Abstract

A new analysis technique for the automatic measurement of a three-dimensional object shape is proposed and verified experimentally. In this structured-light technique the process of projecting a grating pattern upon the object is considered for using carrier frequencies to modulate the object spectrum in the spatial frequency domain or to add a reference surface to the data in the space domain. The projected fringes are considered as interferometric fringes; therefore the interferogram analysis technique can be introduced into the measurement of a three-dimensional object shape.

© 1993 Optical Society of America

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  1. T. C. Strand, “Optical three dimensional sensing for machine vision,” Opt. Eng. 24, 33–40 (1985).
  2. J. A. Jalkio, R. C. Kim, S. K. Case, “Three dimensional inspection using multistripe structured light,” Opt. Eng. 24, 966–974 (1985).
  3. R. A. Jarvis, “A perspective on range finding techniques for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 122–139 (1983).
    [CrossRef]
  4. S. Jin, Y. M. Li, “The distance measurement in three-dimensional computer vision,” Chin. Robot. 3, 57–64 (1989), in Chinese.
  5. K. L. Boyer, A. C. Kak, “Color-encoded structured light for rapid active ranging,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 14–28 (1987).
    [CrossRef]
  6. B. F. Alexander, K. C. Ng, “3-D shape measurement by active triangulation using array of coded light stripes,” in Optics, Illumination, and Image Sensing for Machine Vision II, D. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.850, 199–209 (1987).
  7. P. Vuylsleke, A. Oosterlinck, “Range image acquisition with a single binary-encoded light pattern,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 150–160 (1990).
  8. G. Hu, G. C. Stockman, “3-D surface solution vision structure light and constraint propagation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 390–402 (1989).
    [CrossRef]
  9. H. S. Yang, K. L. Boyer, A. C. Kak, “Range data extraction and interpretation by structure light,” Tech. Rep. 25 (Purdue University, West Lafayette, Ind., 1984), pp. 199–205.
  10. J. Le Moigne, A. M. Waxman, “Multi-resolution grid pattern for building range maps,” Tech. Rep. (University of Maryland, College Park, Md.).
  11. J. L. Posdamer, M. D. Altchuler, “Surface measurement by space-encoded projected beam system,” Comput. Vision Graphics Image Process. 18, 1–17 (1982).
    [CrossRef]
  12. B. Carrihill, R. Hummel, “Experiments with the intensity ratio depth sensor,” Comput. Vision Graphics Image Process. 32, 337–358 (1985).
    [CrossRef]
  13. M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef] [PubMed]
  14. M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  15. J. Li, X. Y. Su, L. R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
    [CrossRef]
  16. Z. X. Chen, X. Y. Su, “3-D object shapes measurement system by quasi-sine modulation optical field,” Chin. J. Sci. Instrum. 10, 409–415 (1989).
  17. M. Goharla'ee, M. Reaberg, “Applications of structured lighting for volume measurement,” in Optics, Illumination, and Image Sensing for Machine Vision, D. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.728, 65–73 (1986).

1990 (2)

P. Vuylsleke, A. Oosterlinck, “Range image acquisition with a single binary-encoded light pattern,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 150–160 (1990).

J. Li, X. Y. Su, L. R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

1989 (3)

Z. X. Chen, X. Y. Su, “3-D object shapes measurement system by quasi-sine modulation optical field,” Chin. J. Sci. Instrum. 10, 409–415 (1989).

G. Hu, G. C. Stockman, “3-D surface solution vision structure light and constraint propagation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 390–402 (1989).
[CrossRef]

S. Jin, Y. M. Li, “The distance measurement in three-dimensional computer vision,” Chin. Robot. 3, 57–64 (1989), in Chinese.

1987 (1)

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

1985 (3)

T. C. Strand, “Optical three dimensional sensing for machine vision,” Opt. Eng. 24, 33–40 (1985).

J. A. Jalkio, R. C. Kim, S. K. Case, “Three dimensional inspection using multistripe structured light,” Opt. Eng. 24, 966–974 (1985).

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

1983 (2)

M. Takeda, K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3-D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
[CrossRef] [PubMed]

R. A. Jarvis, “A perspective on range finding techniques for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 122–139 (1983).
[CrossRef]

1982 (2)

M. Takeda, H. Ina, S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
[CrossRef]

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

Alexander, B. F.

B. F. Alexander, K. C. Ng, “3-D shape measurement by active triangulation using array of coded light stripes,” in Optics, Illumination, and Image Sensing for Machine Vision II, D. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.850, 199–209 (1987).

Altchuler, M. D.

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

Boyer, K. L.

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

H. S. Yang, K. L. Boyer, A. C. Kak, “Range data extraction and interpretation by structure light,” Tech. Rep. 25 (Purdue University, West Lafayette, Ind., 1984), pp. 199–205.

Carrihill, B.

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

Case, S. K.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three dimensional inspection using multistripe structured light,” Opt. Eng. 24, 966–974 (1985).

Chen, Z. X.

Z. X. Chen, X. Y. Su, “3-D object shapes measurement system by quasi-sine modulation optical field,” Chin. J. Sci. Instrum. 10, 409–415 (1989).

Goharla'ee, M.

M. Goharla'ee, M. Reaberg, “Applications of structured lighting for volume measurement,” in Optics, Illumination, and Image Sensing for Machine Vision, D. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.728, 65–73 (1986).

Guo, L. R.

J. Li, X. Y. Su, L. R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

Hu, G.

G. Hu, G. C. Stockman, “3-D surface solution vision structure light and constraint propagation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 390–402 (1989).
[CrossRef]

Hummel, R.

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

Ina, H.

Jalkio, J. A.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three dimensional inspection using multistripe structured light,” Opt. Eng. 24, 966–974 (1985).

Jarvis, R. A.

R. A. Jarvis, “A perspective on range finding techniques for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 122–139 (1983).
[CrossRef]

Jin, S.

S. Jin, Y. M. Li, “The distance measurement in three-dimensional computer vision,” Chin. Robot. 3, 57–64 (1989), in Chinese.

Kak, A. C.

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

H. S. Yang, K. L. Boyer, A. C. Kak, “Range data extraction and interpretation by structure light,” Tech. Rep. 25 (Purdue University, West Lafayette, Ind., 1984), pp. 199–205.

Kim, R. C.

J. A. Jalkio, R. C. Kim, S. K. Case, “Three dimensional inspection using multistripe structured light,” Opt. Eng. 24, 966–974 (1985).

Kobayashi, S.

Le Moigne, J.

J. Le Moigne, A. M. Waxman, “Multi-resolution grid pattern for building range maps,” Tech. Rep. (University of Maryland, College Park, Md.).

Li, J.

J. Li, X. Y. Su, L. R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

Li, Y. M.

S. Jin, Y. M. Li, “The distance measurement in three-dimensional computer vision,” Chin. Robot. 3, 57–64 (1989), in Chinese.

Mutoh, K.

Ng, K. C.

B. F. Alexander, K. C. Ng, “3-D shape measurement by active triangulation using array of coded light stripes,” in Optics, Illumination, and Image Sensing for Machine Vision II, D. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.850, 199–209 (1987).

Oosterlinck, A.

P. Vuylsleke, A. Oosterlinck, “Range image acquisition with a single binary-encoded light pattern,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 150–160 (1990).

Posdamer, J. L.

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

Reaberg, M.

M. Goharla'ee, M. Reaberg, “Applications of structured lighting for volume measurement,” in Optics, Illumination, and Image Sensing for Machine Vision, D. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.728, 65–73 (1986).

Stockman, G. C.

G. Hu, G. C. Stockman, “3-D surface solution vision structure light and constraint propagation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 390–402 (1989).
[CrossRef]

Strand, T. C.

T. C. Strand, “Optical three dimensional sensing for machine vision,” Opt. Eng. 24, 33–40 (1985).

Su, X. Y.

J. Li, X. Y. Su, L. R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

Z. X. Chen, X. Y. Su, “3-D object shapes measurement system by quasi-sine modulation optical field,” Chin. J. Sci. Instrum. 10, 409–415 (1989).

Takeda, M.

Vuylsleke, P.

P. Vuylsleke, A. Oosterlinck, “Range image acquisition with a single binary-encoded light pattern,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 150–160 (1990).

Waxman, A. M.

J. Le Moigne, A. M. Waxman, “Multi-resolution grid pattern for building range maps,” Tech. Rep. (University of Maryland, College Park, Md.).

Yang, H. S.

H. S. Yang, K. L. Boyer, A. C. Kak, “Range data extraction and interpretation by structure light,” Tech. Rep. 25 (Purdue University, West Lafayette, Ind., 1984), pp. 199–205.

Appl. Opt. (1)

Chin. J. Sci. Instrum. (1)

Z. X. Chen, X. Y. Su, “3-D object shapes measurement system by quasi-sine modulation optical field,” Chin. J. Sci. Instrum. 10, 409–415 (1989).

Chin. Robot. (1)

S. Jin, Y. M. Li, “The distance measurement in three-dimensional computer vision,” Chin. Robot. 3, 57–64 (1989), in Chinese.

Comput. Vision Graphics Image Process. (2)

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

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

IEEE Trans. Pattern Anal. Mach. Intell. (4)

R. A. Jarvis, “A perspective on range finding techniques for computer vision,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-5, 122–139 (1983).
[CrossRef]

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

P. Vuylsleke, A. Oosterlinck, “Range image acquisition with a single binary-encoded light pattern,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 150–160 (1990).

G. Hu, G. C. Stockman, “3-D surface solution vision structure light and constraint propagation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 390–402 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (3)

J. Li, X. Y. Su, L. R. Guo, “Improved Fourier transform profilometry for the automatic measurement of three-dimensional object shapes,” Opt. Eng. 29, 1439–1444 (1990).
[CrossRef]

T. C. Strand, “Optical three dimensional sensing for machine vision,” Opt. Eng. 24, 33–40 (1985).

J. A. Jalkio, R. C. Kim, S. K. Case, “Three dimensional inspection using multistripe structured light,” Opt. Eng. 24, 966–974 (1985).

Other (4)

B. F. Alexander, K. C. Ng, “3-D shape measurement by active triangulation using array of coded light stripes,” in Optics, Illumination, and Image Sensing for Machine Vision II, D. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.850, 199–209 (1987).

H. S. Yang, K. L. Boyer, A. C. Kak, “Range data extraction and interpretation by structure light,” Tech. Rep. 25 (Purdue University, West Lafayette, Ind., 1984), pp. 199–205.

J. Le Moigne, A. M. Waxman, “Multi-resolution grid pattern for building range maps,” Tech. Rep. (University of Maryland, College Park, Md.).

M. Goharla'ee, M. Reaberg, “Applications of structured lighting for volume measurement,” in Optics, Illumination, and Image Sensing for Machine Vision, D. J. Svetkoff, ed., Proc. Soc. Photo-Opt. Instrum. Eng.728, 65–73 (1986).

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Figures (4)

Fig. 1
Fig. 1

Object projected by a series of parallel light stripes: (a) side and top views of the object projected by a series of parallel light stripes; (b) object that is added by a reference surface.

Fig. 2
Fig. 2

Object projected by a grating pattern when the projector is not a telecentric optical system.

Fig. 3
Fig. 3

Schematic diagram of the experimental setup.

Fig. 4
Fig. 4

Views of the shape of the object: (a) deformed grating pattern with straight lines in the background for data signals. (b) view of the reconstructed shape of the object.

Equations (46)

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

w ( x , y ) = a + b x + c y + d ( x 2 + y 2 ) + φ ( x , y ) ,
s ( x , y ) = a + b x + c y + d x 2 ,
Δ x = h tan θ .
H = ( cot θ ) X 0 .
s ( x , y ) = a + ( cot θ ) x ,
θ n = θ 0 + arctan O J ¯ P O ¯ .
O P ¯ O J ¯ .
arctan O J ¯ P O ¯ O J ¯ P O ¯ θ 0
cot θ n cot θ 0 ( 1 + cot 2 θ 0 ) O J ¯ P O ¯ ,
P J ¯ O L ¯ ,
O J ¯ = O L ¯ cos θ 0 = x cos θ 0 ,
Δ h = Δ x ( cos θ n ) .
Δ h = Δ x [ cot θ 0 ( 1 + cot 2 θ 0 ) ( cos θ 0 ) x P O ¯ ] .
b = cot θ 0 ,
d = ( cot 2 θ 0 + 1 ) ( cos θ 0 ) 1 2 P O ¯ ,
s ( x , y ) = a + b x + d x 2 .
Δ h = ( cot θ 0 ) Δ x ( 1 + cot 2 θ 0 ) cos θ 0 ( 2 x Δ x Δ x Δ x ) / ( 2 P O ¯ ) = { cot θ 0 ( 1 + cot 2 θ 0 ) ( cos θ 0 ) [ Δ x / ( 2 P O ¯ ) ] } Δ x + ( 1 + cot 2 θ 0 ) ( cos θ 0 x ) ( Δ x / P O ¯ ) .
Δ x P O ¯ ,
Δ h = [ cot θ 0 ( 1 + cot 2 θ 0 ) ( cos θ 0 ) ( x / P O ¯ ) ] Δ x .
f ( x , y ) = a + b x + c y + d x 2 + φ ( x , y ) ,
φ ( x , y ) = 0 .
f ( x , y ) = a + b x + c y + d x 2 .
s ¯ ( x , y ) = a ¯ + b ¯ x + c ¯ y + d ¯ x 2 ,
| δ | 2 = k = 1 N [ s ( x k , y k ) s ¯ ( x k , y k ) ] 2 = min ,
| δ | 2 a ¯ = | δ | 2 b ¯ = | δ | 2 c ¯ = | δ | 2 d ¯
k = 1 N P n ( x k , y k ) [ P m ( x k , y k ) ] = δ n m ,
P 0 = 1 ,
P 1 = x + α 10 P 0 ,
P 2 = y + α 21 P 1 + α 20 P 0 ,
P 3 = x 2 + α 32 P 2 + α 31 P 1 + α 30 P 0 .
s ¯ ( x , y ) = 0 P 0 + 1 P 1 + 2 P 2 + 3 P 3 .
| δ | 2 = k = 1 N [ s ( x k , y k ) ( 0 P 0 + 1 P 1 + 2 P 2 + 3 P 3 ) ] 2 = min .
i = k = 1 N s ( x k , y k ) P i ( x k , y k ) / k = 1 N P i ( x k , y k ) P i ( x k , y k ) .
d 1 = x , d 2 = y , d 3 = x 2 , d 4 = s ( x , y ) .
d ¯ i = 1 N k = 1 N d i k ,
D i j = 1 N k = 1 N ( d i k d ¯ i ) ( d j k d ¯ j ) .
d ¯ = ( D 34 e 2 D 24 e 1 D 14 ) / ( D 33 e 2 D 23 e 1 D 13 ) ,
c ¯ = e 4 e 2 d ¯ ,
b ¯ = e 3 e 1 d ¯ ,
a ¯ = d ¯ 4 b d ¯ 1 c ¯ d ¯ 2 d d ¯ 3 ,
e 1 = ( D 13 D 22 D 12 D 23 ) / Δ ,
e 2 = ( D 11 D 23 D 12 D 13 ) / Δ ,
e 3 = ( D 14 D 22 D 12 D 24 ) / Δ ,
e 4 = ( D 11 D 24 D 12 D 14 ) / Δ ,
Δ = D 11 D 22 D 12 D 12 .
H = h 0 x X 0 ,

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