Abstract

Stereo cameras have been widely used for three-dimensional (3D) photogrammetry, and stereo calibration is a crucial process to estimate the intrinsic and extrinsic parameters. This paper proposes a stereo calibration method with absolute phase target by using horizontal and vertical phase-shifting fringes. The one-to-one mapping from the world points to the image points that can be recovered by referring to the absolute phase and then used to calibrate the stereo cameras. Compared with traditional methods that only use feature points within the overlapping field-of-view (FOV), the proposed method can use all feature points within the overlapping and non-overlapping FOVs. Besides, since phase is more robust against camera defocusing than intensity, the target images can be captured regardless of the depth-of-field (DOF). With the advantages of whole-field capability and defocusing tolerability, the target placement becomes very flexible. Both simulations and experiment results demonstrate the robustness and accuracy of the proposed method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Stereo-camera calibration for large-scale DIC measurements with active phase targets and planar mirrors

Katia Genovese, Yuxi Chi, and Bing Pan
Opt. Express 27(6) 9040-9053 (2019)

Self-calibration approach to stereo cameras with radial distortion based on epipolar constraint

Banglei Guan, Yingjian Yu, Ang Su, Yang Shang, and Qifeng Yu
Appl. Opt. 58(31) 8511-8521 (2019)

Planar self-calibration for stereo cameras with radial distortion

Banglei Guan, Yang Shang, and Qifeng Yu
Appl. Opt. 56(33) 9257-9267 (2017)

References

  • View by:
  • |
  • |
  • |

  1. X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48(2), 191–204 (2010).
    [Crossref]
  2. C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
    [Crossref]
  3. J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1066–1077 (2000).
    [Crossref]
  4. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
    [Crossref]
  5. Z. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 892–899 (2004).
    [Crossref]
  6. Z. Liu, Q. Wu, X. Chen, and Y. Yin, “High-accuracy calibration of low-cost camera using image disturbance factor,” Opt. Express 24(21), 24321–24336 (2016).
    [Crossref]
  7. B. Li and S. Zhang, “Flexible calibration method for microscopic structured light system using telecentric lens,” Opt. Express 23(20), 25795–25803 (2015).
    [Crossref]
  8. J. Jin and X. Li, “Efficient camera self-calibration method based on the absolute dual quadric,” J. Opt. Soc. Am. A 30(3), 287–292 (2013).
    [Crossref]
  9. L. Huang, Q. Zhang, and A. Asundi, “Camera calibration with active phase target: improvement on feature detection and optimization,” Opt. Lett. 38(9), 1446–1448 (2013).
    [Crossref]
  10. Y. Xu, F. Gao, H. Ren, Z. Zhang, and X. Jiang, “An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target,” Sensors 17(6), 1188 (2017).
    [Crossref]
  11. W. Zhao, X. Su, and W. Chen, “Whole-field high precision point to point calibration method,” Opt. Lasers Eng. 111, 71–79 (2018).
    [Crossref]
  12. M. Ma, X. Chen, and K. Wang, “Camera calibration by using fringe patterns and 2D phase-difference pulse detection,” Optik 125(2), 671–674 (2014).
    [Crossref]
  13. C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50(11), 113601 (2011).
    [Crossref]
  14. T. Bell, J. Xu, and S. Zhang, “Method for out-of-focus camera calibration,” Appl. Opt. 55(9), 2346–2352 (2016).
    [Crossref]
  15. Y. Wang, B. Cai, K. Wang, and X. Chen, “Out-of-focus color camera calibration with one normal-sized color-coded pattern,” Opt. Lasers Eng. 98, 17–22 (2017).
    [Crossref]
  16. Y. Wang, X. Chen, J. Tao, K. Wang, and M. Ma, “Accurate feature detection for out-of-focus camera calibration,” Appl. Opt. 55(28), 7964–7971 (2016).
    [Crossref]
  17. R. Juarez-Salazar, F. Guerrero-Sanchez, C. Robledo-Sanchez, and J. Gonzalez-Garcia, “Camera calibration by multiplexed phase encoding of coordinate information,” Appl. Opt. 54(15), 4895–4906 (2015).
    [Crossref]
  18. Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123(2), 171–175 (2012).
    [Crossref]
  19. J. H. Kim and B. K. Koo, “Convenient calibration method for unsynchronized camera networks using an inaccurate small reference object,” Opt. Express 20(23), 25292–25310 (2012).
    [Crossref]
  20. S. Gai, F. Da, and X. Dai, “A novel dual-camera calibration method for 3D optical measurement,” Opt. Lasers Eng. 104, 126–134 (2018).
    [Crossref]
  21. L. Wang, W. Wang, C. Shen, and F. Duan, “A convex relaxation optimization algorithm for multi-camera calibration with 1D objects,” Neurocomputing 215, 82–89 (2016).
    [Crossref]
  22. J. Yu and F. Da, “Bi-tangent line based approach for multi-camera calibration using spheres,” J. Opt. Soc. Am. A 35(2), 221–229 (2018).
    [Crossref]
  23. Z. Liu, Y. Yin, S. Liu, and X. Chen, “Extrinsic parameter calibration of stereo vision sensors using spot laser projector,” Appl. Opt. 55(25), 7098–7105 (2016).
    [Crossref]
  24. J. A. M. Rodríguez and F. C. Mejía Alanís, “Binocular self-calibration performed via adaptive genetic algorithm based on laser line imaging,” J. Mod. Opt. 63(13), 1219–1232 (2016).
    [Crossref]
  25. R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
    [Crossref]
  26. Z. Liu, X. Wei, and G. Zhang, “External parameter calibration of widely distributed vision sensors with non-overlapping fields of view,” Opt. Lasers Eng. 51(6), 643–650 (2013).
    [Crossref]
  27. M. Xie, Z. Wei, G. Zhang, and X. Wei, “A flexible technique for calibrating relative position and orientation of two cameras with no-overlapping FOV,” Measurement 46(1), 34–44 (2013).
    [Crossref]
  28. S. Dong, X. Shao, X. Kang, F. Yang, and X. He, “Extrinsic calibration of a non-overlapping camera network based on close-range photogrammetry,” Appl. Opt. 55(23), 6363–6370 (2016).
    [Crossref]
  29. Y. Xu, G. Feng, Z. Zhang, and X. Jiang, “A calibration method for non-overlapping cameras based on mirrored absolute phase target,” Int. J. Adv. Manuf. Technol.1–7 (2018).
    [Crossref]
  30. Z. Wei, W. Zou, G. Zhang, and K. Zhao, “Extrinsic parameters calibration of multi-camera with non-overlapping fields of view using laser scanning,” Opt. Express 27(12), 16719–16737 (2019).
    [Crossref]
  31. T. Yang, Q. Zhao, X. Wang, and D. Huang, “Accurate calibration approach for non-overlapping multi-camera system,” Opt. Laser Technol. 110, 78–86 (2019).
    [Crossref]
  32. J. A. M. Rodríguez, “Microscope self-calibration based on micro laser line imaging and soft computing algorithms,” Opt. Lasers Eng. 105, 75–85 (2018).
    [Crossref]
  33. J.-Y. Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc .
  34. X. Chen, Y. Wang, Y. Wang, M. Ma, and C. Zeng, “Quantized phase coding and connected region labeling for absolute phase retrieval,” Opt. Express 24(25), 28613–28624 (2016).
    [Crossref]
  35. J. S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55(16), 4395–4401 (2016).
    [Crossref]

2019 (2)

Z. Wei, W. Zou, G. Zhang, and K. Zhao, “Extrinsic parameters calibration of multi-camera with non-overlapping fields of view using laser scanning,” Opt. Express 27(12), 16719–16737 (2019).
[Crossref]

T. Yang, Q. Zhao, X. Wang, and D. Huang, “Accurate calibration approach for non-overlapping multi-camera system,” Opt. Laser Technol. 110, 78–86 (2019).
[Crossref]

2018 (6)

J. A. M. Rodríguez, “Microscope self-calibration based on micro laser line imaging and soft computing algorithms,” Opt. Lasers Eng. 105, 75–85 (2018).
[Crossref]

S. Gai, F. Da, and X. Dai, “A novel dual-camera calibration method for 3D optical measurement,” Opt. Lasers Eng. 104, 126–134 (2018).
[Crossref]

J. Yu and F. Da, “Bi-tangent line based approach for multi-camera calibration using spheres,” J. Opt. Soc. Am. A 35(2), 221–229 (2018).
[Crossref]

R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
[Crossref]

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

W. Zhao, X. Su, and W. Chen, “Whole-field high precision point to point calibration method,” Opt. Lasers Eng. 111, 71–79 (2018).
[Crossref]

2017 (2)

Y. Xu, F. Gao, H. Ren, Z. Zhang, and X. Jiang, “An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target,” Sensors 17(6), 1188 (2017).
[Crossref]

Y. Wang, B. Cai, K. Wang, and X. Chen, “Out-of-focus color camera calibration with one normal-sized color-coded pattern,” Opt. Lasers Eng. 98, 17–22 (2017).
[Crossref]

2016 (9)

Y. Wang, X. Chen, J. Tao, K. Wang, and M. Ma, “Accurate feature detection for out-of-focus camera calibration,” Appl. Opt. 55(28), 7964–7971 (2016).
[Crossref]

T. Bell, J. Xu, and S. Zhang, “Method for out-of-focus camera calibration,” Appl. Opt. 55(9), 2346–2352 (2016).
[Crossref]

Z. Liu, Q. Wu, X. Chen, and Y. Yin, “High-accuracy calibration of low-cost camera using image disturbance factor,” Opt. Express 24(21), 24321–24336 (2016).
[Crossref]

S. Dong, X. Shao, X. Kang, F. Yang, and X. He, “Extrinsic calibration of a non-overlapping camera network based on close-range photogrammetry,” Appl. Opt. 55(23), 6363–6370 (2016).
[Crossref]

Z. Liu, Y. Yin, S. Liu, and X. Chen, “Extrinsic parameter calibration of stereo vision sensors using spot laser projector,” Appl. Opt. 55(25), 7098–7105 (2016).
[Crossref]

J. A. M. Rodríguez and F. C. Mejía Alanís, “Binocular self-calibration performed via adaptive genetic algorithm based on laser line imaging,” J. Mod. Opt. 63(13), 1219–1232 (2016).
[Crossref]

L. Wang, W. Wang, C. Shen, and F. Duan, “A convex relaxation optimization algorithm for multi-camera calibration with 1D objects,” Neurocomputing 215, 82–89 (2016).
[Crossref]

X. Chen, Y. Wang, Y. Wang, M. Ma, and C. Zeng, “Quantized phase coding and connected region labeling for absolute phase retrieval,” Opt. Express 24(25), 28613–28624 (2016).
[Crossref]

J. S. Hyun and S. Zhang, “Enhanced two-frequency phase-shifting method,” Appl. Opt. 55(16), 4395–4401 (2016).
[Crossref]

2015 (2)

2014 (1)

M. Ma, X. Chen, and K. Wang, “Camera calibration by using fringe patterns and 2D phase-difference pulse detection,” Optik 125(2), 671–674 (2014).
[Crossref]

2013 (4)

J. Jin and X. Li, “Efficient camera self-calibration method based on the absolute dual quadric,” J. Opt. Soc. Am. A 30(3), 287–292 (2013).
[Crossref]

L. Huang, Q. Zhang, and A. Asundi, “Camera calibration with active phase target: improvement on feature detection and optimization,” Opt. Lett. 38(9), 1446–1448 (2013).
[Crossref]

Z. Liu, X. Wei, and G. Zhang, “External parameter calibration of widely distributed vision sensors with non-overlapping fields of view,” Opt. Lasers Eng. 51(6), 643–650 (2013).
[Crossref]

M. Xie, Z. Wei, G. Zhang, and X. Wei, “A flexible technique for calibrating relative position and orientation of two cameras with no-overlapping FOV,” Measurement 46(1), 34–44 (2013).
[Crossref]

2012 (2)

2011 (1)

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50(11), 113601 (2011).
[Crossref]

2010 (1)

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

2004 (1)

Z. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 892–899 (2004).
[Crossref]

2000 (2)

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1066–1077 (2000).
[Crossref]

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Angelopoulou, E.

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50(11), 113601 (2011).
[Crossref]

Asundi, A.

Bell, T.

Bouguet, J.-Y.

J.-Y. Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc .

Cai, B.

Y. Wang, B. Cai, K. Wang, and X. Chen, “Out-of-focus color camera calibration with one normal-sized color-coded pattern,” Opt. Lasers Eng. 98, 17–22 (2017).
[Crossref]

Chen, Q.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

Chen, S.

R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
[Crossref]

Chen, W.

W. Zhao, X. Su, and W. Chen, “Whole-field high precision point to point calibration method,” Opt. Lasers Eng. 111, 71–79 (2018).
[Crossref]

Chen, X.

Chen, Y.

R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
[Crossref]

Da, F.

S. Gai, F. Da, and X. Dai, “A novel dual-camera calibration method for 3D optical measurement,” Opt. Lasers Eng. 104, 126–134 (2018).
[Crossref]

J. Yu and F. Da, “Bi-tangent line based approach for multi-camera calibration using spheres,” J. Opt. Soc. Am. A 35(2), 221–229 (2018).
[Crossref]

Dai, X.

S. Gai, F. Da, and X. Dai, “A novel dual-camera calibration method for 3D optical measurement,” Opt. Lasers Eng. 104, 126–134 (2018).
[Crossref]

Dong, S.

Duan, F.

L. Wang, W. Wang, C. Shen, and F. Duan, “A convex relaxation optimization algorithm for multi-camera calibration with 1D objects,” Neurocomputing 215, 82–89 (2016).
[Crossref]

Feng, G.

Y. Xu, G. Feng, Z. Zhang, and X. Jiang, “A calibration method for non-overlapping cameras based on mirrored absolute phase target,” Int. J. Adv. Manuf. Technol.1–7 (2018).
[Crossref]

Feng, S.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

Forster, F.

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50(11), 113601 (2011).
[Crossref]

Fu, S. P.

R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
[Crossref]

Gai, S.

S. Gai, F. Da, and X. Dai, “A novel dual-camera calibration method for 3D optical measurement,” Opt. Lasers Eng. 104, 126–134 (2018).
[Crossref]

Gao, F.

Y. Xu, F. Gao, H. Ren, Z. Zhang, and X. Jiang, “An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target,” Sensors 17(6), 1188 (2017).
[Crossref]

Gonzalez-Garcia, J.

Guerrero-Sanchez, F.

He, X.

Heikkila, J.

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1066–1077 (2000).
[Crossref]

Hu, M.

R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
[Crossref]

Huang, D.

T. Yang, Q. Zhao, X. Wang, and D. Huang, “Accurate calibration approach for non-overlapping multi-camera system,” Opt. Laser Technol. 110, 78–86 (2019).
[Crossref]

Huang, L.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

L. Huang, Q. Zhang, and A. Asundi, “Camera calibration with active phase target: improvement on feature detection and optimization,” Opt. Lett. 38(9), 1446–1448 (2013).
[Crossref]

Hyun, J. S.

Jiang, X.

Y. Xu, F. Gao, H. Ren, Z. Zhang, and X. Jiang, “An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target,” Sensors 17(6), 1188 (2017).
[Crossref]

Y. Xu, G. Feng, Z. Zhang, and X. Jiang, “A calibration method for non-overlapping cameras based on mirrored absolute phase target,” Int. J. Adv. Manuf. Technol.1–7 (2018).
[Crossref]

Jin, J.

Juarez-Salazar, R.

Kang, X.

Kim, J. H.

Koo, B. K.

Li, B.

Li, X.

Liu, S.

Liu, Y.

Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123(2), 171–175 (2012).
[Crossref]

Liu, Z.

Ma, M.

Mejía Alanís, F. C.

J. A. M. Rodríguez and F. C. Mejía Alanís, “Binocular self-calibration performed via adaptive genetic algorithm based on laser line imaging,” J. Mod. Opt. 63(13), 1219–1232 (2016).
[Crossref]

Ren, H.

Y. Xu, F. Gao, H. Ren, Z. Zhang, and X. Jiang, “An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target,” Sensors 17(6), 1188 (2017).
[Crossref]

Robledo-Sanchez, C.

Rodríguez, J. A. M.

J. A. M. Rodríguez, “Microscope self-calibration based on micro laser line imaging and soft computing algorithms,” Opt. Lasers Eng. 105, 75–85 (2018).
[Crossref]

J. A. M. Rodríguez and F. C. Mejía Alanís, “Binocular self-calibration performed via adaptive genetic algorithm based on laser line imaging,” J. Mod. Opt. 63(13), 1219–1232 (2016).
[Crossref]

Schmalz, C.

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50(11), 113601 (2011).
[Crossref]

Shao, X.

Shen, C.

L. Wang, W. Wang, C. Shen, and F. Duan, “A convex relaxation optimization algorithm for multi-camera calibration with 1D objects,” Neurocomputing 215, 82–89 (2016).
[Crossref]

Su, X.

W. Zhao, X. Su, and W. Chen, “Whole-field high precision point to point calibration method,” Opt. Lasers Eng. 111, 71–79 (2018).
[Crossref]

Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123(2), 171–175 (2012).
[Crossref]

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

Tao, J.

Tao, T.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

Wang, K.

Y. Wang, B. Cai, K. Wang, and X. Chen, “Out-of-focus color camera calibration with one normal-sized color-coded pattern,” Opt. Lasers Eng. 98, 17–22 (2017).
[Crossref]

Y. Wang, X. Chen, J. Tao, K. Wang, and M. Ma, “Accurate feature detection for out-of-focus camera calibration,” Appl. Opt. 55(28), 7964–7971 (2016).
[Crossref]

M. Ma, X. Chen, and K. Wang, “Camera calibration by using fringe patterns and 2D phase-difference pulse detection,” Optik 125(2), 671–674 (2014).
[Crossref]

Wang, L.

L. Wang, W. Wang, C. Shen, and F. Duan, “A convex relaxation optimization algorithm for multi-camera calibration with 1D objects,” Neurocomputing 215, 82–89 (2016).
[Crossref]

Wang, W.

L. Wang, W. Wang, C. Shen, and F. Duan, “A convex relaxation optimization algorithm for multi-camera calibration with 1D objects,” Neurocomputing 215, 82–89 (2016).
[Crossref]

Wang, X.

T. Yang, Q. Zhao, X. Wang, and D. Huang, “Accurate calibration approach for non-overlapping multi-camera system,” Opt. Laser Technol. 110, 78–86 (2019).
[Crossref]

Wang, Y.

Wei, X.

M. Xie, Z. Wei, G. Zhang, and X. Wei, “A flexible technique for calibrating relative position and orientation of two cameras with no-overlapping FOV,” Measurement 46(1), 34–44 (2013).
[Crossref]

Z. Liu, X. Wei, and G. Zhang, “External parameter calibration of widely distributed vision sensors with non-overlapping fields of view,” Opt. Lasers Eng. 51(6), 643–650 (2013).
[Crossref]

Wei, Z.

Z. Wei, W. Zou, G. Zhang, and K. Zhao, “Extrinsic parameters calibration of multi-camera with non-overlapping fields of view using laser scanning,” Opt. Express 27(12), 16719–16737 (2019).
[Crossref]

M. Xie, Z. Wei, G. Zhang, and X. Wei, “A flexible technique for calibrating relative position and orientation of two cameras with no-overlapping FOV,” Measurement 46(1), 34–44 (2013).
[Crossref]

Wu, Q.

Xia, R.

R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
[Crossref]

Xie, M.

M. Xie, Z. Wei, G. Zhang, and X. Wei, “A flexible technique for calibrating relative position and orientation of two cameras with no-overlapping FOV,” Measurement 46(1), 34–44 (2013).
[Crossref]

Xu, J.

Xu, Y.

Y. Xu, F. Gao, H. Ren, Z. Zhang, and X. Jiang, “An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target,” Sensors 17(6), 1188 (2017).
[Crossref]

Y. Xu, G. Feng, Z. Zhang, and X. Jiang, “A calibration method for non-overlapping cameras based on mirrored absolute phase target,” Int. J. Adv. Manuf. Technol.1–7 (2018).
[Crossref]

Yang, F.

Yang, T.

T. Yang, Q. Zhao, X. Wang, and D. Huang, “Accurate calibration approach for non-overlapping multi-camera system,” Opt. Laser Technol. 110, 78–86 (2019).
[Crossref]

Yin, W.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

Yin, Y.

Yu, J.

Zeng, C.

Zhang, G.

Z. Wei, W. Zou, G. Zhang, and K. Zhao, “Extrinsic parameters calibration of multi-camera with non-overlapping fields of view using laser scanning,” Opt. Express 27(12), 16719–16737 (2019).
[Crossref]

M. Xie, Z. Wei, G. Zhang, and X. Wei, “A flexible technique for calibrating relative position and orientation of two cameras with no-overlapping FOV,” Measurement 46(1), 34–44 (2013).
[Crossref]

Z. Liu, X. Wei, and G. Zhang, “External parameter calibration of widely distributed vision sensors with non-overlapping fields of view,” Opt. Lasers Eng. 51(6), 643–650 (2013).
[Crossref]

Zhang, Q.

Zhang, S.

Zhang, Z.

Y. Xu, F. Gao, H. Ren, Z. Zhang, and X. Jiang, “An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target,” Sensors 17(6), 1188 (2017).
[Crossref]

Z. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 892–899 (2004).
[Crossref]

Y. Xu, G. Feng, Z. Zhang, and X. Jiang, “A calibration method for non-overlapping cameras based on mirrored absolute phase target,” Int. J. Adv. Manuf. Technol.1–7 (2018).
[Crossref]

Zhang, Z. Y.

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Zhao, J.

R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
[Crossref]

Zhao, K.

Zhao, Q.

T. Yang, Q. Zhao, X. Wang, and D. Huang, “Accurate calibration approach for non-overlapping multi-camera system,” Opt. Laser Technol. 110, 78–86 (2019).
[Crossref]

Zhao, W.

W. Zhao, X. Su, and W. Chen, “Whole-field high precision point to point calibration method,” Opt. Lasers Eng. 111, 71–79 (2018).
[Crossref]

Zou, W.

Zuo, C.

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

Appl. Opt. (6)

IEEE Trans. Pattern Anal. Mach. Intell. (3)

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Mach. Intell. 22(10), 1066–1077 (2000).
[Crossref]

Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22(11), 1330–1334 (2000).
[Crossref]

Z. Zhang, “Camera calibration with one-dimensional objects,” IEEE Trans. Pattern Anal. Mach. Intell. 26(7), 892–899 (2004).
[Crossref]

J. Mod. Opt. (1)

J. A. M. Rodríguez and F. C. Mejía Alanís, “Binocular self-calibration performed via adaptive genetic algorithm based on laser line imaging,” J. Mod. Opt. 63(13), 1219–1232 (2016).
[Crossref]

J. Opt. Soc. Am. A (2)

Measurement (1)

M. Xie, Z. Wei, G. Zhang, and X. Wei, “A flexible technique for calibrating relative position and orientation of two cameras with no-overlapping FOV,” Measurement 46(1), 34–44 (2013).
[Crossref]

Neurocomputing (1)

L. Wang, W. Wang, C. Shen, and F. Duan, “A convex relaxation optimization algorithm for multi-camera calibration with 1D objects,” Neurocomputing 215, 82–89 (2016).
[Crossref]

Opt. Eng. (1)

C. Schmalz, F. Forster, and E. Angelopoulou, “Camera calibration: active versus passive targets,” Opt. Eng. 50(11), 113601 (2011).
[Crossref]

Opt. Express (5)

Opt. Laser Technol. (1)

T. Yang, Q. Zhao, X. Wang, and D. Huang, “Accurate calibration approach for non-overlapping multi-camera system,” Opt. Laser Technol. 110, 78–86 (2019).
[Crossref]

Opt. Lasers Eng. (7)

J. A. M. Rodríguez, “Microscope self-calibration based on micro laser line imaging and soft computing algorithms,” Opt. Lasers Eng. 105, 75–85 (2018).
[Crossref]

Z. Liu, X. Wei, and G. Zhang, “External parameter calibration of widely distributed vision sensors with non-overlapping fields of view,” Opt. Lasers Eng. 51(6), 643–650 (2013).
[Crossref]

S. Gai, F. Da, and X. Dai, “A novel dual-camera calibration method for 3D optical measurement,” Opt. Lasers Eng. 104, 126–134 (2018).
[Crossref]

Y. Wang, B. Cai, K. Wang, and X. Chen, “Out-of-focus color camera calibration with one normal-sized color-coded pattern,” Opt. Lasers Eng. 98, 17–22 (2017).
[Crossref]

W. Zhao, X. Su, and W. Chen, “Whole-field high precision point to point calibration method,” Opt. Lasers Eng. 111, 71–79 (2018).
[Crossref]

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

C. Zuo, S. Feng, L. Huang, T. Tao, W. Yin, and Q. Chen, “Phase shifting algorithms for fringe projection profilometry: A review,” Opt. Lasers Eng. 109, 23–59 (2018).
[Crossref]

Opt. Lett. (1)

Optik (3)

M. Ma, X. Chen, and K. Wang, “Camera calibration by using fringe patterns and 2D phase-difference pulse detection,” Optik 125(2), 671–674 (2014).
[Crossref]

Y. Liu and X. Su, “Camera calibration with planar crossed fringe patterns,” Optik 123(2), 171–175 (2012).
[Crossref]

R. Xia, M. Hu, J. Zhao, S. Chen, Y. Chen, and S. P. Fu, “Global calibration of non-overlapping cameras: State of the art,” Optik 158, 951–961 (2018).
[Crossref]

Sensors (1)

Y. Xu, F. Gao, H. Ren, Z. Zhang, and X. Jiang, “An Iterative Distortion Compensation Algorithm for Camera Calibration Based on Phase Target,” Sensors 17(6), 1188 (2017).
[Crossref]

Other (2)

Y. Xu, G. Feng, Z. Zhang, and X. Jiang, “A calibration method for non-overlapping cameras based on mirrored absolute phase target,” Int. J. Adv. Manuf. Technol.1–7 (2018).
[Crossref]

J.-Y. Bouguet, “Camera Calibration Toolbox for Matlab,” http://www.vision.caltech.edu/bouguetj/calib_doc .

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1.
Fig. 1. Transformations between the world coordinate and two camera coordinates.
Fig. 2.
Fig. 2. Schematic diagram of stereo calibration.
Fig. 3.
Fig. 3. Framework of feature detection.
Fig. 4.
Fig. 4. Simulated images.
Fig. 5.
Fig. 5. Absolute errors with different noise levels. (a) Focal lengths;(b) Principal points; (c) Rotation angles; (d) Translation distances.
Fig. 6.
Fig. 6. Absolute errors with different blur levels. (a) Focal lengths;(b) Principal points; (c) Rotation angles; (d) Translation distances.
Fig. 7.
Fig. 7. Absolute errors with different focal lengths. (a) Focal lengths;(b) Principal points; (c) Rotation angles; (d) Translation distances.
Fig. 8.
Fig. 8. In-focus images for overlapping cameras calibration. (a) Horizontal fringe captured by left camera and (b) its phase map; (c) Vertical fringe captured by left camera and (d) its phase map; (e) Horizontal fringe captured by right camera and (f) its phase map; (g) Vertical fringe captured by right camera and (h) its phase map.
Fig. 9.
Fig. 9. Defocused images for overlapping cameras calibration. (a) Horizontal fringe captured by left camera and (b) its phase map; (c) Vertical fringe captured by left camera and (d) its phase map; (e) Horizontal fringe captured by right camera and (f) its phase map; (g) Vertical fringe captured by right camera and (h) its phase map.
Fig. 10.
Fig. 10. Target poses. (a) In-focus; (b) Defocus.
Fig. 11.
Fig. 11. Chessboard corners reconstructed using (a) In-focus calibration results; and (b) Defocus calibration results.
Fig. 12.
Fig. 12. In-focus images for non-overlapping cameras calibration. (a) Horizontal fringe captured by left camera and (b) its phase map; (c) Vertical fringe captured by left camera and (d) its phase map; (e) Horizontal fringe captured by right camera and (f) its phase map; (g) Vertical fringe captured by right camera and (h) its phase map.
Fig. 13.
Fig. 13. Defocused images for non-overlapping cameras calibration. (a) Horizontal fringe captured by left camera and (b) its phase map; (c) Vertical fringe captured by left camera and (d) its phase map; (e) Horizontal fringe captured by right camera and (f) its phase map; (g) Vertical fringe captured by right camera and (h) its phase map.

Tables (5)

Tables Icon

Table 1. Calibrated intrinsic parameters of first experiment.

Tables Icon

Table 2. Calibrated extrinsic parameters of first experiment.

Tables Icon

Table 3. Mean reconstruction errors of square size using in-focus/defocus calibration results (unit: µm).

Tables Icon

Table 4. Calibrated intrinsic parameters of second experiment.

Tables Icon

Table 5. Calibrated extrinsic parameters of second experiment.

Equations (15)

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

s P ~ = K [ R t ] P ~
K = [ f u γ u 0 0 f v v 0 0 0 1 ] , R = r o d r i g u e s [ θ x θ y θ z ] , t = [ t x t y t z ]
{ u ~ d = u ~ ( 1 + k 1 r 2 + k 2 r 4 ) + 2 p 1 u ~ v ~ + p 2 ( r 2 + 2 u ~ 2 ) v ~ d = v ~ ( 1 + k 1 r 2 + k 2 r 4 ) + 2 p 2 u ~ v ~ + p 1 ( r 2 + 2 v ~ 2 )
[ u ~ d v ~ d ] = [ u d v d ] [ u 0 v 0 ] , [ u ~ v ~ ] = [ u v ] [ u 0 v 0 ] , r 2 = u ~ 2 + v ~ 2
{ P l = R w l P w + t w l P r = R w r P w + t w r
P r = R l r P l + t l r = R w r R w l T P l + ( t w r R w r R w l T t w l )
I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) 2 π / 3 ]
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) ]
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos [ ϕ ( x , y ) + 2 π / 3 ]
ϕ ( x , y ) = tan 1 ( 3 I 1 I 3 2 I 2 I 1 I 3 )
k ( x , y ) = round [ ( f / f r ) ϕ r ( x , y ) ϕ ( x , y ) 2 π ]
Φ ( x , y ) = ϕ ( x , y ) + 2 π k ( x , y )
{ u = a 1 Φ u + b 1 Φ v + c 1 v = a 2 Φ u + b 2 Φ v + c 2
[ X Y ] = q P 2 π [ Φ u Φ v ]
K l = K r = [ 8 00 0 320 0 8 00 240 0 0 1 ] , R l r = [ 1 0 0 0 1 0 0 0 1 ] , t l r = [ 5 00 0 0 ]

Metrics