Abstract

This paper presents an intensity ratio approach for 3D object profilometry measurement based on projection of triangular patterns. Compared to existing intensity ratio approaches, the proposed one is not influenced by the surface reflectivity and ambient light. Moreover, the proposed intensity ratio is point-by-point-based and thus does not suffer from the influence of surrounding points. The performance of the proposed technique has been tested and the advantages have been demonstrated by experiments.

© 2014 Optical Society of America

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  1. M. Takeda and K. Mutoh, “Fourier transform profilometry for the automatic measurement of 3D object shapes,” Appl. Opt. 22, 3977–3982 (1983).
    [CrossRef]
  2. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. A 72, 156–160 (1982).
    [CrossRef]
  3. X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Laser Eng. 35, 263–284 (2001).
    [CrossRef]
  4. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3D diffuse objects,” Appl. Opt. 23, 3105–3108 (1984).
    [CrossRef]
  5. 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]
  6. C. Guan, L. G. Hassebrook, and D. L. Lau, “Composite structured light pattern for three-dimensional video,” Opt. Express 11, 406–417 (2003).
    [CrossRef]
  7. S. Zhang and P. S. Huang, “High-resolution, real-time 3D shape acquisition,” in IEEE Computer Vision and Pattern Recognition Workshop, (IEEE, 2004), Vol. 3,  28–35.
  8. P. S. Huang, S. Zhang, and F.-P. Chiang, “Trapezoidal phase-shifting method for the three-dimensional shape measurement,” Opt. Eng. 44, 123601 (2005).
    [CrossRef]
  9. B. Carrihill and R. Hummel, “Experiments with the intensity ratio depth sensor,” Comput. Vis. Graph. Image Process. 32, 337–358 (1985).
    [CrossRef]
  10. T. Miyasaka and K. Araki, “Development of real time 3D measurement system using intensity ratio method,” in Proc. ISPRS Commission III, Vol. 34, Part 3B (Photogrammetric Computer Vision, 2002), pp. 181–185.
  11. Q. Fang, “Linearly coded profilometry with a coding light that has isosceles triangle teeth: even-number-sample decoding method,” Appl. Opt. 36, 1615–1620 (1997).
    [CrossRef]
  12. Q. Fang and S. Zheng, “Linearly coded profilometry,” Appl. Opt. 36, 2401–2407 (1997).
    [CrossRef]
  13. P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
    [CrossRef]
  14. P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase-shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
    [CrossRef]
  15. P. S. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45, 5086–5091 (2006).
    [CrossRef]
  16. S. Zhang and P. S. Huang, “Phase error compensation for a 3D shape measurement system based on the phaseshifting method,” Opt. Eng. 46, 063601 (2007).
    [CrossRef]
  17. S. Zhang and S. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46, 36–43 (2007).
    [CrossRef]
  18. K. Wu, J. Xi, Y. Yu, and Z. Yang, “3D profile measurement based on estimation of spatial shifts between intensity ratios from multiple-step triangular patterns,” Opt. Laser Eng. 51, 440–445 (2013).
    [CrossRef]
  19. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
    [CrossRef]
  20. Y. Hu, J. Xi, E. Li, J. Chicharo, and Z. Yang, “Three-dimensional profilometry based on shift estimation of projected fringe patterns,” Appl. Opt. 45, 678–687 (2006).
    [CrossRef]
  21. S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns vs focusing sinusoidal patterns,” Opt. Laser Eng. 48, 561–569 (2010).
    [CrossRef]

2013 (1)

K. Wu, J. Xi, Y. Yu, and Z. Yang, “3D profile measurement based on estimation of spatial shifts between intensity ratios from multiple-step triangular patterns,” Opt. Laser Eng. 51, 440–445 (2013).
[CrossRef]

2010 (1)

S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns vs focusing sinusoidal patterns,” Opt. Laser Eng. 48, 561–569 (2010).
[CrossRef]

2007 (4)

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

S. Zhang and P. S. Huang, “Phase error compensation for a 3D shape measurement system based on the phaseshifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

S. Zhang and S. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46, 36–43 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase-shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
[CrossRef]

2006 (2)

2005 (1)

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

2003 (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]

C. Guan, L. G. Hassebrook, and D. L. Lau, “Composite structured light pattern for three-dimensional video,” Opt. Express 11, 406–417 (2003).
[CrossRef]

2001 (1)

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Laser Eng. 35, 263–284 (2001).
[CrossRef]

2000 (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

1997 (2)

1985 (1)

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

1984 (1)

1983 (1)

1982 (1)

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

Araki, K.

T. Miyasaka and K. Araki, “Development of real time 3D measurement system using intensity ratio method,” in Proc. ISPRS Commission III, Vol. 34, Part 3B (Photogrammetric Computer Vision, 2002), pp. 181–185.

Carrihill, B.

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

Chen, W.

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Laser Eng. 35, 263–284 (2001).
[CrossRef]

Chiang, F. P.

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]

Chiang, F.-P.

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

Chicharo, J.

English, C.

P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase-shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

Fang, Q.

Guan, C.

Halioua, M.

Hassebrook, L. G.

Hu, Y.

Huang, P. S.

S. Zhang and P. S. Huang, “Phase error compensation for a 3D shape measurement system based on the phaseshifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

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

P. S. Huang, S. Zhang, and F.-P. Chiang, “Trapezoidal phase-shifting method for the three-dimensional shape measurement,” Opt. Eng. 44, 123601 (2005).
[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, “High-resolution, real-time 3D shape acquisition,” in IEEE Computer Vision and Pattern Recognition Workshop, (IEEE, 2004), Vol. 3,  28–35.

Hummel, R.

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

Ina, H.

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

Jia, P.

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase-shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
[CrossRef]

Kobayashi, S.

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

Kofman, J.

P. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

P. Jia, J. Kofman, and C. English, “Multiple-step triangular-pattern phase-shifting and the influence of number of steps and pitch on measurement accuracy,” Appl. Opt. 46, 3253–3262 (2007).
[CrossRef]

Lau, D. L.

Lei, S.

S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns vs focusing sinusoidal patterns,” Opt. Laser Eng. 48, 561–569 (2010).
[CrossRef]

Li, E.

Liu, H. C.

Miyasaka, T.

T. Miyasaka and K. Araki, “Development of real time 3D measurement system using intensity ratio method,” in Proc. ISPRS Commission III, Vol. 34, Part 3B (Photogrammetric Computer Vision, 2002), pp. 181–185.

Mutoh, K.

Srinivasan, V.

Su, X.

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Laser Eng. 35, 263–284 (2001).
[CrossRef]

Takeda, M.

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

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

Wu, K.

K. Wu, J. Xi, Y. Yu, and Z. Yang, “3D profile measurement based on estimation of spatial shifts between intensity ratios from multiple-step triangular patterns,” Opt. Laser Eng. 51, 440–445 (2013).
[CrossRef]

Xi, J.

K. Wu, J. Xi, Y. Yu, and Z. Yang, “3D profile measurement based on estimation of spatial shifts between intensity ratios from multiple-step triangular patterns,” Opt. Laser Eng. 51, 440–445 (2013).
[CrossRef]

Y. Hu, J. Xi, E. Li, J. Chicharo, and Z. Yang, “Three-dimensional profilometry based on shift estimation of projected fringe patterns,” Appl. Opt. 45, 678–687 (2006).
[CrossRef]

Yang, Z.

K. Wu, J. Xi, Y. Yu, and Z. Yang, “3D profile measurement based on estimation of spatial shifts between intensity ratios from multiple-step triangular patterns,” Opt. Laser Eng. 51, 440–445 (2013).
[CrossRef]

Y. Hu, J. Xi, E. Li, J. Chicharo, and Z. Yang, “Three-dimensional profilometry based on shift estimation of projected fringe patterns,” Appl. Opt. 45, 678–687 (2006).
[CrossRef]

Yau, S.

Yu, Y.

K. Wu, J. Xi, Y. Yu, and Z. Yang, “3D profile measurement based on estimation of spatial shifts between intensity ratios from multiple-step triangular patterns,” Opt. Laser Eng. 51, 440–445 (2013).
[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. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns vs focusing sinusoidal patterns,” Opt. Laser Eng. 48, 561–569 (2010).
[CrossRef]

S. Zhang and P. S. Huang, “Phase error compensation for a 3D shape measurement system based on the phaseshifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

S. Zhang and S. Yau, “Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector,” Appl. Opt. 46, 36–43 (2007).
[CrossRef]

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

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

S. Zhang and P. S. Huang, “High-resolution, real-time 3D shape acquisition,” in IEEE Computer Vision and Pattern Recognition Workshop, (IEEE, 2004), Vol. 3,  28–35.

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

Zheng, S.

Appl. Opt. (8)

Comput. Vis. Graph. Image Process. (1)

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

IEEE Trans. Pattern Anal. Mach. Intell. (1)

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330–1334 (2000).
[CrossRef]

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

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

Opt. Eng. (4)

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. Jia, J. Kofman, and C. English, “Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement,” Opt. Eng. 46, 083201 (2007).
[CrossRef]

S. Zhang and P. S. Huang, “Phase error compensation for a 3D shape measurement system based on the phaseshifting method,” Opt. Eng. 46, 063601 (2007).
[CrossRef]

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

Opt. Express (1)

Opt. Laser Eng. (3)

K. Wu, J. Xi, Y. Yu, and Z. Yang, “3D profile measurement based on estimation of spatial shifts between intensity ratios from multiple-step triangular patterns,” Opt. Laser Eng. 51, 440–445 (2013).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Laser Eng. 35, 263–284 (2001).
[CrossRef]

S. Lei and S. Zhang, “Digital sinusoidal fringe generation: defocusing binary patterns vs focusing sinusoidal patterns,” Opt. Laser Eng. 48, 561–569 (2010).
[CrossRef]

Other (2)

S. Zhang and P. S. Huang, “High-resolution, real-time 3D shape acquisition,” in IEEE Computer Vision and Pattern Recognition Workshop, (IEEE, 2004), Vol. 3,  28–35.

T. Miyasaka and K. Araki, “Development of real time 3D measurement system using intensity ratio method,” in Proc. ISPRS Commission III, Vol. 34, Part 3B (Photogrammetric Computer Vision, 2002), pp. 181–185.

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Figures (5)

Fig. 1.
Fig. 1.

Intensity ratio calculation for three-step triangular-pattern method. (a) Cross section of three triangular patterns shifted by one third of the fringe period. (b) Cross section of triangular shape intensity ratio. (c) Cross section of intensity ratio after removal of triangles.

Fig. 2.
Fig. 2.

Camera image generation procedure [17].

Fig. 3.
Fig. 3.

Height measurements across the flat board positioned 20 mm from the reference position using different algorisms with pitch values 60 and different shifting steps. The measurement results are for the three-, four-, and five-step triangular-pattern spatial shifting methods as follows: (a)–(c) Intensity ratio method in [18] for pitch 60, (d)–(f) proposed intensity ratio method for pitch 60.

Fig. 4.
Fig. 4.

Measurement accuracy comparison between proposed three-step intensity ratio method and method in [18] by measuring different height of flat board using a pitch of 40 pixels. (a) RMS comparison between proposed method and method in [18]. (b) Max error comparison between proposed method and method in [18].

Fig. 5.
Fig. 5.

3D reconstruction of a plaster face model by proposed four-step intensity ratio method with a pitch of 30 pixels. (a) Triangular patterns on the plaster face model and reference plane with pitch 30. (b) Reconstructed 3D models model using surfl() function in MATLAB.

Tables (3)

Tables Icon

Table 1. RMS and Max Error (in mm) of Measuring a Flat Board Using the Proposed Approach and Method in [18] with Different Shifting Steps and Pitch Values

Tables Icon

Table 2. RMS and Max Error (in mm) of Measuring a Flat Board with Different Surface Reflectivity Using the Proposed Approach and Method in [18] with Different Shifting Steps and Pitch Values

Tables Icon

Table 3. RMS and Max Error (in mm) of Measuring Different Height of Flat Board Using the Proposed Approach and Method in [18] with Three Steps Triangular Patterns and Pitch 40 Pixels

Equations (20)

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

r0(x)=i=1N(1)i+1Ih,i(x)mod(N,2)×IminIv,N2,
rs(x)={(1)k+1r0(x)+2×round(k12),k=1,2,,2N,N2,Nis the odd number(1)kr0(x)+2×round(k2)1,k=1,2,,2N,N2,Nis the even number,
I1(x)={2IvTx+Imin,x[0,T2)2IvTx+Imin+2Iv,x[T2,T)
I2(x)={2IvTx+Imin+2Iv3,x[0,T3)2IvTx+Imin2Iv3,x[T3,5T6)2IvTx+Imin+8Iv3,x[5T6,T)
I3(x)={2IvTx+Imin+2Iv3,x[0,T6)2IvTx+Imin+4Iv3,x[T6,2T3)2IvTx+Imin4Iv3,x[2T3,T).
r0(x)=Ih,1(x)Ih,2(x)Ih,1(x)Ih,3(x)={I3(x)I2(x)I3(x)I1(x)=6Tx,x[0,T6)I3(x)I1(x)I3(x)I2(x)=6Tx+2,x[T6,T3)I1(x)I3(x)I1(x)I2(x)=6Tx2,x[T3,T2)I1(x)I2(x)I1(x)I3(x)=6Tx+4,x[T2,2T3)I2(x)I1(x)I2(x)I3(x)=6Tx4,x[2T3,5T6)I2(x)I3(x)I2(x)I1(x)=6Tx+6,x[5T6,T).
rs(x)=(1)k+1r0(x)+2×round(k12),k=1,2,3,4,5,6.
r0(x)=i=1N1(1)i+1Ih,i(x)Ih,1(x)Ih,N(x),
rs(x)=(1)k+1r0(x)+2×round(k12),k=1,2,,2N,N3.
r0(x)=i=1N(1)i+1Ih,i(x)Ih,1(x)+Ih,2(x)Ih,3(x)Ih,N(x),
rs(x)=(1)kr0(x)+2×round(k2)1,k=1,2,,2N,N4.
Inp(x)=p(In(x)),
Ino(x)=f(x)(Inp(x)+b1(x)).
Inc(x)=α(Ino(x)+b2(x)),
Inc(x)=f(x)Inp(x)+f(x)b1(x)+b2(x)=R(x)Inp(x)+B(x),
r0(x)=R(x)i=1N(1)i+1Ih,ip(x)Imin+B(x)Iv,N3,whenNis even
r0(x)=R(x)i=1N(1)i+1Ih,ip(x)Iv,N4,whenNis odd
r0(x)=R(x)i=1N1(1)i+1Ih,ip(x)R(x)Ih,1p(x)+B(x)R(x)Ih,Np(x)B(x)=i=1N1(1)i+1Ih,ip(x)Ih,1p(x)Ih,Np(x),N3.
r0(x)=R(x)i=1N(1)i+1Ih,ip(x)R(x)Ih,1p(x)+B(x)+R(x)Ih,2p(x)+B(x)R(x)Ih,3p(x)B(x)R(x)Ih,Np(x)B(x)=i=1N(1)i+1Ih,ip(x)Ih,1p(x)+Ih,2p(x)Ih,3p(x)Ih,Np(x),N4.
h(x)=H·u(x)d+u(x),

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