Abstract

Three-dimensional (3D) shape measurement system with binary defocusing technique can perform high-speed and flexible measurements if binary fringe patterns are defocused by projector properly. However, the actual defocusing degree is difficult to set, and the fringe period is difficult to determine accordingly. In this study, we present a square-binary defocusing parameter selection framework. First, we analyze the fringe formation process mathematically. The defocusing degree is quantified and manipulated by using the focusing distance of projector, which is calibrated by point spread function measurement. To optimize parameter selection, single-point sinusoidal error is modeled as the objective function for the evaluation of the defocusing effect. We verify the correctness by using different parameter combinations and object measurements in our experiments. The appropriate defocusing parameters can be easily obtained according to the analysis of practical system setup, which improves the quality and robustness of the system.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. S. S. Gorthi and P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
    [Crossref]
  2. X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
    [Crossref]
  3. S. Zhang, “Flexible 3D shape measurement using projector defocusing: extended measurement range,” Opt. Lett. 35(7), 934–936 (2010).
    [Crossref] [PubMed]
  4. S. Y. Lei and S. Zhang, “Digital sinusoidal fringe pattern generation: Defocusing binary patterns VS focusing sinusoidal patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010).
    [Crossref]
  5. Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three-dimensional shape measurement with projector defocusing,” Appl. Opt. 50(17), 2572–2581 (2011).
    [Crossref] [PubMed]
  6. B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54(1), 236–246 (2014).
    [Crossref]
  7. G. A. Ayubi, J. A. Ayubi, J. M. Di Martino, and J. A. Ferrari, “Pulse-width modulation in defocused three-dimensional fringe projection,” Opt. Lett. 35(21), 3682–3684 (2010).
    [Crossref] [PubMed]
  8. Y. Wang and S. Zhang, “Superfast multifrequency phase-shifting technique with optimal pulse width modulation,” Opt. Express 19(6), 5149–5155 (2011).
    [Crossref] [PubMed]
  9. C. Zuo, Q. Chen, S. Feng, F. Feng, G. Gu, and X. Sui, “Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing,” Appl. Opt. 51(19), 4477–4490 (2012).
    [Crossref] [PubMed]
  10. Y. Wang and S. Zhang, “Three-dimensional shape measurement with binary dithered patterns,” Appl. Opt. 51(27), 6631–6636 (2012).
    [Crossref] [PubMed]
  11. W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38(4), 540–542 (2013).
    [Crossref] [PubMed]
  12. J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
    [Crossref]
  13. D. Zheng, F. Da, Q. Kemao, and H. S. Seah, “Phase error analysis and compensation for phase shifting profilometry with projector defocusing,” Appl. Opt. 55(21), 5721–5728 (2016).
    [Crossref] [PubMed]
  14. M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
    [Crossref] [PubMed]
  15. A. Kamagara, X. Wang, and S. Li, “Optimal defocus selection based on normed Fourier transform for digital fringe pattern profilometry,” Appl. Opt. 56(28), 8014–8022 (2017).
    [Crossref] [PubMed]
  16. A. Mosleh, P. Green, E. Onzon, I. Begin, J. M. P. Langlois, and Ieee, “Camera Intrinsic Blur Kernel Estimation: A Reliable Framework,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2015), pp. 4961–4968.
  17. A. Mosleh, J. M. P. Langlois, and P. Green, “Image Deconvolution Ringing Artifact Detection and Removal via PSF Frequency Analysis,” in Proceedings of European Conference on Computer Vision (Springer, 2014), pp. 247–262.
    [Crossref]
  18. O. Bimber and A. Emmerling, “Multifocal projection: A multiprojector technique for increasing focal depth,” IEEE Trans. Vis. Comput. Graph. 12(4), 658–667 (2006).
    [Crossref] [PubMed]
  19. M. Nagase, D. Iwai, and K. Sato, “Dynamic Control of Multiple Focal-Plane Projections for Eliminating Defocus and Occlusion,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2010), pp. 293–294.
    [Crossref]
  20. T. Nakamura, R. Horisaki, and J. Tanida, “Computational superposition projector for extended depth of field and field of view,” Opt. Lett. 38(9), 1560–1562 (2013).
    [Crossref] [PubMed]
  21. A. Pentland, T. Darrell, M. Turk, and W. Huang, “A simple, real-time range camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256–261.
    [Crossref]
  22. H. Hu and G. D. Haan, “Low Cost Robust Blur Estimator,” in in Proceedings of IEEE Conference on Image Processing (IEEE, 2006), pp. 617–620.
  23. M. Servín, J. A. Quiroga, and J. M. Padilla, Fringe pattern analysis for optical metrology: theory, algorithms, and applications. (Wiley-VCH, 2014).
  24. V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
    [Crossref]
  25. L. Zhang and S. Nayar, “Projection defocus analysis for scene capture and image display,” in Proceedings of ACM SIGGRAPH (ACM, 2006), pp. 907–915.
    [Crossref]
  26. 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(1), 106–115 (2003).
    [Crossref] [PubMed]
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    [Crossref]

2017 (2)

2016 (2)

D. Zheng, F. Da, Q. Kemao, and H. S. Seah, “Phase error analysis and compensation for phase shifting profilometry with projector defocusing,” Appl. Opt. 55(21), 5721–5728 (2016).
[Crossref] [PubMed]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

2015 (1)

J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
[Crossref]

2014 (1)

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54(1), 236–246 (2014).
[Crossref]

2013 (2)

2012 (2)

2011 (2)

2010 (5)

S. Zhang, “Flexible 3D shape measurement using projector defocusing: extended measurement range,” Opt. Lett. 35(7), 934–936 (2010).
[Crossref] [PubMed]

G. A. Ayubi, J. A. Ayubi, J. M. Di Martino, and J. A. Ferrari, “Pulse-width modulation in defocused three-dimensional fringe projection,” Opt. Lett. 35(21), 3682–3684 (2010).
[Crossref] [PubMed]

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

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

S. Y. Lei and S. Zhang, “Digital sinusoidal fringe pattern generation: Defocusing binary patterns VS focusing sinusoidal patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010).
[Crossref]

2007 (1)

V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
[Crossref]

2006 (1)

O. Bimber and A. Emmerling, “Multifocal projection: A multiprojector technique for increasing focal depth,” IEEE Trans. Vis. Comput. Graph. 12(4), 658–667 (2006).
[Crossref] [PubMed]

2003 (1)

Asundi, A.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Ayubi, G. A.

Ayubi, J. A.

Bimber, O.

O. Bimber and A. Emmerling, “Multifocal projection: A multiprojector technique for increasing focal depth,” IEEE Trans. Vis. Comput. Graph. 12(4), 658–667 (2006).
[Crossref] [PubMed]

Chaudhuri, S.

V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
[Crossref]

Chen, Q.

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref] [PubMed]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
[Crossref]

C. Zuo, Q. Chen, S. Feng, F. Feng, G. Gu, and X. Sui, “Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing,” Appl. Opt. 51(19), 4477–4490 (2012).
[Crossref] [PubMed]

Da, F.

Dai, J.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54(1), 236–246 (2014).
[Crossref]

Y. Xu, L. Ekstrand, J. Dai, and S. Zhang, “Phase error compensation for three-dimensional shape measurement with projector defocusing,” Appl. Opt. 50(17), 2572–2581 (2011).
[Crossref] [PubMed]

Darrell, T.

A. Pentland, T. Darrell, M. Turk, and W. Huang, “A simple, real-time range camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256–261.
[Crossref]

Di Martino, J. M.

Ekstrand, L.

Emmerling, A.

O. Bimber and A. Emmerling, “Multifocal projection: A multiprojector technique for increasing focal depth,” IEEE Trans. Vis. Comput. Graph. 12(4), 658–667 (2006).
[Crossref] [PubMed]

Feng, F.

Feng, S.

Feng, S. J.

J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
[Crossref]

Ferrari, J. A.

Gorthi, S. S.

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

Green, P.

A. Mosleh, J. M. P. Langlois, and P. Green, “Image Deconvolution Ringing Artifact Detection and Removal via PSF Frequency Analysis,” in Proceedings of European Conference on Computer Vision (Springer, 2014), pp. 247–262.
[Crossref]

Gu, G.

Guan, C.

Haan, G. D.

H. Hu and G. D. Haan, “Low Cost Robust Blur Estimator,” in in Proceedings of IEEE Conference on Image Processing (IEEE, 2006), pp. 617–620.

Hassebrook, L. G.

Horisaki, R.

Hu, H.

H. Hu and G. D. Haan, “Low Cost Robust Blur Estimator,” in in Proceedings of IEEE Conference on Image Processing (IEEE, 2006), pp. 617–620.

Hu, Y.

Huang, L.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Huang, W.

A. Pentland, T. Darrell, M. Turk, and W. Huang, “A simple, real-time range camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256–261.
[Crossref]

Iwai, D.

M. Nagase, D. Iwai, and K. Sato, “Dynamic Control of Multiple Focal-Plane Projections for Eliminating Defocus and Occlusion,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2010), pp. 293–294.
[Crossref]

Kamagara, A.

Kemao, Q.

Langlois, J. M. P.

A. Mosleh, J. M. P. Langlois, and P. Green, “Image Deconvolution Ringing Artifact Detection and Removal via PSF Frequency Analysis,” in Proceedings of European Conference on Computer Vision (Springer, 2014), pp. 247–262.
[Crossref]

Lei, S. Y.

S. Y. Lei and S. Zhang, “Digital sinusoidal fringe pattern generation: Defocusing binary patterns VS focusing sinusoidal patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010).
[Crossref]

Li, B.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54(1), 236–246 (2014).
[Crossref]

Li, H.

Li, J.

Li, S.

Lohry, W.

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54(1), 236–246 (2014).
[Crossref]

W. Lohry and S. Zhang, “Genetic method to optimize binary dithering technique for high-quality fringe generation,” Opt. Lett. 38(4), 540–542 (2013).
[Crossref] [PubMed]

Mosleh, A.

A. Mosleh, J. M. P. Langlois, and P. Green, “Image Deconvolution Ringing Artifact Detection and Removal via PSF Frequency Analysis,” in Proceedings of European Conference on Computer Vision (Springer, 2014), pp. 247–262.
[Crossref]

Nagase, M.

M. Nagase, D. Iwai, and K. Sato, “Dynamic Control of Multiple Focal-Plane Projections for Eliminating Defocus and Occlusion,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2010), pp. 293–294.
[Crossref]

Nakamura, T.

Namboodiri, V. P.

V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
[Crossref]

Nayar, S.

L. Zhang and S. Nayar, “Projection defocus analysis for scene capture and image display,” in Proceedings of ACM SIGGRAPH (ACM, 2006), pp. 907–915.
[Crossref]

Pentland, A.

A. Pentland, T. Darrell, M. Turk, and W. Huang, “A simple, real-time range camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256–261.
[Crossref]

Rastogi, P.

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

Sato, K.

M. Nagase, D. Iwai, and K. Sato, “Dynamic Control of Multiple Focal-Plane Projections for Eliminating Defocus and Occlusion,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2010), pp. 293–294.
[Crossref]

Seah, H. S.

Su, X. Y.

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

Sui, X.

Sun, J. S.

J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
[Crossref]

Tanida, J.

Tao, T.

Turk, M.

A. Pentland, T. Darrell, M. Turk, and W. Huang, “A simple, real-time range camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256–261.
[Crossref]

Wang, X.

Wang, Y.

Xu, Y.

Yu, S. L.

J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
[Crossref]

Zhang, L.

L. Zhang and S. Nayar, “Projection defocus analysis for scene capture and image display,” in Proceedings of ACM SIGGRAPH (ACM, 2006), pp. 907–915.
[Crossref]

Zhang, M.

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref] [PubMed]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Zhang, Q. C.

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

Zhang, S.

Zhang, Y. Z.

J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
[Crossref]

Zheng, D.

Zuo, C.

M. Zhang, Q. Chen, T. Tao, S. Feng, Y. Hu, H. Li, and C. Zuo, “Robust and efficient multi-frequency temporal phase unwrapping: optimal fringe frequency and pattern sequence selection,” Opt. Express 25(17), 20381–20400 (2017).
[Crossref] [PubMed]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
[Crossref]

C. Zuo, Q. Chen, S. Feng, F. Feng, G. Gu, and X. Sui, “Optimized pulse width modulation pattern strategy for three-dimensional profilometry with projector defocusing,” Appl. Opt. 51(19), 4477–4490 (2012).
[Crossref] [PubMed]

Appl. Opt. (5)

IEEE Trans. Vis. Comput. Graph. (1)

O. Bimber and A. Emmerling, “Multifocal projection: A multiprojector technique for increasing focal depth,” IEEE Trans. Vis. Comput. Graph. 12(4), 658–667 (2006).
[Crossref] [PubMed]

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

Opt. Express (2)

Opt. Lasers Eng. (6)

S. Y. Lei and S. Zhang, “Digital sinusoidal fringe pattern generation: Defocusing binary patterns VS focusing sinusoidal patterns,” Opt. Lasers Eng. 48(5), 561–569 (2010).
[Crossref]

B. Li, Y. Wang, J. Dai, W. Lohry, and S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54(1), 236–246 (2014).
[Crossref]

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

X. Y. Su and Q. C. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
[Crossref]

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

J. S. Sun, C. Zuo, S. J. Feng, S. L. Yu, Y. Z. Zhang, and Q. Chen, “Improved intensity-optimized dithering technique for 3D shape measurement,” Opt. Lasers Eng. 66, 158–164 (2015).
[Crossref]

Opt. Lett. (4)

Pattern Recognit. Lett. (1)

V. P. Namboodiri and S. Chaudhuri, “On defocus, diffusion and depth estimation,” Pattern Recognit. Lett. 28(3), 311–319 (2007).
[Crossref]

Other (7)

L. Zhang and S. Nayar, “Projection defocus analysis for scene capture and image display,” in Proceedings of ACM SIGGRAPH (ACM, 2006), pp. 907–915.
[Crossref]

M. Nagase, D. Iwai, and K. Sato, “Dynamic Control of Multiple Focal-Plane Projections for Eliminating Defocus and Occlusion,” in Proceedings of IEEE Conference on Virtual Reality (IEEE, 2010), pp. 293–294.
[Crossref]

A. Pentland, T. Darrell, M. Turk, and W. Huang, “A simple, real-time range camera,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1989), pp. 256–261.
[Crossref]

H. Hu and G. D. Haan, “Low Cost Robust Blur Estimator,” in in Proceedings of IEEE Conference on Image Processing (IEEE, 2006), pp. 617–620.

M. Servín, J. A. Quiroga, and J. M. Padilla, Fringe pattern analysis for optical metrology: theory, algorithms, and applications. (Wiley-VCH, 2014).

A. Mosleh, P. Green, E. Onzon, I. Begin, J. M. P. Langlois, and Ieee, “Camera Intrinsic Blur Kernel Estimation: A Reliable Framework,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2015), pp. 4961–4968.

A. Mosleh, J. M. P. Langlois, and P. Green, “Image Deconvolution Ringing Artifact Detection and Removal via PSF Frequency Analysis,” in Proceedings of European Conference on Computer Vision (Springer, 2014), pp. 247–262.
[Crossref]

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Figures (16)

Fig. 1
Fig. 1 Parameter-choosing pipeline.
Fig. 2
Fig. 2 (a) Cross-section of a square-binary fringe, which can be represented as a square wave, rect(x), mathematically: x is the spatial coordinate; A is the amplitude; T is the spatial period. (b) Absolute value of the Fourier spectrum of rect(x): ω is the angular frequency coordinate, and the angular frequency of rect(x) is ω0 = /T.
Fig. 3
Fig. 3 Simplified optical path diagram of a projector with defocus blur where 2r is the approximated diameter of the DMD unit, D is the diameter of the aperture, R is the radius of the blur spot, U is the object distance, V is the image distance, and S is the focusing distance. The focus plane is where the clearest image can be observed, whereas the image plane is where the light screen is located.
Fig. 4
Fig. 4 Principle of PSF measurement: (a) Principle of measurement used to estimate the defocus PSF. (b) Setup of PSF measurement pipeline. The defocus blur spot under different focusing distances can be observed on the light screen and recorded by the camera.
Fig. 5
Fig. 5 Principle of single-point sinusoidal error criteria: (a) The setup of the single-point sinusoidal error consists of a projector, a camera, and a light screen. (b) The recorded intensity variation of the red point in (a) at each phase step and its fitted ideal sinusoidal wave. (c) The residual between the measured and fitted at each phase step.
Fig. 6
Fig. 6 Simulation of the single-point sinusoidal error: (a) Sinusoidal error in different combinations of R and T. (b) Cross section of the surface when T = 25 pixels, which is denoted on the surface by a blue line. (c) Cross section of the surface when R = 15 pixels, which is denoted on the surface by a red line.
Fig. 7
Fig. 7 Simulation of the projector defocus: (a) The relationship between blur spot radius R in the raw input image coordinate and projector focusing distance S. (b) The estimated cutoff frequency.
Fig. 8
Fig. 8 Sinusoidal error with different normalized noise sets: (a) 0.00001π, (b) 0.0001π, which is also the top view of Fig. 6(a), (c) 0.001π, and (d) 0.01π. The white lines denote the cutoff frequency that is equal to the integral multiples of ω0 from D0 = ω0 to D0 = 10ω0. The minimum sinusoidal error region rotates clockwise and shrinks when the noises increase.
Fig. 9
Fig. 9 Experimental setup.
Fig. 10
Fig. 10 Experimental results: (a) Radius estimated result based on PSF measurement. (b) Measured sinusoidal error under different fringe periods where the focusing distance is fixed at 85 cm where the blur spot radius is approximately 14.6 pixels.
Fig. 11
Fig. 11 Sinusoidal error evaluation experimental results. The focusing distance is fixed at 85 cm where the blur spot radius is approximately 14.6 pixels. The period of the square-binary fringe is 9, 15, 18, 21, 27, 32, 36, 40, 45, 51, 54, and 72 pixels. The first and third rows are the measured wave formed by intensity variation and the fitted sinusoidal wave, respectively. The second and fourth rows are the residual between measured wave and fitted sinusoidal wave at each phase step.
Fig. 12
Fig. 12 Result of the sinusoidal error experiment. (a) 3D surface of different combination results. (b) Top view of the surface.
Fig. 13
Fig. 13 Experimental and simulation results of the parameter combinations in the same coordinate. The red spots denote the measured data. The simulation result displayed as the surface is the crop of Fig. 6(a).
Fig. 14
Fig. 14 Simulation results Single-point sinusoidal error for different defocusing degrees, which is calculated by Eq. (24).
Fig. 15
Fig. 15 Measurement results of a standard plane board: (a) Standard plane board. (b) S = 65 cm with T = 16 pixels. (c) S = 65 cm with T = 20 pixels. (d) S = 65 cm with T = 24 pixels. (e) S = 75 cm with T = 16 pixels. (f) S = 75 cm with T = 20 pixels. (g) S = 75 cm with T = 24 pixels. (h) S = 110 cm with T = 16 pixels. (i) S = 110 cm with T = 20 pixels. (h) S = 110 cm with T = 24 pixels.
Fig. 16
Fig. 16 Measurement results of a plaster model: (a) Plaster model. (b) Measurement results when the focusing distance is set at 110 cm with T = 44 pixels. (c) Measurement results when the focusing distance is set at 90 cm with T = 44 pixels. (d) Layered measurement results when the focusing distance is set at 65 cm with T = 16 pixels. (e) The fringe pattern captured when the focusing distance is set at 65 cm with T = 16 pixels.

Tables (1)

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Table 1 Fitting plane error comparison

Equations (24)

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I ( x , y ) = r e c t ( x , y ) h ( x , y ) ,
I i ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) + 2 π N i ] ,
ϕ ( x , y ) = ϕ ( x c , y c ) = arc tan [ i = 0 N I i c ( x c , y c ) sin ( 2 i π N ) i = 0 N I i c ( x c , y c ) cos ( 2 i π N ) ] ,
R E C T ( j ω ) = A π n = sin ( n π 2 ) n π 2 δ ( ω n ω 0 ) = A π δ ( ω ) + 2 A k = 0 ( 1 ) k 2 k + 1 δ [ ω ± ( 2 k + 1 ) ω 0 ] ,
ω 0 = 2 π T .
h ( x ) = 1 2 π σ h 2 e x 2 2 σ h 2 ,
H ( j ω ) = e ω 2 2 D 0 2 ,
F ( j ω ) = R E C T ( j ω ) H ( j ω ) = A π δ ( ω ) + 2 A e ω 0 2 2 D 0 2 [ δ ( ω + ω 0 ) + δ ( ω ω 0 ) ] + 2 A k = 1 ( 1 ) k 2 k + 1 e [ ( 2 k + 1 ) ω 0 ] 2 2 D 0 2 [ δ ( ω ± ( 2 k + 1 ) ω 0 ) ] .
g ( j ω ) = A π δ ( ω ) + 2 A e ω 0 2 2 D 0 2 [ δ ( ω + ω 0 ) + δ ( ω ω 0 ) ] ,
R n ( j ω ) = 2 A k = 1 ( 1 ) k 2 k + 1 e [ ( 2 k + 1 ) ω 0 ] 2 2 D 0 2 [ δ ( ω ± ( 2 k + 1 ) ω 0 ) ] .
G ( x ) = A 2 + 2 A π e ω 0 2 2 D 0 2 cos ( 2 π T x ) .
a = A 2 ,
b = 2 A π e ω 0 2 2 D 0 2 .
R = | D 2 ( V S 1 ) | + r V U ,
R ( S ) = | k 1 S k 2 | + k 3 ,
R = 3 σ h ,
D 0 = 3 R .
D 0 ( S ) = 3 | k 1 S k 2 | + k 3 .
σ ϕ 2 = 2 σ 2 N b 2 ,
I i c ( x c , y c ) = I i ( x c , y c ) + η i ( x c , y c ) ,
σ s t d = { σ T b if σ b 1 otherwise × 100 % .
σ = k = 1 ( 2 A π ( 2 k + 1 ) ) 2 e [ ( 2 k + 1 ) ω 0 ] 2 D 0 2 + N .
σ s t d = T ' k = 1 1 ( 2 k + 1 ) 2 e [ ( 2 k + 1 ) 2 1 ] ω 0 2 D 0 2 + N ' e ω 0 2 D 0 2 × 100 % ,
{ σ s t d = T ' k = 1 1 ( 2 k + 1 ) 2 e [ ( 2 k + 1 ) 2 1 ] ω 0 2 D 0 2 + N ' e ω 0 2 D 0 2 × 100 % ω 0 = 2 π T D 0 = 3 R R ( S ) = | k 1 S k 2 | + k 3 .

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