Abstract

Temporal frame-to-frame noise in multipattern structured light projection can significantly corrupt depth measurement repeatability. We present a rigorous stochastic analysis of phase-measuring-profilometry temporal noise as a function of the pattern parameters and the reconstruction coefficients. The analysis is used to optimize the two-frequency phase measurement technique. In phase-measuring profilometry, a sequence of phase-shifted sine-wave patterns is projected onto a surface. In two-frequency phase measurement, two sets of pattern sequences are used. The first, low-frequency set establishes a nonambiguous depth estimate, and the second, high-frequency set is unwrapped, based on the low-frequency estimate, to obtain an accurate depth estimate. If the second frequency is too low, then depth error is caused directly by temporal noise in the phase measurement. If the second frequency is too high, temporal noise triggers ambiguous unwrapping, resulting in depth measurement error. We present a solution for finding the second frequency, where intensity noise variance is at its minimum.

© 2003 Optical Society of America

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  1. F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
    [CrossRef]
  2. J. Batlle, E. Mouaddib, J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
    [CrossRef]
  3. X. Y. Su, W. S. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Applications of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, Hong Liu, H. Podbielska, A. O. Wist, L. J. Eamorano, eds., Proc. SPIE2132, 484–489 (1994).
    [CrossRef]
  4. G. Sansoni, F. Docchio, U. Minoni, L. Biancardi, “Adaptive profilometry for industrial applications,” in Laser Applications to Mechanical Industry, S. Martellucci, A. N. Chester, eds. (Kluwer Academic, Norwell, Mass., 1993), pp. 351–365.
  5. R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin, H. Fuchs, “The office of the future: a unified approach to image-based modeling and spatially immersive displays,” presented at SIGGRAPH 98, Orlando, Fla., July 19–24, 1998.
  6. G. Schmaltz, “A method for presenting the profile curves of rough surfaces,” Naturwissenschaften 18, 315–316 (1932).
    [CrossRef]
  7. Y. Shirai, M. Suwa, “Recognition of polyhedrons with a range finder,” in Proceeding of the International Joint Conference on Artificial Intelligence (Morgan Kaufman, San Francisco, Calif., 1971), pp. 80–87.
  8. P. M. Will, K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
    [CrossRef]
  9. B. Carrihill, R. Hummel, “Experiments with intensity ratio depth sensor,” Comput. Vision Graph. Image Process. 32, 337–358 (1985).
    [CrossRef]
  10. D. S. Goodman, L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27(4B), 2671–2673 (1984).
  11. J. L. Posdamer, M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Vision Graph. Image Process. 18, 1–17 (1982).
    [CrossRef]
  12. D. M. Meadows, W. O. Johnson, J. B. Allen, “Generation of surface contours by moire patterns,” Appl. Opt. 9, 942 (1970).
    [CrossRef] [PubMed]
  13. G. Goli, Chun Guan, L. G. Hassebrook, D. L. Lau, “Video rate three dimensional data acquisition using composite light structure patterns,” (May30, 2002).
  14. V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase measuring profilometry: a phase mapping approach,” Appl. Opt. 24, 185–188 (1985).
    [CrossRef]
  15. K. L. Boyer, A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 14–28 (1987).
    [CrossRef]
  16. L. G. Hassebrook, R. C. Daley, W. Chimitt, “Application of communication theory to high speed structured light illumination,” in Three-Dimensional Imaging and Laser-Based Systems for Metrology and Inspection III, K. G. Harding, D. J. Svetproff, eds., Proc. SPIE3204, 102–113 (1997).
    [CrossRef]
  17. J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
    [CrossRef]
  18. H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497–4500 (1994).
    [CrossRef] [PubMed]
  19. M. Trobina, “Error model of a coded-light range sensor,” (September21, 1995), pp. 1–35.
  20. R. C. Daley, L. G. Hassebrook, “Channel capacity model of binary encoded structured light-stripe illumination,” Appl. Opt. 37, 3689–3696 (1998).
    [CrossRef]
  21. O. D. Faugeras, G. Toscani, “The calibration problem for stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition ’86 (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 15–20 (1986).
  22. R. Y. Tsai, “A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE Trans. Rob. Autom. RA-3, 323–344 (1987).
    [CrossRef]
  23. R. J. Valkenburg, A. M. McIvor, “Accurate 3D measurement using a structured light system,” Image Vision Comput. 16, 99–110 (1998).
    [CrossRef]
  24. R. W. DePiero, M. M. Trivedi, “3-D computer vision using structured light: design, calibration and implementation issues,” Adv. Comput. 43, 243–278 (1996).
    [CrossRef]
  25. Behrooz Kamgar-parsi, Behzad Kamgar-parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–939 (1989).
    [CrossRef]
  26. W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt., 41, 89–94 (1994).
    [CrossRef]
  27. F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1993).
  28. J. Weng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
    [CrossRef]
  29. E. Trucco, A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice-Hall, Englewood Cliffs, N.J., 1998), Chap. 6, pp. 123–138.

2000 (1)

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

1998 (3)

J. Batlle, E. Mouaddib, J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[CrossRef]

R. C. Daley, L. G. Hassebrook, “Channel capacity model of binary encoded structured light-stripe illumination,” Appl. Opt. 37, 3689–3696 (1998).
[CrossRef]

R. J. Valkenburg, A. M. McIvor, “Accurate 3D measurement using a structured light system,” Image Vision Comput. 16, 99–110 (1998).
[CrossRef]

1997 (1)

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
[CrossRef]

1996 (1)

R. W. DePiero, M. M. Trivedi, “3-D computer vision using structured light: design, calibration and implementation issues,” Adv. Comput. 43, 243–278 (1996).
[CrossRef]

1994 (2)

W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt., 41, 89–94 (1994).
[CrossRef]

H. Zhao, W. Chen, Y. Tan, “Phase-unwrapping algorithm for the measurement of three-dimensional object shapes,” Appl. Opt. 33, 4497–4500 (1994).
[CrossRef] [PubMed]

1992 (1)

J. Weng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

1989 (1)

Behrooz Kamgar-parsi, Behzad Kamgar-parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–939 (1989).
[CrossRef]

1987 (2)

R. Y. Tsai, “A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE Trans. Rob. Autom. RA-3, 323–344 (1987).
[CrossRef]

K. L. Boyer, A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 14–28 (1987).
[CrossRef]

1985 (2)

V. Srinivasan, H. C. Liu, M. Halioua, “Automated phase measuring profilometry: a phase mapping approach,” Appl. Opt. 24, 185–188 (1985).
[CrossRef]

B. Carrihill, R. Hummel, “Experiments with intensity ratio depth sensor,” Comput. Vision Graph. Image Process. 32, 337–358 (1985).
[CrossRef]

1984 (1)

D. S. Goodman, L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27(4B), 2671–2673 (1984).

1982 (1)

J. L. Posdamer, M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Vision Graph. Image Process. 18, 1–17 (1982).
[CrossRef]

1971 (1)

P. M. Will, K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
[CrossRef]

1970 (1)

1932 (1)

G. Schmaltz, “A method for presenting the profile curves of rough surfaces,” Naturwissenschaften 18, 315–316 (1932).
[CrossRef]

Allen, J. B.

Altschuler, M. D.

J. L. Posdamer, M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Vision Graph. Image Process. 18, 1–17 (1982).
[CrossRef]

Batlle, J.

J. Batlle, E. Mouaddib, J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[CrossRef]

Biancardi, L.

G. Sansoni, F. Docchio, U. Minoni, L. Biancardi, “Adaptive profilometry for industrial applications,” in Laser Applications to Mechanical Industry, S. Martellucci, A. N. Chester, eds. (Kluwer Academic, Norwell, Mass., 1993), pp. 351–365.

Boyer, K. L.

K. L. Boyer, A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 14–28 (1987).
[CrossRef]

Brown, G. M.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Carrihill, B.

B. Carrihill, R. Hummel, “Experiments with intensity ratio depth sensor,” Comput. Vision Graph. Image Process. 32, 337–358 (1985).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Chen, W.

Chimitt, W.

L. G. Hassebrook, R. C. Daley, W. Chimitt, “Application of communication theory to high speed structured light illumination,” in Three-Dimensional Imaging and Laser-Based Systems for Metrology and Inspection III, K. G. Harding, D. J. Svetproff, eds., Proc. SPIE3204, 102–113 (1997).
[CrossRef]

Cohen, P.

J. Weng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Cutts, M.

R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin, H. Fuchs, “The office of the future: a unified approach to image-based modeling and spatially immersive displays,” presented at SIGGRAPH 98, Orlando, Fla., July 19–24, 1998.

Daley, R. C.

R. C. Daley, L. G. Hassebrook, “Channel capacity model of binary encoded structured light-stripe illumination,” Appl. Opt. 37, 3689–3696 (1998).
[CrossRef]

L. G. Hassebrook, R. C. Daley, W. Chimitt, “Application of communication theory to high speed structured light illumination,” in Three-Dimensional Imaging and Laser-Based Systems for Metrology and Inspection III, K. G. Harding, D. J. Svetproff, eds., Proc. SPIE3204, 102–113 (1997).
[CrossRef]

DePiero, R. W.

R. W. DePiero, M. M. Trivedi, “3-D computer vision using structured light: design, calibration and implementation issues,” Adv. Comput. 43, 243–278 (1996).
[CrossRef]

Docchio, F.

G. Sansoni, F. Docchio, U. Minoni, L. Biancardi, “Adaptive profilometry for industrial applications,” in Laser Applications to Mechanical Industry, S. Martellucci, A. N. Chester, eds. (Kluwer Academic, Norwell, Mass., 1993), pp. 351–365.

Faugeras, O. D.

O. D. Faugeras, G. Toscani, “The calibration problem for stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition ’86 (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 15–20 (1986).

Fuchs, H.

R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin, H. Fuchs, “The office of the future: a unified approach to image-based modeling and spatially immersive displays,” presented at SIGGRAPH 98, Orlando, Fla., July 19–24, 1998.

Goli, G.

G. Goli, Chun Guan, L. G. Hassebrook, D. L. Lau, “Video rate three dimensional data acquisition using composite light structure patterns,” (May30, 2002).

Goodman, D. S.

D. S. Goodman, L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27(4B), 2671–2673 (1984).

Guan, Chun

G. Goli, Chun Guan, L. G. Hassebrook, D. L. Lau, “Video rate three dimensional data acquisition using composite light structure patterns,” (May30, 2002).

Halioua, M.

Hassebrook, L. G.

R. C. Daley, L. G. Hassebrook, “Channel capacity model of binary encoded structured light-stripe illumination,” Appl. Opt. 37, 3689–3696 (1998).
[CrossRef]

D. S. Goodman, L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27(4B), 2671–2673 (1984).

G. Goli, Chun Guan, L. G. Hassebrook, D. L. Lau, “Video rate three dimensional data acquisition using composite light structure patterns,” (May30, 2002).

L. G. Hassebrook, R. C. Daley, W. Chimitt, “Application of communication theory to high speed structured light illumination,” in Three-Dimensional Imaging and Laser-Based Systems for Metrology and Inspection III, K. G. Harding, D. J. Svetproff, eds., Proc. SPIE3204, 102–113 (1997).
[CrossRef]

Herniou, M.

J. Weng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Hummel, R.

B. Carrihill, R. Hummel, “Experiments with intensity ratio depth sensor,” Comput. Vision Graph. Image Process. 32, 337–358 (1985).
[CrossRef]

Huntley, J. M.

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
[CrossRef]

Johnson, W. O.

Kak, A. C.

K. L. Boyer, A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 14–28 (1987).
[CrossRef]

Kamgar-parsi, Behrooz

Behrooz Kamgar-parsi, Behzad Kamgar-parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–939 (1989).
[CrossRef]

Kamgar-parsi, Behzad

Behrooz Kamgar-parsi, Behzad Kamgar-parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–939 (1989).
[CrossRef]

Lake, A.

R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin, H. Fuchs, “The office of the future: a unified approach to image-based modeling and spatially immersive displays,” presented at SIGGRAPH 98, Orlando, Fla., July 19–24, 1998.

Lau, D. L.

G. Goli, Chun Guan, L. G. Hassebrook, D. L. Lau, “Video rate three dimensional data acquisition using composite light structure patterns,” (May30, 2002).

Liu, H. C.

McIvor, A. M.

R. J. Valkenburg, A. M. McIvor, “Accurate 3D measurement using a structured light system,” Image Vision Comput. 16, 99–110 (1998).
[CrossRef]

Meadows, D. M.

Minoni, U.

G. Sansoni, F. Docchio, U. Minoni, L. Biancardi, “Adaptive profilometry for industrial applications,” in Laser Applications to Mechanical Industry, S. Martellucci, A. N. Chester, eds. (Kluwer Academic, Norwell, Mass., 1993), pp. 351–365.

Mouaddib, E.

J. Batlle, E. Mouaddib, J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[CrossRef]

Pedrotti, F. L.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Pedrotti, L. S.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Pennington, K. S.

P. M. Will, K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
[CrossRef]

Posdamer, J. L.

J. L. Posdamer, M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Vision Graph. Image Process. 18, 1–17 (1982).
[CrossRef]

Raskar, R.

R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin, H. Fuchs, “The office of the future: a unified approach to image-based modeling and spatially immersive displays,” presented at SIGGRAPH 98, Orlando, Fla., July 19–24, 1998.

Saldner, H. O.

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
[CrossRef]

Salvi, J.

J. Batlle, E. Mouaddib, J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[CrossRef]

Sansoni, G.

G. Sansoni, F. Docchio, U. Minoni, L. Biancardi, “Adaptive profilometry for industrial applications,” in Laser Applications to Mechanical Industry, S. Martellucci, A. N. Chester, eds. (Kluwer Academic, Norwell, Mass., 1993), pp. 351–365.

Schmaltz, G.

G. Schmaltz, “A method for presenting the profile curves of rough surfaces,” Naturwissenschaften 18, 315–316 (1932).
[CrossRef]

Shirai, Y.

Y. Shirai, M. Suwa, “Recognition of polyhedrons with a range finder,” in Proceeding of the International Joint Conference on Artificial Intelligence (Morgan Kaufman, San Francisco, Calif., 1971), pp. 80–87.

Song, M.

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Srinivasan, V.

Stesin, L.

R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin, H. Fuchs, “The office of the future: a unified approach to image-based modeling and spatially immersive displays,” presented at SIGGRAPH 98, Orlando, Fla., July 19–24, 1998.

Su, X. Y.

W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt., 41, 89–94 (1994).
[CrossRef]

X. Y. Su, W. S. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Applications of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, Hong Liu, H. Podbielska, A. O. Wist, L. J. Eamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

Suwa, M.

Y. Shirai, M. Suwa, “Recognition of polyhedrons with a range finder,” in Proceeding of the International Joint Conference on Artificial Intelligence (Morgan Kaufman, San Francisco, Calif., 1971), pp. 80–87.

Tan, Y.

Toscani, G.

O. D. Faugeras, G. Toscani, “The calibration problem for stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition ’86 (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 15–20 (1986).

Trivedi, M. M.

R. W. DePiero, M. M. Trivedi, “3-D computer vision using structured light: design, calibration and implementation issues,” Adv. Comput. 43, 243–278 (1996).
[CrossRef]

Trobina, M.

M. Trobina, “Error model of a coded-light range sensor,” (September21, 1995), pp. 1–35.

Trucco, E.

E. Trucco, A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice-Hall, Englewood Cliffs, N.J., 1998), Chap. 6, pp. 123–138.

Tsai, R. Y.

R. Y. Tsai, “A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE Trans. Rob. Autom. RA-3, 323–344 (1987).
[CrossRef]

Valkenburg, R. J.

R. J. Valkenburg, A. M. McIvor, “Accurate 3D measurement using a structured light system,” Image Vision Comput. 16, 99–110 (1998).
[CrossRef]

Verri, A.

E. Trucco, A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice-Hall, Englewood Cliffs, N.J., 1998), Chap. 6, pp. 123–138.

Welch, G.

R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin, H. Fuchs, “The office of the future: a unified approach to image-based modeling and spatially immersive displays,” presented at SIGGRAPH 98, Orlando, Fla., July 19–24, 1998.

Weng, J.

J. Weng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

Will, P. M.

P. M. Will, K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
[CrossRef]

Zhao, H.

Zhou, W. S.

W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt., 41, 89–94 (1994).
[CrossRef]

X. Y. Su, W. S. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Applications of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, Hong Liu, H. Podbielska, A. O. Wist, L. J. Eamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

Adv. Comput. (1)

R. W. DePiero, M. M. Trivedi, “3-D computer vision using structured light: design, calibration and implementation issues,” Adv. Comput. 43, 243–278 (1996).
[CrossRef]

Appl. Opt. (4)

Artif. Intell. (1)

P. M. Will, K. S. Pennington, “Grid coding: a preprocessing technique for robot and machine vision,” Artif. Intell. 2, 319–329 (1971).
[CrossRef]

Comput. Vision Graph. Image Process. (2)

B. Carrihill, R. Hummel, “Experiments with intensity ratio depth sensor,” Comput. Vision Graph. Image Process. 32, 337–358 (1985).
[CrossRef]

J. L. Posdamer, M. D. Altschuler, “Surface measurement by space-encoded projected beam systems,” Comput. Vision Graph. Image Process. 18, 1–17 (1982).
[CrossRef]

IBM Tech. Discl. Bull. (1)

D. S. Goodman, L. G. Hassebrook, “Surface contour measuring instrument,” IBM Tech. Discl. Bull. 27(4B), 2671–2673 (1984).

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

K. L. Boyer, A. C. Kak, “Colored-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 14–28 (1987).
[CrossRef]

Behrooz Kamgar-parsi, Behzad Kamgar-parsi, “Evaluation of quantization error in computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 929–939 (1989).
[CrossRef]

J. Weng, P. Cohen, M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 965–980 (1992).
[CrossRef]

IEEE Trans. Rob. Autom. (1)

R. Y. Tsai, “A versatile camera calibration technique for high accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE Trans. Rob. Autom. RA-3, 323–344 (1987).
[CrossRef]

Image Vision Comput. (1)

R. J. Valkenburg, A. M. McIvor, “Accurate 3D measurement using a structured light system,” Image Vision Comput. 16, 99–110 (1998).
[CrossRef]

J. Mod. Opt. (1)

W. S. Zhou, X. Y. Su, “A direct mapping algorithm for phase-measuring profilometry,” J. Mod. Opt., 41, 89–94 (1994).
[CrossRef]

Meas. Sci. Technol. (1)

J. M. Huntley, H. O. Saldner, “Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms,” Meas. Sci. Technol. 8, 986–992 (1997).
[CrossRef]

Naturwissenschaften (1)

G. Schmaltz, “A method for presenting the profile curves of rough surfaces,” Naturwissenschaften 18, 315–316 (1932).
[CrossRef]

Opt. Eng. (1)

F. Chen, G. M. Brown, M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng. 39, 10–22 (2000).
[CrossRef]

Pattern Recogn. (1)

J. Batlle, E. Mouaddib, J. Salvi, “Recent progress in coded structured light as a technique to solve the correspondence problem: a survey,” Pattern Recogn. 31, 963–982 (1998).
[CrossRef]

Other (10)

X. Y. Su, W. S. Zhou, “Complex object profilometry and its application for dentistry,” in Clinical Applications of Modern Imaging Technology II, L. J. Cerullo, K. S. Heiferman, Hong Liu, H. Podbielska, A. O. Wist, L. J. Eamorano, eds., Proc. SPIE2132, 484–489 (1994).
[CrossRef]

G. Sansoni, F. Docchio, U. Minoni, L. Biancardi, “Adaptive profilometry for industrial applications,” in Laser Applications to Mechanical Industry, S. Martellucci, A. N. Chester, eds. (Kluwer Academic, Norwell, Mass., 1993), pp. 351–365.

R. Raskar, G. Welch, M. Cutts, A. Lake, L. Stesin, H. Fuchs, “The office of the future: a unified approach to image-based modeling and spatially immersive displays,” presented at SIGGRAPH 98, Orlando, Fla., July 19–24, 1998.

Y. Shirai, M. Suwa, “Recognition of polyhedrons with a range finder,” in Proceeding of the International Joint Conference on Artificial Intelligence (Morgan Kaufman, San Francisco, Calif., 1971), pp. 80–87.

M. Trobina, “Error model of a coded-light range sensor,” (September21, 1995), pp. 1–35.

L. G. Hassebrook, R. C. Daley, W. Chimitt, “Application of communication theory to high speed structured light illumination,” in Three-Dimensional Imaging and Laser-Based Systems for Metrology and Inspection III, K. G. Harding, D. J. Svetproff, eds., Proc. SPIE3204, 102–113 (1997).
[CrossRef]

G. Goli, Chun Guan, L. G. Hassebrook, D. L. Lau, “Video rate three dimensional data acquisition using composite light structure patterns,” (May30, 2002).

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N.J., 1993).

O. D. Faugeras, G. Toscani, “The calibration problem for stereo,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition ’86 (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 15–20 (1986).

E. Trucco, A. Verri, Introductory Techniques for 3-D Computer Vision (Prentice-Hall, Englewood Cliffs, N.J., 1998), Chap. 6, pp. 123–138.

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Figures (10)

Fig. 1
Fig. 1

Geometry of single-stripe SL range finder.

Fig. 2
Fig. 2

Coordinates in active range finder.

Fig. 3
Fig. 3

Base frequency projections onto a Space Shuttle model for N=4.

Fig. 4
Fig. 4

Perspective projection model.

Fig. 5
Fig. 5

Phase STD change with increase of N, with scanning frequency f=1, BP=128, and σ = 2.8309.

Fig. 6
Fig. 6

Phase STD change with increase of BP, with scanning frequency f=1, N=4, and σ = 2.8309.

Fig. 7
Fig. 7

Reconstructed world coordinate STD change with increase of frequency when N=4 and BP=128.

Fig. 8
Fig. 8

Two data sets of simulated and experimental normalized unwrapped phase STD with increase of frequency for σϕ=0.025346 and σϕ=0.047689. Experimental sets are scanned with N=4. BP=48 and BP=88 for circles and squares, respectively. f1 and f2 are the optimal frequencies predicted by the mathematical model.

Fig. 9
Fig. 9

Range data of a face under (a) unit frequency and (b) two frequencies.

Fig. 10
Fig. 10

Reconstructed world coordinates of a face with intensity values.

Equations (42)

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In(xp, yp)=Ap+Bp cos(2πfyp-2πn/N),
In(xc, yc)=A(xc, yc)+B(xc, yc)cos[ϕ(xc, yc)-2πn/N],
ϕ(xc, yc)=arctann=1NIn(xc, yc)sin(2πn/N)n=1NIn(xc, yc)cos(2πn/N).
yp=ϕ(xc, yc)/(2πf).
xc=m11wcXw+m12wcYw+m13wcZw+m14wcm31wcXw+m32wcYw+m33wcZw+m34wc,
yc=m21wcXw+m22wcYw+m23wcZw+m24wcm31wcXw+m32wcYw+m33wcZw+m34wc,
Mwc=m11wcm12wcm13wcm14wcm21wcm22wcm23wcm24wcm31wcm32wcm33wcm34wc.
A=X1wY1wZ1w10000-x1cX1w-x1cY1w-x1cZ1w-x1c0000X1wY1wZ1w1-y1cX1w-y1cY1w-y1cZ1w-y1cX2wY2wZ2w10000-x2cX2w-x2cY2w-x2cZ2w-x2c0000X2wY2wZ2w1-y2cX2w-y2cY2w-y2cZ2w-y2cXMwYMwZMw10000-xMcXMw-xMcYMw-xMcZMw-xMc0000XMwYMwZMw1-yMcXMw-yNcYMw-yMcZMw-yMc,
m=[m11wcm12wcm13wcm34wc]T.
A=UDVT,
Mwp=m11wpm12wpm13wpm14wpm21wpm22wpm23wpm24wpm31wpm32wpm33wpm34wp,
yp=m21wpXw+m22wpYw+m23wpZw+m24wpm31wpXw+m32wpYw+m33wpZw+m34wp.
C=m11wc-m31wcxcm12wc-m32wcxcm13wc-m33wcxcm21wc-m31wcycm22wc-m32wcycm23wc-m33wcycm21wp-m31wpypm22wp-m32wpypm23wp-m33wpyp,
D=m34wcxc-m14wcm34wcyc-m24wcm34wpyp-m24wp,
Pw=[XwYwZw]T=C-1D.
An=A(xc, yc)=A0(xc, yc)+ΔAn(xc, yc),
S(An)=n=1NIn sin(2πn/N)=n=1NAn sin(2πn/N)+N2 B sin(ϕ).
C(An)=n=1NIn cos(2πn/N)=n=1NAn cos(2πn/N)+N2 B cos(ϕ).
ϕ=arctanS(An)C(An).
Δϕ=n=1NϕAnAn=An0ΔAn,
ϕAnAn0=11+[S(An0)/C(An0)]2×S(An0) C(An)An-C(An0) S(An)AnC(An)2An=An0,
S(An0)=N2 B sin(ϕ),
C(An0)=N2 B cos(ϕ).
S(An)AnAn0=sin(2πn/N),
C(An)AnAn0=cos(2πn/N).
ϕAnAn=An0=2NB sin(ϕ+2πn/N).
Δϕ=2NB n=1N sin(ϕ+2πn/N)ΔAn.
σϕ2=2NB2σ2n=1N sin2(ϕ+2πn/N)=2N σ2B2.
CPypw+C1Pw=D1,
Pypw=XwypYwypZwypT=[XeYeZe]T,
C1=000000-m31wp-m32wp-m33wp,
D1=[00m34wp]T.
Pypw=C-1(D1-C1C-1D).
ΔPw=[dXwdYwdZw]T=PypwΔϕ/(2πf).
ΔPw=PypwπfNB n=1N sin(ϕ-2πn/N)ΔAn.
[σXwσYwσZw]=[|Xe||Ye||Ze|] σ2NπfB.
In(xc, yc)=Q256(A(xc, yc))+Q256(B(xc, yc))×cos[2πfQNp(ypNp)/Np-2πn/N].
Nf=ϕ1f-ϕ22π,
Δϕu=Δϕ2/fwhen |Δϕ1|π/fΔϕ1when π/f<|Δϕ1|π,
E{Δϕu2}=E{E{Δϕu2|Δϕ1}}=--Δϕu2f(Δϕu, Δϕ1)d(Δϕ1)d(Δϕu).
σϕu2=P1πf σϕ2f2+σϕ2-P2πf,
P1(x)=12πσϕ -xx exp-y22σϕ2dy,P2(x)=12πσϕ -xxy2 exp-y22σϕ2dy.

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