Abstract

This paper proposes a high-speed FPGA architecture for the phase measuring profilometry (PMP) algorithm. The whole PMP algorithm is designed and implemented based on the principle of full-pipeline and parallelism. The results show that the accuracy of the FPGA system is comparable with those of current top-performing software implementations. The FPGA system achieves 3D sharp reconstruction using 12 phase-shifting images and completes in 21 ms with 1024 × 768 pixel resolution. To the best of our knowledge, this is the first fully pipelined architecture for PMP systems, and this makes the PMP system very suitable for high-speed embedded 3D shape measurement applications.

© 2017 Optical Society of America

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References

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  1. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35(1), 51–60 (1996).
    [Crossref] [PubMed]
  2. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23(18), 3105–3108 (1984).
    [Crossref] [PubMed]
  3. S. Zhang, D. Royer, and S.-T. Yau, “GPU-assisted high-resolution, real-time 3-D shape measurement,” Opt. Express 14(20), 9120–9129 (2006).
    [Crossref] [PubMed]
  4. H. Nguyen, D. Nguyen, Z. Wang, H. Kieu, and M. Le, “Real-time, high-accuracy 3D imaging and shape measurement,” Appl. Opt. 54(1), A9–A17 (2015).
    [Crossref] [PubMed]
  5. K. Zhong, Z. Li, X. Zhou, Y. Shi, and C. Wang, “Hybrid parallel computing architecture for multiview phase shifting,” Opt. Eng. 53(11), 112214 (2014).
    [Crossref]
  6. Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express 18(19), 19743–19754 (2010).
    [Crossref] [PubMed]
  7. X. Liu, H. Zhao, G. Zhan, K. Zhong, Z. Li, Y. Chao, and Y. Shi, “Rapid and automatic 3D body measurement system based on a GPU-Steger line detector,” Appl. Opt. 55(21), 5539–5547 (2016).
    [Crossref] [PubMed]
  8. S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
    [Crossref]
  9. J. Wang, Z. Xiong, Z. Wang, Y. Zhang, and F. Wu, “FPGA Design and Implementation of Kinect-Like Depth Sensing,” IEEE Trans. Circ. Syst. Video Tech. 26(6), 1175–1186 (2016).
    [Crossref]
  10. Z. Li and Y. Li, “Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry,” Opt. Lett. 36(2), 154–156 (2011).
    [Crossref] [PubMed]
  11. R. Andraka, “A Survey of CORDIC Algorithms for FPGA Based Computers,” in Proceedings of the 1998 ACM/SIGDA Sixth International Symposium on Field Programmable Gate Arrays, FPGA ’98 (ACM, 1998), pp. 191–200.
    [Crossref]
  12. M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41(35), 7437–7444 (2002).
    [Crossref] [PubMed]
  13. T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” in Computer Vision and Pattern Recognition,2007. CVPR’07. IEEE Conference on (IEEE, 2007), pp. 1–8.
    [Crossref]
  14. R. Cusack and N. Papadakis, “New robust 3-D phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” Neuroimage 16(3 Pt 1), 754–764 (2002).
    [Crossref] [PubMed]
  15. T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (2016).
    [Crossref] [PubMed]
  16. Z. Li, Y. Shi, and C. Wang, “Real-Time Complex Object 3D Measurement,” in 2009 International Conference on Computer Modeling and Simulation (2009), pp. 191–193.
    [Crossref]
  17. 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]
  18. G. Bradski and A. Kaehler, Learning OpenCV: Computer Vision with the OpenCV Library (O’Reilly Media, Inc., 2008).
  19. D. V. Papadimitriou and T. J. Dennis, “Epipolar line estimation and rectification for stereo image pairs,” IEEE Trans. Image Process. 5(4), 672–676 (1996).
    [Crossref] [PubMed]

2016 (4)

J. Wang, Z. Xiong, Z. Wang, Y. Zhang, and F. Wu, “FPGA Design and Implementation of Kinect-Like Depth Sensing,” IEEE Trans. Circ. Syst. Video Tech. 26(6), 1175–1186 (2016).
[Crossref]

X. Liu, H. Zhao, G. Zhan, K. Zhong, Z. Li, Y. Chao, and Y. Shi, “Rapid and automatic 3D body measurement system based on a GPU-Steger line detector,” Appl. Opt. 55(21), 5539–5547 (2016).
[Crossref] [PubMed]

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (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)

2014 (1)

K. Zhong, Z. Li, X. Zhou, Y. Shi, and C. Wang, “Hybrid parallel computing architecture for multiview phase shifting,” Opt. Eng. 53(11), 112214 (2014).
[Crossref]

2011 (1)

2010 (2)

Y. Gong and S. Zhang, “Ultrafast 3-D shape measurement with an off-the-shelf DLP projector,” Opt. Express 18(19), 19743–19754 (2010).
[Crossref] [PubMed]

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

2006 (1)

2002 (2)

M. A. Herráez, D. R. Burton, M. J. Lalor, and M. A. Gdeisat, “Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path,” Appl. Opt. 41(35), 7437–7444 (2002).
[Crossref] [PubMed]

R. Cusack and N. Papadakis, “New robust 3-D phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” Neuroimage 16(3 Pt 1), 754–764 (2002).
[Crossref] [PubMed]

1996 (2)

Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35(1), 51–60 (1996).
[Crossref] [PubMed]

D. V. Papadimitriou and T. J. Dennis, “Epipolar line estimation and rectification for stereo image pairs,” IEEE Trans. Image Process. 5(4), 672–676 (1996).
[Crossref] [PubMed]

1984 (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]

Burton, D. R.

Chao, Y.

Chen, Q.

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (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]

Cho, J.

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

Cusack, R.

R. Cusack and N. Papadakis, “New robust 3-D phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” Neuroimage 16(3 Pt 1), 754–764 (2002).
[Crossref] [PubMed]

Da, J.

Dennis, T. J.

D. V. Papadimitriou and T. J. Dennis, “Epipolar line estimation and rectification for stereo image pairs,” IEEE Trans. Image Process. 5(4), 672–676 (1996).
[Crossref] [PubMed]

Feng, S.

Gdeisat, M. A.

Gong, Y.

Halioua, M.

Herráez, M. A.

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]

Jeon, J. W.

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

Jin, S.

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

Kieu, H.

Kim, M.

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

Lalor, M. J.

Le, M.

Lee, K. M.

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

Li, Y.

Li, Z.

X. Liu, H. Zhao, G. Zhan, K. Zhong, Z. Li, Y. Chao, and Y. Shi, “Rapid and automatic 3D body measurement system based on a GPU-Steger line detector,” Appl. Opt. 55(21), 5539–5547 (2016).
[Crossref] [PubMed]

K. Zhong, Z. Li, X. Zhou, Y. Shi, and C. Wang, “Hybrid parallel computing architecture for multiview phase shifting,” Opt. Eng. 53(11), 112214 (2014).
[Crossref]

Z. Li and Y. Li, “Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry,” Opt. Lett. 36(2), 154–156 (2011).
[Crossref] [PubMed]

Z. Li, Y. Shi, and C. Wang, “Real-Time Complex Object 3D Measurement,” in 2009 International Conference on Computer Modeling and Simulation (2009), pp. 191–193.
[Crossref]

Liu, H. C.

Liu, X.

Nguyen, D.

Nguyen, H.

Papadakis, N.

R. Cusack and N. Papadakis, “New robust 3-D phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” Neuroimage 16(3 Pt 1), 754–764 (2002).
[Crossref] [PubMed]

Papadimitriou, D. V.

D. V. Papadimitriou and T. J. Dennis, “Epipolar line estimation and rectification for stereo image pairs,” IEEE Trans. Image Process. 5(4), 672–676 (1996).
[Crossref] [PubMed]

Park, S.-K.

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

Pham, X. D.

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

Royer, D.

Shi, Y.

X. Liu, H. Zhao, G. Zhan, K. Zhong, Z. Li, Y. Chao, and Y. Shi, “Rapid and automatic 3D body measurement system based on a GPU-Steger line detector,” Appl. Opt. 55(21), 5539–5547 (2016).
[Crossref] [PubMed]

K. Zhong, Z. Li, X. Zhou, Y. Shi, and C. Wang, “Hybrid parallel computing architecture for multiview phase shifting,” Opt. Eng. 53(11), 112214 (2014).
[Crossref]

Z. Li, Y. Shi, and C. Wang, “Real-Time Complex Object 3D Measurement,” in 2009 International Conference on Computer Modeling and Simulation (2009), pp. 191–193.
[Crossref]

Srinivasan, V.

Surrel, Y.

Tao, T.

Wang, C.

K. Zhong, Z. Li, X. Zhou, Y. Shi, and C. Wang, “Hybrid parallel computing architecture for multiview phase shifting,” Opt. Eng. 53(11), 112214 (2014).
[Crossref]

Z. Li, Y. Shi, and C. Wang, “Real-Time Complex Object 3D Measurement,” in 2009 International Conference on Computer Modeling and Simulation (2009), pp. 191–193.
[Crossref]

Wang, J.

J. Wang, Z. Xiong, Z. Wang, Y. Zhang, and F. Wu, “FPGA Design and Implementation of Kinect-Like Depth Sensing,” IEEE Trans. Circ. Syst. Video Tech. 26(6), 1175–1186 (2016).
[Crossref]

Wang, Z.

J. Wang, Z. Xiong, Z. Wang, Y. Zhang, and F. Wu, “FPGA Design and Implementation of Kinect-Like Depth Sensing,” IEEE Trans. Circ. Syst. Video Tech. 26(6), 1175–1186 (2016).
[Crossref]

H. Nguyen, D. Nguyen, Z. Wang, H. Kieu, and M. Le, “Real-time, high-accuracy 3D imaging and shape measurement,” Appl. Opt. 54(1), A9–A17 (2015).
[Crossref] [PubMed]

Wu, F.

J. Wang, Z. Xiong, Z. Wang, Y. Zhang, and F. Wu, “FPGA Design and Implementation of Kinect-Like Depth Sensing,” IEEE Trans. Circ. Syst. Video Tech. 26(6), 1175–1186 (2016).
[Crossref]

Xiong, Z.

J. Wang, Z. Xiong, Z. Wang, Y. Zhang, and F. Wu, “FPGA Design and Implementation of Kinect-Like Depth Sensing,” IEEE Trans. Circ. Syst. Video Tech. 26(6), 1175–1186 (2016).
[Crossref]

Yau, S.-T.

Zhan, G.

Zhang, M.

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, S.

Zhang, Y.

J. Wang, Z. Xiong, Z. Wang, Y. Zhang, and F. Wu, “FPGA Design and Implementation of Kinect-Like Depth Sensing,” IEEE Trans. Circ. Syst. Video Tech. 26(6), 1175–1186 (2016).
[Crossref]

Zhao, H.

Zhong, K.

X. Liu, H. Zhao, G. Zhan, K. Zhong, Z. Li, Y. Chao, and Y. Shi, “Rapid and automatic 3D body measurement system based on a GPU-Steger line detector,” Appl. Opt. 55(21), 5539–5547 (2016).
[Crossref] [PubMed]

K. Zhong, Z. Li, X. Zhou, Y. Shi, and C. Wang, “Hybrid parallel computing architecture for multiview phase shifting,” Opt. Eng. 53(11), 112214 (2014).
[Crossref]

Zhou, X.

K. Zhong, Z. Li, X. Zhou, Y. Shi, and C. Wang, “Hybrid parallel computing architecture for multiview phase shifting,” Opt. Eng. 53(11), 112214 (2014).
[Crossref]

Zuo, C.

T. Tao, Q. Chen, J. Da, S. Feng, Y. Hu, and C. Zuo, “Real-time 3-D shape measurement with composite phase-shifting fringes and multi-view system,” Opt. Express 24(18), 20253–20269 (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]

Appl. Opt. (5)

IEEE Trans. Circ. Syst. Video Tech. (2)

S. Jin, J. Cho, X. D. Pham, K. M. Lee, S.-K. Park, M. Kim, and J. W. Jeon, “FPGA Design and Implementation of a Real-Time Stereo Vision System,” IEEE Trans. Circ. Syst. Video Tech. 20(1), 15–26 (2010).
[Crossref]

J. Wang, Z. Xiong, Z. Wang, Y. Zhang, and F. Wu, “FPGA Design and Implementation of Kinect-Like Depth Sensing,” IEEE Trans. Circ. Syst. Video Tech. 26(6), 1175–1186 (2016).
[Crossref]

IEEE Trans. Image Process. (1)

D. V. Papadimitriou and T. J. Dennis, “Epipolar line estimation and rectification for stereo image pairs,” IEEE Trans. Image Process. 5(4), 672–676 (1996).
[Crossref] [PubMed]

Neuroimage (1)

R. Cusack and N. Papadakis, “New robust 3-D phase unwrapping algorithms: application to magnetic field mapping and undistorting echoplanar images,” Neuroimage 16(3 Pt 1), 754–764 (2002).
[Crossref] [PubMed]

Opt. Eng. (1)

K. Zhong, Z. Li, X. Zhou, Y. Shi, and C. Wang, “Hybrid parallel computing architecture for multiview phase shifting,” Opt. Eng. 53(11), 112214 (2014).
[Crossref]

Opt. Express (3)

Opt. Lasers Eng. (1)

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]

Opt. Lett. (1)

Other (4)

G. Bradski and A. Kaehler, Learning OpenCV: Computer Vision with the OpenCV Library (O’Reilly Media, Inc., 2008).

T. Weise, B. Leibe, and L. Van Gool, “Fast 3d scanning with automatic motion compensation,” in Computer Vision and Pattern Recognition,2007. CVPR’07. IEEE Conference on (IEEE, 2007), pp. 1–8.
[Crossref]

R. Andraka, “A Survey of CORDIC Algorithms for FPGA Based Computers,” in Proceedings of the 1998 ACM/SIGDA Sixth International Symposium on Field Programmable Gate Arrays, FPGA ’98 (ACM, 1998), pp. 191–200.
[Crossref]

Z. Li, Y. Shi, and C. Wang, “Real-Time Complex Object 3D Measurement,” in 2009 International Conference on Computer Modeling and Simulation (2009), pp. 191–193.
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 High-level FPGA architecture adopted for the PMP Computing Unit.
Fig. 2
Fig. 2 Phase/SNR calculation module: (a) overview and (b) detailed design of CORDIC in the FPGA.
Fig. 3
Fig. 3 Phase calculation results using FPGA: (a) captured phase shift image, (b) phase calculation result, and (c) SNR calculation result.
Fig. 4
Fig. 4 Deviation between FPGA and MATLAB over different iterations.
Fig. 5
Fig. 5 Gaussian filter module: (a) buffer design and (b) Gaussian filter kernel.
Fig. 6
Fig. 6 Phase unwrapping result (a) and its calculation deviation with respect to MATLAB (b)
Fig. 7
Fig. 7 Framework of the phase rectification module.
Fig. 8
Fig. 8 Rectified phase map obtained by FPGA (a) and its calculation deviation with respect to MATLAB (b).
Fig. 9
Fig. 9 Phase matching module design.
Fig. 10
Fig. 10 3D reconstruction results obtained by the FPGA and MATLAB platforms: (a) front view and side view of point clouds (FPGA point cloud: red, and MATLAB point cloud: green) and (b) histogram of the deviation distance between FPGA and MATLAB.
Fig. 11
Fig. 11 Implemented FPGA-based PMP system: (a) schematic diagram of our system and (b) image of our implemented system.
Fig. 12
Fig. 12 Measurement results: (a) rat (b) industrial part, and (c) horse model.

Tables (2)

Tables Icon

Table 1 Performance summary of comparison systems.

Tables Icon

Table 2 Resource utilization.

Equations (6)

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

I 1 (x,y)= I ' (x,y)+ I '' (x,y)cos[ϕ(x,y)], I 2 (x,y)= I ' (x,y)+ I '' (x,y)cos[ϕ(x,y)+π/2], I 3 (x,y)= I ' (x,y)+ I '' (x,y)cos[ϕ(x,y)+π], I 4 (x,y)= I ' (x,y)+ I '' (x,y)cos[ϕ(x,y)+3π/2],
ϕ(x,y)=arctan( I 4 (x,y) I 2 (x,y) I 1 (x,y) I 3 (x,y) ).
γ=B/A= [ ( I 2 I 4 ) 2 + ( I 1 I 3 ) 2 ] 0.5 / n=1 4 I n .
x i+1 = x i y i d i 2 i y i+1 = y i + x i d i 2 i z i+1 = z i d i tan 1 ( 2 i ) d i =+1, if y i <0, -1 otherwise.
x n = A n x 0 2 + y 0 2 y n =0 z n = z 0 + tan 1 ( y 0 x 0 ) A n = n 1+ 2 2i
{ Z= fT (d( C x l C x r )) X=( x l C x l )Z/f Y=( y l C y l )Z/f .

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