Abstract

In this paper, a temporal shift unwrapping technique is presented for solving the problem of shift wrapping associated with spatial shift estimation (SSE)-based fringe pattern profilometry (FPP). Based on this technique, a novel 3D shape measurement method is proposed, where triangular patterns of two different spatial frequencies are projected. The patterns of the higher frequency are used to implement the FPP, and the one with lower frequency is utilized to achieve shift unwrapping. The proposed method is able to solve the shift unwrapping problem associated with the existing multi-step triangular pattern FPP by projection of an additional fringe pattern. The effectiveness of the proposed method is verified by experimental results, where the same accuracy as existing multi-step triangular pattern FPP can be achieved, but enabling the measurement of objects with complex surface shape and high steps.

© 2014 Optical Society of America

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References

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  13. Z. Zhang, C. E. Towers, and D. P. Towers, “Robust color and shape measurement of full color artifacts by RGB fringe projection,” Opt. Eng. 51(2), 021109 (2012).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  27. Y. Ding, J. Xi, Y. Yu, W. Q. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express 20(12), 13238–13251 (2012).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2014 (2)

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Spatial shift unwrapping for digital fringe profilometry based on spatial shift estimation,” J. Electron. Imaging 23(4), 043002 (2014).
[Crossref]

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Digital fringe profilometry based on triangular fringe patterns and spatial shift estimation,” Proc. SPIE 9110, 91100C (2014).
[Crossref]

2013 (2)

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. Lasers Eng. 51(4), 440–445 (2013).
[Crossref]

J. Guo, X. Peng, J. Yu, X. Liu, A. Li, and M. Wang, “Real-time 3D imaging by using color structured light based on Hilbert transform,” Proc. SPIE 8856, 885624 (2013).
[Crossref]

2012 (2)

Z. Zhang, C. E. Towers, and D. P. Towers, “Robust color and shape measurement of full color artifacts by RGB fringe projection,” Opt. Eng. 51(2), 021109 (2012).
[Crossref]

Y. Ding, J. Xi, Y. Yu, W. Q. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express 20(12), 13238–13251 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (2)

2009 (2)

Y. Hu, J. Xi, J. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern Profilometry,” IEEE Trans. Instrum. Meas. 58(9), 3305–3314 (2009).
[Crossref]

P. Cao, J. Xi, J. Chicharo, and Y. Yu, “A fringe period unwrapping technique for digital fringe profilometry based on spatial shift estimation,” Proc. SPIE 7432, 743208 (2009).
[Crossref]

2007 (2)

2006 (2)

2003 (1)

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

2001 (1)

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

1999 (4)

H. Zhang, M. J. Lalor, and D. R. Burton, “Spatiotemporal phase unwrapping for the measurement of discontinuous objects in dynamic fringe-projection phase-shifting profilometry,” Appl. Opt. 38(16), 3534–3541 (1999).
[Crossref] [PubMed]

J. Villa, M. Servin, and L. Castillo, “Profilometry for the measurement of 3-D object shapes based on regularized filters,” Opt. Commun. 161(1–3), 13–18 (1999).
[Crossref]

A. Asundi and Z. Wensen, “Unified calibration technique and its applications in optical triangular profilometry,” Appl. Opt. 38(16), 3556–3561 (1999).
[Crossref] [PubMed]

P. Huang, Q. Ho, F. Jin, and F. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3-D surface contouring,” Opt. Eng. 38(6), 1065–1071 (1999).
[Crossref]

1998 (1)

X. Su, L. Su, W. Li, and L. Xiang, “New 3D profilometry based on modulation measurement,” Proc. SPIE 3853, 1–7 (1998).
[Crossref]

1995 (1)

A. J. Moore and F. Mendoza-Santoyo, “Phase demodulation in the space domain without a fringe carrier,” Opt. Lasers Eng. 23(5), 319–330 (1995).
[Crossref]

1994 (1)

R. Rodríguez-Vera and M. Servin, “Phase locked loop profilometry,” Opt. Laser Technol. 26(6), 393–398 (1994).
[Crossref]

1989 (1)

M. Halioua and H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Lasers Eng. 11(3), 185–215 (1989).
[Crossref]

1986 (1)

1984 (1)

S. Toyooka and M. Tominga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51(2), 68–70 (1984).
[Crossref]

1983 (1)

1982 (1)

1970 (1)

Allen, J. B.

Asundi, A.

Burton, D. R.

Cao, P.

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Spatial shift unwrapping for digital fringe profilometry based on spatial shift estimation,” J. Electron. Imaging 23(4), 043002 (2014).
[Crossref]

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Digital fringe profilometry based on triangular fringe patterns and spatial shift estimation,” Proc. SPIE 9110, 91100C (2014).
[Crossref]

P. Cao, J. Xi, J. Chicharo, and Y. Yu, “A fringe period unwrapping technique for digital fringe profilometry based on spatial shift estimation,” Proc. SPIE 7432, 743208 (2009).
[Crossref]

Castillo, L.

J. Villa, M. Servin, and L. Castillo, “Profilometry for the measurement of 3-D object shapes based on regularized filters,” Opt. Commun. 161(1–3), 13–18 (1999).
[Crossref]

Chen, W.

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

Cheng, W.

Y. Hu, J. Xi, J. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern Profilometry,” IEEE Trans. Instrum. Meas. 58(9), 3305–3314 (2009).
[Crossref]

Cheng, W. Q.

Chiang, F.

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

P. Huang, Q. Ho, F. Jin, and F. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3-D surface contouring,” Opt. Eng. 38(6), 1065–1071 (1999).
[Crossref]

Chicharo, J.

Chicharo, J. F.

Ding, Y.

English, C.

Fu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Fu, Y.

Gorthi, S.

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Guo, J.

J. Guo, X. Peng, J. Yu, X. Liu, A. Li, and M. Wang, “Real-time 3D imaging by using color structured light based on Hilbert transform,” Proc. SPIE 8856, 885624 (2013).
[Crossref]

Guo, Q.

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Digital fringe profilometry based on triangular fringe patterns and spatial shift estimation,” Proc. SPIE 9110, 91100C (2014).
[Crossref]

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Spatial shift unwrapping for digital fringe profilometry based on spatial shift estimation,” J. Electron. Imaging 23(4), 043002 (2014).
[Crossref]

Halioua, M.

M. Halioua and H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Lasers Eng. 11(3), 185–215 (1989).
[Crossref]

Hao, Q.

Hassebrook, L. G.

Ho, Q.

P. Huang, Q. Ho, F. Jin, and F. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3-D surface contouring,” Opt. Eng. 38(6), 1065–1071 (1999).
[Crossref]

Hu, Q.

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Hu, Y.

Huang, P.

P. Huang, Q. Ho, F. Jin, and F. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3-D surface contouring,” Opt. Eng. 38(6), 1065–1071 (1999).
[Crossref]

Huang, P. S.

Q. Hu, P. S. Huang, Q. Fu, and F. Chiang, “Calibration of a three-dimensional shape measurement system,” Opt. Eng. 42(2), 482–493 (2003).
[Crossref]

Ina, H.

Iwaasa, Y.

Jia, P.

Jin, F.

P. Huang, Q. Ho, F. Jin, and F. Chiang, “Colour-enhanced digital fringe projection technique for high-speed 3-D surface contouring,” Opt. Eng. 38(6), 1065–1071 (1999).
[Crossref]

Johnson, W. O.

Kobayashi, S.

Kofman, J.

Lalor, M. J.

Lau, D. L.

Li, A.

J. Guo, X. Peng, J. Yu, X. Liu, A. Li, and M. Wang, “Real-time 3D imaging by using color structured light based on Hilbert transform,” Proc. SPIE 8856, 885624 (2013).
[Crossref]

Li, E.

Li, W.

X. Su, L. Su, W. Li, and L. Xiang, “New 3D profilometry based on modulation measurement,” Proc. SPIE 3853, 1–7 (1998).
[Crossref]

Liu, H. C.

M. Halioua and H. C. Liu, “Optical three-dimensional sensing by phase measuring profilometry,” Opt. Lasers Eng. 11(3), 185–215 (1989).
[Crossref]

Liu, K.

Liu, X.

J. Guo, X. Peng, J. Yu, X. Liu, A. Li, and M. Wang, “Real-time 3D imaging by using color structured light based on Hilbert transform,” Proc. SPIE 8856, 885624 (2013).
[Crossref]

Luo, Q.

Meadows, D. M.

Mendoza-Santoyo, F.

A. J. Moore and F. Mendoza-Santoyo, “Phase demodulation in the space domain without a fringe carrier,” Opt. Lasers Eng. 23(5), 319–330 (1995).
[Crossref]

Moore, A. J.

A. J. Moore and F. Mendoza-Santoyo, “Phase demodulation in the space domain without a fringe carrier,” Opt. Lasers Eng. 23(5), 319–330 (1995).
[Crossref]

Mutoh, K.

Peng, X.

J. Guo, X. Peng, J. Yu, X. Liu, A. Li, and M. Wang, “Real-time 3D imaging by using color structured light based on Hilbert transform,” Proc. SPIE 8856, 885624 (2013).
[Crossref]

Rastogi, P.

S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[Crossref]

Rodríguez-Vera, R.

R. Rodríguez-Vera and M. Servin, “Phase locked loop profilometry,” Opt. Laser Technol. 26(6), 393–398 (1994).
[Crossref]

Servin, M.

J. Villa, M. Servin, and L. Castillo, “Profilometry for the measurement of 3-D object shapes based on regularized filters,” Opt. Commun. 161(1–3), 13–18 (1999).
[Crossref]

R. Rodríguez-Vera and M. Servin, “Phase locked loop profilometry,” Opt. Laser Technol. 26(6), 393–398 (1994).
[Crossref]

Su, L.

X. Su, L. Su, W. Li, and L. Xiang, “New 3D profilometry based on modulation measurement,” Proc. SPIE 3853, 1–7 (1998).
[Crossref]

Su, X.

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

X. Su, L. Su, W. Li, and L. Xiang, “New 3D profilometry based on modulation measurement,” Proc. SPIE 3853, 1–7 (1998).
[Crossref]

Takeda, M.

Tominga, M.

S. Toyooka and M. Tominga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51(2), 68–70 (1984).
[Crossref]

Towers, C. E.

Z. Zhang, C. E. Towers, and D. P. Towers, “Robust color and shape measurement of full color artifacts by RGB fringe projection,” Opt. Eng. 51(2), 021109 (2012).
[Crossref]

Towers, D. P.

Z. Zhang, C. E. Towers, and D. P. Towers, “Robust color and shape measurement of full color artifacts by RGB fringe projection,” Opt. Eng. 51(2), 021109 (2012).
[Crossref]

Toyooka, S.

S. Toyooka and Y. Iwaasa, “Automatic profilometry of 3-D diffuse objects by spatial phase detection,” Appl. Opt. 25(10), 1630–1633 (1986).
[Crossref] [PubMed]

S. Toyooka and M. Tominga, “Spatial fringe scanning for optical phase measurement,” Opt. Commun. 51(2), 68–70 (1984).
[Crossref]

Villa, J.

J. Villa, M. Servin, and L. Castillo, “Profilometry for the measurement of 3-D object shapes based on regularized filters,” Opt. Commun. 161(1–3), 13–18 (1999).
[Crossref]

Wang, M.

J. Guo, X. Peng, J. Yu, X. Liu, A. Li, and M. Wang, “Real-time 3D imaging by using color structured light based on Hilbert transform,” Proc. SPIE 8856, 885624 (2013).
[Crossref]

Wang, S.

Wang, Y.

Wensen, Z.

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. Lasers Eng. 51(4), 440–445 (2013).
[Crossref]

Xi, J.

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Spatial shift unwrapping for digital fringe profilometry based on spatial shift estimation,” J. Electron. Imaging 23(4), 043002 (2014).
[Crossref]

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Digital fringe profilometry based on triangular fringe patterns and spatial shift estimation,” Proc. SPIE 9110, 91100C (2014).
[Crossref]

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. Lasers Eng. 51(4), 440–445 (2013).
[Crossref]

Y. Ding, J. Xi, Y. Yu, W. Q. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express 20(12), 13238–13251 (2012).
[Crossref] [PubMed]

Y. Ding, J. Xi, Y. Yu, and J. Chicharo, “Recovering the absolute phase maps of two fringe patterns with selected frequencies,” Opt. Lett. 36(13), 2518–2520 (2011).
[Crossref] [PubMed]

P. Cao, J. Xi, J. Chicharo, and Y. Yu, “A fringe period unwrapping technique for digital fringe profilometry based on spatial shift estimation,” Proc. SPIE 7432, 743208 (2009).
[Crossref]

Y. Hu, J. Xi, J. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern Profilometry,” IEEE Trans. Instrum. Meas. 58(9), 3305–3314 (2009).
[Crossref]

Y. Hu, J. Xi, J. Chicharo, E. Li, and Z. Yang, “Discrete cosine transform-based shift estimation for fringe pattern profilometry using a generalized analysis model,” Appl. Opt. 45(25), 6560–6567 (2006).
[Crossref] [PubMed]

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(4), 678–687 (2006).
[Crossref] [PubMed]

Xiang, L.

X. Su, L. Su, W. Li, and L. Xiang, “New 3D profilometry based on modulation measurement,” Proc. SPIE 3853, 1–7 (1998).
[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. Lasers Eng. 51(4), 440–445 (2013).
[Crossref]

Y. Hu, J. Xi, J. Chicharo, W. Cheng, and Z. Yang, “Inverse function analysis method for fringe pattern Profilometry,” IEEE Trans. Instrum. Meas. 58(9), 3305–3314 (2009).
[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(4), 678–687 (2006).
[Crossref] [PubMed]

Y. Hu, J. Xi, J. Chicharo, E. Li, and Z. Yang, “Discrete cosine transform-based shift estimation for fringe pattern profilometry using a generalized analysis model,” Appl. Opt. 45(25), 6560–6567 (2006).
[Crossref] [PubMed]

Yau, S. T.

Yu, J.

J. Guo, X. Peng, J. Yu, X. Liu, A. Li, and M. Wang, “Real-time 3D imaging by using color structured light based on Hilbert transform,” Proc. SPIE 8856, 885624 (2013).
[Crossref]

Yu, Y.

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Digital fringe profilometry based on triangular fringe patterns and spatial shift estimation,” Proc. SPIE 9110, 91100C (2014).
[Crossref]

P. Cao, J. Xi, Y. Yu, and Q. Guo, “Spatial shift unwrapping for digital fringe profilometry based on spatial shift estimation,” J. Electron. Imaging 23(4), 043002 (2014).
[Crossref]

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. Lasers Eng. 51(4), 440–445 (2013).
[Crossref]

Y. Ding, J. Xi, Y. Yu, W. Q. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express 20(12), 13238–13251 (2012).
[Crossref] [PubMed]

Y. Ding, J. Xi, Y. Yu, and J. Chicharo, “Recovering the absolute phase maps of two fringe patterns with selected frequencies,” Opt. Lett. 36(13), 2518–2520 (2011).
[Crossref] [PubMed]

P. Cao, J. Xi, J. Chicharo, and Y. Yu, “A fringe period unwrapping technique for digital fringe profilometry based on spatial shift estimation,” Proc. SPIE 7432, 743208 (2009).
[Crossref]

Zhang, H.

Zhang, S.

Zhang, Z.

Z. Zhang, C. E. Towers, and D. P. Towers, “Robust color and shape measurement of full color artifacts by RGB fringe projection,” Opt. Eng. 51(2), 021109 (2012).
[Crossref]

Appl. Opt. (9)

H. Zhang, M. J. Lalor, and D. R. Burton, “Spatiotemporal phase unwrapping for the measurement of discontinuous objects in dynamic fringe-projection phase-shifting profilometry,” Appl. Opt. 38(16), 3534–3541 (1999).
[Crossref] [PubMed]

S. Toyooka and Y. Iwaasa, “Automatic profilometry of 3-D diffuse objects by spatial phase detection,” Appl. Opt. 25(10), 1630–1633 (1986).
[Crossref] [PubMed]

D. M. Meadows, W. O. Johnson, and J. B. Allen, “Generation of surface contours by moiré patterns,” Appl. Opt. 9(4), 942–947 (1970).
[Crossref] [PubMed]

A. Asundi and Z. Wensen, “Unified calibration technique and its applications in optical triangular profilometry,” Appl. Opt. 38(16), 3556–3561 (1999).
[Crossref] [PubMed]

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Figures (10)

Fig. 1
Fig. 1 Schematic diagram of FPP system.
Fig. 2
Fig. 2 Flow chart of the proposed method.
Fig. 3
Fig. 3 Captured fringe images of flat box. (a) object; (b) fringe image (f = 5); (c)–(f) fringe images (f = 8).
Fig. 4
Fig. 4 Cross Section of flat box. (a) result using single frequency algorithm(f = 8); (b) result using select frequency algorithm( f 1 = 5, f 2 = 8)
Fig. 5
Fig. 5 3D reconstruct results of flat box. (a) result using single frequency algorithm(f = 8); (b) result using select frequency algorithm( f 1 = 5, f 2 = 8).
Fig. 6
Fig. 6 Captured fringe images of separate objects with different wavelengths. (a) objects; (b) fringes image ( f 1 = 8).
Fig. 7
Fig. 7 Captured 3-step fringe images of objects with f 2 = 13. (a)–(c) fringe images in different step
Fig. 8
Fig. 8 Captured 6-step fringe images of objects with f 2 = 13. (a)–(f) fringe images in different step
Fig. 9
Fig. 9 3D reconstruct results of two separated objects using 3-step fringe images. (a)–(d) results in different angle of view
Fig. 10
Fig. 10 3D reconstruct results of two separated objects using 6-step fringe images. (a)–(d) results in different angle of view

Tables (1)

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Table 1 mapping from m 2 ( x ) f 1 m 1 ( x ) f 2 to m 1 ( x ) and m 2 ( x )

Equations (12)

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s ( x ) = k = 0 + b k cos ( 2 π k f 0 x + Ψ k )
d ( x ) = k = 0 + b k cos ( 2 π k f 0 x + k ϕ ( x ) + Ψ k )
h ( x ) = l 0 ϕ ( x ) 2 π f 0 d 0
h ( x ) = l 0 u ( x ) d 0
d ( x ) = s ( x u ( x ) )
Φ ( x ) = 2 π m ( x ) + ϕ ( x )
U ( x ) = λ m ( x ) + u ( x )
U i ( x ) = H f i m i ( x ) + u i ( x ) , i = 1 , 2
H f 1 m 1 ( x ) + u 1 ( x ) = H f 2 m 2 ( x ) + u 2 ( x )
f 1 f 2 H [ u 1 ( x ) u 2 ( x ) ] = m 2 ( x ) f 1 m 1 ( x ) f 2
m 1 ( x ) = { f 1 1 ( f 1 1 ) H f 1 U ( x ) < H 2 2 H f 1 U ( x ) < 3 H f 1 1 H f 1 U ( x ) < 2 H f 1 0 0 U ( x ) < H f 1
m 2 ( x ) = { f 2 1 ( f 2 1 ) H f 2 U ( x ) < H 2 2 H f 2 U ( x ) < 3 H f 2 1 H f 2 U ( x ) < 2 H f 2 0 0 U ( x ) < H f 2

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