Niu, and X. He, “Fast acquisition of dense depth data by a new structured light scheme,” Comput. Vis. Image Underst. 98, 398–422 (2005).
    [Crossref]
  19. P. S. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45, 5086–5091 (2006).
    [Crossref] [PubMed]
  20. E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vis. Comput. 17, 87–97 (1999).
    [Crossref]
  21. Y. Wang, K. Liu, D. L. Lau, and L. G. Hassebrook, “Multicamera phase measuring profilometry for accurate depth measurement,” Proc. SPIE 6555, 655509.1–12 (2007).
    [Crossref]
  22. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Two dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
    [Crossref]
  23. J. Bonny, J. Renou, and M. Zanca, “Optimal measurement of magnitude and phase from mr data,” J. Magn. Reson., Ser. B 113, 136–144 (1996).
    [Crossref]
  24. H. Gudbjartsson and S. Patz, “The rician distribution of noisy mri data,” Magn. Reson. Med. 34, 910–914 (1995).
    [Crossref] [PubMed]
  25. V. G. Valla and L. G. Hassebrook, “Very high resolution 3-d surface scanning using multi-frequency phase measuring profilometry,” Proc. SPIE 5798-09, 44–53 (2010)
  26. K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Gamma model and its analysis for phase measuring profilometry,” J. Opt. Soc. Am. A 27, 553–562 (2010).
    [Crossref]

2010 (2)

V. G. Valla and L. G. Hassebrook, “Very high resolution 3-d surface scanning using multi-frequency phase measuring profilometry,” Proc. SPIE 5798-09, 44–53 (2010)

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Gamma model and its analysis for phase measuring profilometry,” J. Opt. Soc. Am. A 27, 553–562 (2010).
[Crossref]

2008 (1)

S. Y. Chen, Y. F. Li, and J. Zhang, “Vision processing for realtime 3-d data acquisition based on coded structured light,” IEEE Trans. Image Process. 17, 167–176 (2008).
[Crossref] [PubMed]

2007 (4)

S. Zhang and S. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase shifting algorithm,” Opt. Eng. (Bellingham) 46, 113603 (2007).
[Crossref]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-d shape measurement system based on the phase-shifting method,” Opt. Eng. (Bellingham) 46, 063601 (2007).
[Crossref]

Y. Wang, K. Liu, D. L. Lau, and L. G. Hassebrook, “Multicamera phase measuring profilometry for accurate depth measurement,” Proc. SPIE 6555, 655509.1–12 (2007).
[Crossref]

P. Jia, J. Kofman, and C. English, “Intensity-ratio error compensation for triangular-pattern phase-shifting profilometry,” J. Opt. Soc. Am. A 24, 3150–3158 (2007).
[Crossref]

2006 (2)

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

T. P. Koninckx and L. V. Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 432–445 (2006).
[Crossref] [PubMed]

2005 (2)

P. Huang, S. Zhang, and F. Chiang, “Trapezoidal phase-shifting method for three-dimensional shape measurement,” Opt. Eng. (Bellingham) 44, 123601 (2005).
[Crossref]

A. K. Wong, P. Niu, and X. He, “Fast acquisition of dense depth data by a new structured light scheme,” Comput. Vis. Image Underst. 98, 398–422 (2005).
[Crossref]

2004 (1)

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light system,” Pattern Recogn. 37, 827–849 (2004).
[Crossref]

2003 (2)

1999 (1)

E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vis. Comput. 17, 87–97 (1999).
[Crossref]

1998 (1)

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[Crossref]

1996 (1)

J. Bonny, J. Renou, and M. Zanca, “Optimal measurement of magnitude and phase from mr data,” J. Magn. Reson., Ser. B 113, 136–144 (1996).
[Crossref]

1995 (1)

H. Gudbjartsson and S. Patz, “The rician distribution of noisy mri data,” Magn. Reson. Med. 34, 910–914 (1995).
[Crossref] [PubMed]

1989 (1)

B. Kamgar-Parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–940 (1989).
[Crossref]

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Two dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

1984 (1)

Batlle, J.

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light system,” Pattern Recogn. 37, 827–849 (2004).
[Crossref]

Belhumeur, P. N.

Y. Y. Schechner, S. K. Nayar, and P. N. Belhumeur, “A theory of multiplexed illumination,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (IEEE, 2003), Vol. 2, pp. 808–815.
[Crossref]

Bonny, J.

J. Bonny, J. Renou, and M. Zanca, “Optimal measurement of magnitude and phase from mr data,” J. Magn. Reson., Ser. B 113, 136–144 (1996).
[Crossref]

Caspi, D.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[Crossref]

Chen, S. Y.

S. Y. Chen, Y. F. Li, and J. Zhang, “Vision processing for realtime 3-d data acquisition based on coded structured light,” IEEE Trans. Image Process. 17, 167–176 (2008).
[Crossref] [PubMed]

Chiang, F.

P. Huang, S. Zhang, and F. Chiang, “Trapezoidal phase-shifting method for three-dimensional shape measurement,” Opt. Eng. (Bellingham) 44, 123601 (2005).
[Crossref]

English, C.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Two dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Gool, L. V.

T. P. Koninckx and L. V. Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 432–445 (2006).
[Crossref] [PubMed]

T. Weise, B. Leibe, and L. V. Gool, “Fast 3D scanning with automatic motion compensation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Guan, C.

Gudbjartsson, H.

H. Gudbjartsson and S. Patz, “The rician distribution of noisy mri data,” Magn. Reson. Med. 34, 910–914 (1995).
[Crossref] [PubMed]

Halioua, M.

Hall-Holt, O.

S. Rusinkiewicz, O. Hall-Holt, and M. Levoy, “Real-time 3D model acquisition,” in Proceedings of SIGGRAPH 2006 (ACM SIGGRAPH, 2002), Vol. 21, pp. 438–446.

Hao, Q.

Hassebrook, L. G.

He, X.

A. K. Wong, P. Niu, and X. He, “Fast acquisition of dense depth data by a new structured light scheme,” Comput. Vis. Image Underst. 98, 398–422 (2005).
[Crossref]

Horn, E.

E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vis. Comput. 17, 87–97 (1999).
[Crossref]

Huang, P.

P. Huang, S. Zhang, and F. Chiang, “Trapezoidal phase-shifting method for three-dimensional shape measurement,” Opt. Eng. (Bellingham) 44, 123601 (2005).
[Crossref]

Huang, P. S.

S. Zhang and P. S. Huang, “Phase error compensation for a 3-d shape measurement system based on the phase-shifting method,” Opt. Eng. (Bellingham) 46, 063601 (2007).
[Crossref]

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

Jia, P.

Kamgar-Parsi, B.

B. Kamgar-Parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–940 (1989).
[Crossref]

Kiryati, N.

E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vis. Comput. 17, 87–97 (1999).
[Crossref]

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[Crossref]

Kofman, J.

Koninckx, T. P.

T. P. Koninckx and L. V. Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 432–445 (2006).
[Crossref] [PubMed]

Lau, D. L.

Leibe, B.

T. Weise, B. Leibe, and L. V. Gool, “Fast 3D scanning with automatic motion compensation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Leonardis, A.

D. Skocaj and A. Leonardis, “Range image acquisition of objects with non-uniform albedo using structured light range sensor,” in Proceedings of the 15th International Conference on Pattern Recognition (IEEE, 2000), Vol. 1, pp. 778–781.
[Crossref]

Levoy, M.

S. Rusinkiewicz, O. Hall-Holt, and M. Levoy, “Real-time 3D model acquisition,” in Proceedings of SIGGRAPH 2006 (ACM SIGGRAPH, 2002), Vol. 21, pp. 438–446.

Li, J.

Li, Y. F.

S. Y. Chen, Y. F. Li, and J. Zhang, “Vision processing for realtime 3-d data acquisition based on coded structured light,” IEEE Trans. Image Process. 17, 167–176 (2008).
[Crossref] [PubMed]

Liu, H.

Liu, K.

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Gamma model and its analysis for phase measuring profilometry,” J. Opt. Soc. Am. A 27, 553–562 (2010).
[Crossref]

Y. Wang, K. Liu, D. L. Lau, and L. G. Hassebrook, “Multicamera phase measuring profilometry for accurate depth measurement,” Proc. SPIE 6555, 655509.1–12 (2007).
[Crossref]

Nayar, S. K.

Y. Y. Schechner, S. K. Nayar, and P. N. Belhumeur, “A theory of multiplexed illumination,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (IEEE, 2003), Vol. 2, pp. 808–815.
[Crossref]

Niu, P.

A. K. Wong, P. Niu, and X. He, “Fast acquisition of dense depth data by a new structured light scheme,” Comput. Vis. Image Underst. 98, 398–422 (2005).
[Crossref]

Pages, J.

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light system,” Pattern Recogn. 37, 827–849 (2004).
[Crossref]

Patz, S.

H. Gudbjartsson and S. Patz, “The rician distribution of noisy mri data,” Magn. Reson. Med. 34, 910–914 (1995).
[Crossref] [PubMed]

Renou, J.

J. Bonny, J. Renou, and M. Zanca, “Optimal measurement of magnitude and phase from mr data,” J. Magn. Reson., Ser. B 113, 136–144 (1996).
[Crossref]

Royer, D.

S. Zhang, D. Royer, and S. T. Yau, “High-resolution, real-time-geometry video acquisition system,” in Proceedings of ACM SIGGRAPH 2006 (ACM, SIGGRAPH, 2006), Article 14.

Rusinkiewicz, S.

S. Rusinkiewicz, O. Hall-Holt, and M. Levoy, “Real-time 3D model acquisition,” in Proceedings of SIGGRAPH 2006 (ACM SIGGRAPH, 2002), Vol. 21, pp. 438–446.

Salvi, J.

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light system,” Pattern Recogn. 37, 827–849 (2004).
[Crossref]

Schechner, Y. Y.

Y. Y. Schechner, S. K. Nayar, and P. N. Belhumeur, “A theory of multiplexed illumination,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (IEEE, 2003), Vol. 2, pp. 808–815.
[Crossref]

Shamir, J.

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[Crossref]

Skocaj, D.

D. Skocaj and A. Leonardis, “Range image acquisition of objects with non-uniform albedo using structured light range sensor,” in Proceedings of the 15th International Conference on Pattern Recognition (IEEE, 2000), Vol. 1, pp. 778–781.
[Crossref]

Srinivasan, V.

Valla, V. G.

V. G. Valla and L. G. Hassebrook, “Very high resolution 3-d surface scanning using multi-frequency phase measuring profilometry,” Proc. SPIE 5798-09, 44–53 (2010)

Wang, Y.

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Gamma model and its analysis for phase measuring profilometry,” J. Opt. Soc. Am. A 27, 553–562 (2010).
[Crossref]

Y. Wang, K. Liu, D. L. Lau, and L. G. Hassebrook, “Multicamera phase measuring profilometry for accurate depth measurement,” Proc. SPIE 6555, 655509.1–12 (2007).
[Crossref]

Weise, T.

T. Weise, B. Leibe, and L. V. Gool, “Fast 3D scanning with automatic motion compensation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Two dimensional phase unwrapping,” Radio Sci. 23, 713–720 (1988).
[Crossref]

Wong, A. K.

A. K. Wong, P. Niu, and X. He, “Fast acquisition of dense depth data by a new structured light scheme,” Comput. Vis. Image Underst. 98, 398–422 (2005).
[Crossref]

Yau, S.

S. Zhang and S. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase shifting algorithm,” Opt. Eng. (Bellingham) 46, 113603 (2007).
[Crossref]

Yau, S. T.

S. Zhang, D. Royer, and S. T. Yau, “High-resolution, real-time-geometry video acquisition system,” in Proceedings of ACM SIGGRAPH 2006 (ACM, SIGGRAPH, 2006), Article 14.

Zanca, M.

J. Bonny, J. Renou, and M. Zanca, “Optimal measurement of magnitude and phase from mr data,” J. Magn. Reson., Ser. B 113, 136–144 (1996).
[Crossref]

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, J.

S. Y. Chen, Y. F. Li, and J. Zhang, “Vision processing for realtime 3-d data acquisition based on coded structured light,” IEEE Trans. Image Process. 17, 167–176 (2008).
[Crossref] [PubMed]

Zhang, S.

S. Zhang and S. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase shifting algorithm,” Opt. Eng. (Bellingham) 46, 113603 (2007).
[Crossref]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-d shape measurement system based on the phase-shifting method,” Opt. Eng. (Bellingham) 46, 063601 (2007).
[Crossref]

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

P. Huang, S. Zhang, and F. Chiang, “Trapezoidal phase-shifting method for three-dimensional shape measurement,” Opt. Eng. (Bellingham) 44, 123601 (2005).
[Crossref]

S. Zhang, D. Royer, and S. T. Yau, “High-resolution, real-time-geometry video acquisition system,” in Proceedings of ACM SIGGRAPH 2006 (ACM, SIGGRAPH, 2006), Article 14.

Appl. Opt. (2)

Comput. Vis. Image Underst. (1)

A. K. Wong, P. Niu, and X. He, “Fast acquisition of dense depth data by a new structured light scheme,” Comput. Vis. Image Underst. 98, 398–422 (2005).
[Crossref]

IEEE Trans. Image Process. (1)

S. Y. Chen, Y. F. Li, and J. Zhang, “Vision processing for realtime 3-d data acquisition based on coded structured light,” IEEE Trans. Image Process. 17, 167–176 (2008).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell. (3)

T. P. Koninckx and L. V. Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28, 432–445 (2006).
[Crossref] [PubMed]

D. Caspi, N. Kiryati, and J. Shamir, “Range imaging with adaptive color structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 470–480 (1998).
[Crossref]

B. Kamgar-Parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–940 (1989).
[Crossref]

Image Vis. Comput. (1)

E. Horn and N. Kiryati, “Toward optimal structured light patterns,” Image Vis. Comput. 17, 87–97 (1999).
[Crossref]

J. Magn. Reson., Ser. B (1)

J. Bonny, J. Renou, and M. Zanca, “Optimal measurement of magnitude and phase from mr data,” J. Magn. Reson., Ser. B 113, 136–144 (1996).
[Crossref]

J. Opt. Soc. Am. A (3)

Magn. Reson. Med. (1)

H. Gudbjartsson and S. Patz, “The rician distribution of noisy mri data,” Magn. Reson. Med. 34, 910–914 (1995).
[Crossref] [PubMed]

Opt. Eng. (Bellingham) (3)

P. Huang, S. Zhang, and F. Chiang, “Trapezoidal phase-shifting method for three-dimensional shape measurement,” Opt. Eng. (Bellingham) 44, 123601 (2005).
[Crossref]

S. Zhang and S. Yau, “High-speed three-dimensional shape measurement system using a modified two-plus-one phase shifting algorithm,” Opt. Eng. (Bellingham) 46, 113603 (2007).
[Crossref]

S. Zhang and P. S. Huang, “Phase error compensation for a 3-d shape measurement system based on the phase-shifting method,” Opt. Eng. (Bellingham) 46, 063601 (2007).
[Crossref]

Opt. Express (1)

Pattern Recogn. (1)

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light system,” Pattern Recogn. 37, 827–849 (2004).
[Crossref]

Proc. SPIE (2)

Y. Wang, K. Liu, D. L. Lau, and L. G. Hassebrook, “Multicamera phase measuring profilometry for accurate depth measurement,” Proc. SPIE 6555, 655509.1–12 (2007).
[Crossref]

V. G. Valla and L. G. Hassebrook, “Very high resolution 3-d surface scanning using multi-frequency phase measuring profilometry,” Proc. SPIE 5798-09, 44–53 (2010)

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 (5)

S. Rusinkiewicz, O. Hall-Holt, and M. Levoy, “Real-time 3D model acquisition,” in Proceedings of SIGGRAPH 2006 (ACM SIGGRAPH, 2002), Vol. 21, pp. 438–446.

S. Zhang, D. Royer, and S. T. Yau, “High-resolution, real-time-geometry video acquisition system,” in Proceedings of ACM SIGGRAPH 2006 (ACM, SIGGRAPH, 2006), Article 14.

D. Skocaj and A. Leonardis, “Range image acquisition of objects with non-uniform albedo using structured light range sensor,” in Proceedings of the 15th International Conference on Pattern Recognition (IEEE, 2000), Vol. 1, pp. 778–781.
[Crossref]

Y. Y. Schechner, S. K. Nayar, and P. N. Belhumeur, “A theory of multiplexed illumination,” in Proceedings of the Ninth IEEE International Conference on Computer Vision (IEEE, 2003), Vol. 2, pp. 808–815.
[Crossref]

T. Weise, B. Leibe, and L. V. Gool, “Fast 3D scanning with automatic motion compensation,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2007), pp. 1–8.

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Figures (14)

Fig. 1
Fig. 1

Cross sections of three-pattern unit frequency PMP with pattern height of 1024 pixels.

Fig. 2
Fig. 2

Three-pattern PMP in coding space R 3 .

Fig. 3
Fig. 3

Reflection process in coding space R N .

Fig. 4
Fig. 4

Two points P 1 and P 2 in R 3 , with L 1 > L 2 , are affected by the same noise ( w 0 , w 1 , w 2 ) such that the errors in phases Φ 1 e and Φ 2 e are, respectively, generated.

Fig. 5
Fig. 5

Three-pattern EP in coding space R 3 .

Fig. 6
Fig. 6

Cross sections of the three-pattern EP strategy.

Fig. 7
Fig. 7

Component patterns from the (left) PMP and (right) EP strategies.

Fig. 8
Fig. 8

The prototype system setup.

Fig. 9
Fig. 9

Three EP pattern strategy is employed. (Left) The first projected pattern in projector. (Middle) The corresponding captured image in camera. (Right) The phase image after processing the three captured EP patterns.

Fig. 10
Fig. 10

Cross sections of phase error for the scanned board using (left) three-pattern, (middle) four-pattern, and (right) five-pattern PMP and EP strategies.

Fig. 11
Fig. 11

The ratio between standard deviations of phase error using PMP and EP strategies, σ PMP / σ EP , for different numbers of patterns.

Fig. 12
Fig. 12

Comparison of 3-D reconstructions using PMP and EP. (a) 3-D reconstructions using three-pattern strategies. (b) 3-D reconstructions using four-pattern strategies. (c) 3-D reconstructions using five-pattern strategies. Left: 3-D reconstructions using PMP. Right: 3-D reconstructions using EP. Top: Front views. Bottom: Side views.

Fig. 13
Fig. 13

The distributions of phase error for (left) three-pattern, (middle) four-pattern, and (right) five-pattern PMP and EP strategies.

Fig. 14
Fig. 14

Cross sections of phase error of the scanned board from three-pattern PMP and EP strategies using traditional ambiguous four frequencies.

Tables (5)

Tables Icon

Table 1 Four-Pattern EP Strategy

Tables Icon

Table 2 Edge Order for Three-Pattern Strategy

Tables Icon

Table 3 Theoretical Improvements of SNR for Different Numbers of Patterns

Tables Icon

Table 4 Standard Deviation Values of Phase Error of the Scanned Board for PMP and EP

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Table 5 Standard Deviation Values of Phase Error of the Scanned Alice for PMP and EP

Equations (17)

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I n ( x p , y p ) = A + B   cos ( Φ ( y p ) 2 π n N ) ,
I n c ( x c , y c ) = α ( x c , y c ) [ A + B   cos ( Φ ( y p ) 2 π n N ) + β ( x c , y c ) ] ,
ϕ ( x c , y c ) = arctan [ n = 0 N 1 I n c ( x c , y c ) sin ( 2 π n N ) n = 0 N 1 I n c ( x c , y c ) cos ( 2 π n N ) ] = arctan [ α ( x c , y c ) B   sin ( Φ ( y p ) ) α ( x c , y c ) B   cos ( Φ ( y p ) ) ] ,
O ( o 0 , o 1 , , o N 1 ) = ( lim B 0 I 0 , lim B 0 I 1 , , lim B 0 I N 1 ) ,
L ( y p ) = { n = 0 N 1 [ I n ( y p ) o n ] 2 } 1 / 2 ,
I ̃ n c ( x c , y c ) = I n c ( x c , y c ) + w n ( x c , y c ) ,
Φ e ( x c , y c ) = Φ ( x c , y c ) Φ ̃ ( x c , y c ) = arctan ( Y X ) ,
Φ e ( x c , y c ) 2 N n = 0 N 1 w n c   cos ( Φ ( y p ) 2 π n N ) α ( x c , y c ) L ( y p ) .
f L ̃ , Φ e ( l ̃ , ϕ e ) = 2 N α l ̃ 4 π σ 2 exp [ α 2 ( l ̃ ) 2 + L 2 2 l ̃ ( L   cos ( ϕ e ) ) 2 σ 2 ] .
f Φ e ( ϕ e ) = exp ( α 2 L 2 2 σ 2 ) 1 + κ π   exp ( κ 2 ) ( 1 + erf ( κ ) ) 2 π ,
f Φ e ( ϕ e ) α L   cos ( ϕ e ) 2 π σ exp [ α 2 L 2 sin 2 ( ϕ e ) 2 σ 2 ] α L 2 π σ exp [ α 2 L 2 ϕ e 2 2 σ 2 ] ,
σ Φ ( x c , y c ) σ α ( x c , y c ) F L ( y p ) .
SNR ( x c , y c ) = L ( y p ) F σ .
L y p = [ n = 0 N 1 ( I n ( y p ) 0.5 ) 2 ] 1 / 2 .
λ ( y p ) = tan [ Φ ( y p ) ] cos ( 2 π k 1 N ) sin ( 2 π k 1 N ) sin ( 2 π k 2 N ) tan [ Φ ( y p ) ] cos ( 2 π k 2 N ) .
ϕ ( x c , y c ) = arctan [ 3 0.5 ( I 1 c ( x c , y c ) I 2 c ( x c , y c ) ) 2 I 0 c ( x c , y c ) I 1 c ( x c , y c ) I 2 c ( x c , y c ) ] .
E = ( N 1 ) ( 2 N 1 2 ) ,

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