Abstract

We demonstrate a global calibration method for the laser plane using a 3D calibration board to generate the two horizontal coordinates and a height gauge to generate the height coordinate of the point in the laser plane. A sigmoid-Gaussian function for the candidate centers is employed to normalize the eigenvalues of the Hessian matrix to prevent centers missing or muti-centers. Then camera calibration and laser plane calibration are accomplished at the same time. Finally the reconstructed 3D points are transformed to the horizontal plane by the forward process that involves one translation and two rotations. The parametric equation of the 3D curve is reconstructed by the inverse process that performs on the 2D fitting curve.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
  6. G. A. Al-Kindi and B. Shirinzadeh, “An evaluation of surface roughness parameters measurement using vision-based data,” Int. J. Mach. Tools Manuf. 47(3), 697–708 (2007).
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  7. K. Zhang, B. Xu, L. Tang, and H. Shi, “Modeling of binocular vision system for 3D reconstruction with improved genetic algorithms,” Int. J. Adv. Manuf. Technol. 29(7–8), 722–728 (2006).
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  8. Z. Hu, C. Marshall, R. Bicker, and P. Taylor, “Automatic surface roughing with 3D machine vision and cooperative robot control,” Robot. Auton. Syst. 55(7), 552–560 (2007).
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    [Crossref]
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    [Crossref]
  24. M. A. Luengo-Oroz, E. Faure, and J. Angulo, “Robust iris segmentation on uncalibrated noisy images using mathematical morphology,” Image Vis. Comput. 28(2), 278–284 (2010).
    [Crossref]
  25. C. Steger, “An unbiased detector of curvilinear structures”, IEEE Trans. Pattern Anal. 20(2), 113–125 (1998).
    [Crossref]
  26. L. Qi, Y. Zhang, X. Zhang, S. Wang, and F. Xie, “Statistical behavior analysis and precision optimization for the laser stripe center detector based on Steger’s algorithm,” Opt. Express 21(11), 13442–13449 (2013).
    [Crossref] [PubMed]
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    [Crossref]
  28. G. Xu, L. N. Sun, X. T. Li, J. Su, Z. B. Hao, and X. Lu, “Adaptable center detection of a laser line with a normalization approach using Hessian-matrix eigenvalues,” J. Opt. Soc. Korea 18(4), 317–330 (2014).
  29. G. J. Zhang and Z. Z. Wei, “A novel calibration approach to structured light 3D vision inspection,” Opt. Laser Technol. 34(5), 373–380 (2002).
    [Crossref]
  30. F. Q. Zhou and G. J. Zhang, “Complete calibration of a structured light stripe vision sensor through planar target of unknown orientations,” Image Vis. Comput. 23(1), 59–67 (2005).
    [Crossref]
  31. R. Legarda-Saenz, T. Bothe, and W. P. Ju, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
    [Crossref]
  32. I. Leandry, C. Breque, and V. Valle, “Calibration of a structured-light projection system: development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
    [Crossref]
  33. J. Yan, G. H. Gong, and C. Tian, “Hue-based feature detection for geometry calibration of multiprojector arrays,” Opt. Eng. 53(6), 063108 (2014).
    [Crossref]
  34. C. Alard and R. H. Lupton, “A method for optimal image subtraction,” Astrophys. J. 503(1), 325–331 (1998).
    [Crossref]
  35. C. Steger, “Unbiased extraction of lines with parabolic and Gaussian profiles,” Comput. Vis. Image Underst. 117(2), 97–112 (2013).
  36. Y. I. Abdel-Aziz and H. M. Karara, “Direct linear transformation into object space coordinates in close-range photogrammetry,” in Proceedings of the Symposium on Close-Range Photogrammetry (Falls Church, VA, USA, 1971), pp. 1–18.
  37. G. Xu, X. T. Li, J. Su, H. D. Pan, and L. X. Geng, “Integrative evaluation of the optimal configuration for the measurement of the line segments using stereo vision,” Optik (Stuttg.) 124(11), 1015–1018 (2013).
    [Crossref]

2014 (2)

G. Xu, L. N. Sun, X. T. Li, J. Su, Z. B. Hao, and X. Lu, “Adaptable center detection of a laser line with a normalization approach using Hessian-matrix eigenvalues,” J. Opt. Soc. Korea 18(4), 317–330 (2014).

J. Yan, G. H. Gong, and C. Tian, “Hue-based feature detection for geometry calibration of multiprojector arrays,” Opt. Eng. 53(6), 063108 (2014).
[Crossref]

2013 (3)

C. Steger, “Unbiased extraction of lines with parabolic and Gaussian profiles,” Comput. Vis. Image Underst. 117(2), 97–112 (2013).

G. Xu, X. T. Li, J. Su, H. D. Pan, and L. X. Geng, “Integrative evaluation of the optimal configuration for the measurement of the line segments using stereo vision,” Optik (Stuttg.) 124(11), 1015–1018 (2013).
[Crossref]

L. Qi, Y. Zhang, X. Zhang, S. Wang, and F. Xie, “Statistical behavior analysis and precision optimization for the laser stripe center detector based on Steger’s algorithm,” Opt. Express 21(11), 13442–13449 (2013).
[Crossref] [PubMed]

2012 (3)

I. Leandry, C. Breque, and V. Valle, “Calibration of a structured-light projection system: development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
[Crossref]

Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
[Crossref]

F. Felberer, J. S. Kroisamer, C. K. Hitzenberger, and M. Pircher, “Lens based adaptive optics scanning laser ophthalmoscope,” Opt. Express 20(16), 17297–17310 (2012).
[Crossref] [PubMed]

2011 (3)

2010 (4)

O. Laligant and F. Truchetet, “A nonlinear derivative scheme applied to edge detection,” IEEE Trans. Pattern Anal. 32(2), 242–257 (2010).
[Crossref]

M. A. Luengo-Oroz, E. Faure, and J. Angulo, “Robust iris segmentation on uncalibrated noisy images using mathematical morphology,” Image Vis. Comput. 28(2), 278–284 (2010).
[Crossref]

S. Zhang, D. Van Der Weide, and J. Oliver, “Superfast phase-shifting method for 3-D shape measurement,” Opt. Express 18(9), 9684–9689 (2010).
[Crossref] [PubMed]

S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
[Crossref]

2008 (1)

M. J. Milford and G. F. Wyeth, “Mapping a suburb with a single camera using a biologically inspired SLAM system,” IEEE Trans. Robot. 24(5), 1038–1053 (2008).
[Crossref]

2007 (3)

L. W. Tsai, J. W. Hsieh, and K. C. Fan, “Vehicle detection using normalized color and edge map,” IEEE Trans. Image Process. 16(3), 850–864 (2007).
[Crossref] [PubMed]

Z. Hu, C. Marshall, R. Bicker, and P. Taylor, “Automatic surface roughing with 3D machine vision and cooperative robot control,” Robot. Auton. Syst. 55(7), 552–560 (2007).
[Crossref]

G. A. Al-Kindi and B. Shirinzadeh, “An evaluation of surface roughness parameters measurement using vision-based data,” Int. J. Mach. Tools Manuf. 47(3), 697–708 (2007).
[Crossref]

2006 (2)

K. Zhang, B. Xu, L. Tang, and H. Shi, “Modeling of binocular vision system for 3D reconstruction with improved genetic algorithms,” Int. J. Adv. Manuf. Technol. 29(7–8), 722–728 (2006).
[Crossref]

S. Zhang and S. T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14(7), 2644–2649 (2006).
[Crossref] [PubMed]

2005 (2)

J. van de Weijer, T. Gevers, and J. M. Geusebroek, “Edge and corner detection by photometric quasi-invariants,” IEEE Trans. Pattern Anal. 27(4), 625–630 (2005).
[Crossref]

F. Q. Zhou and G. J. Zhang, “Complete calibration of a structured light stripe vision sensor through planar target of unknown orientations,” Image Vis. Comput. 23(1), 59–67 (2005).
[Crossref]

2004 (1)

R. Legarda-Saenz, T. Bothe, and W. P. Ju, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

2002 (1)

G. J. Zhang and Z. Z. Wei, “A novel calibration approach to structured light 3D vision inspection,” Opt. Laser Technol. 34(5), 373–380 (2002).
[Crossref]

1998 (2)

C. Steger, “An unbiased detector of curvilinear structures”, IEEE Trans. Pattern Anal. 20(2), 113–125 (1998).
[Crossref]

C. Alard and R. H. Lupton, “A method for optimal image subtraction,” Astrophys. J. 503(1), 325–331 (1998).
[Crossref]

1996 (1)

D. Geman and B. Jedynak, “An active testing model for tracking roads in satellite images,” IEEE Trans. Pattern Anal. 18(1), 1–14 (1996).
[Crossref]

1994 (1)

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

1991 (1)

D. Ziou, “Line detection using an optimal IIR filter,” Pattern Recognit. 24(6), 465–478 (1991).
[Crossref]

1990 (1)

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. 12(7), 629–639 (1990).
[Crossref]

1989 (1)

S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, “Detection of blood vessels in retinal images using two-dimensional matched filters,” IEEE Trans. Med. Imaging 8(3), 263–269 (1989).
[Crossref] [PubMed]

1986 (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986).
[Crossref] [PubMed]

1981 (1)

M. A. Fischler, J. M. Tenenbaum, and H. C. Wolf, “Detection of roads and linear structures in low-resolution aerial imagery using a multisource knowledge integration technique,” Comput. Graph. Image Process. 15(3), 201–223 (1981).
[Crossref]

Abdel-Aziz, Y. I.

Y. I. Abdel-Aziz and H. M. Karara, “Direct linear transformation into object space coordinates in close-range photogrammetry,” in Proceedings of the Symposium on Close-Range Photogrammetry (Falls Church, VA, USA, 1971), pp. 1–18.

Alard, C.

C. Alard and R. H. Lupton, “A method for optimal image subtraction,” Astrophys. J. 503(1), 325–331 (1998).
[Crossref]

Al-Kindi, G. A.

G. A. Al-Kindi and B. Shirinzadeh, “An evaluation of surface roughness parameters measurement using vision-based data,” Int. J. Mach. Tools Manuf. 47(3), 697–708 (2007).
[Crossref]

Angulo, J.

M. A. Luengo-Oroz, E. Faure, and J. Angulo, “Robust iris segmentation on uncalibrated noisy images using mathematical morphology,” Image Vis. Comput. 28(2), 278–284 (2010).
[Crossref]

Bicker, R.

Z. Hu, C. Marshall, R. Bicker, and P. Taylor, “Automatic surface roughing with 3D machine vision and cooperative robot control,” Robot. Auton. Syst. 55(7), 552–560 (2007).
[Crossref]

Bothe, T.

R. Legarda-Saenz, T. Bothe, and W. P. Ju, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

Breque, C.

I. Leandry, C. Breque, and V. Valle, “Calibration of a structured-light projection system: development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
[Crossref]

Canny, J.

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell. 8(6), 679–698 (1986).
[Crossref] [PubMed]

Chatterjee, S.

S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, “Detection of blood vessels in retinal images using two-dimensional matched filters,” IEEE Trans. Med. Imaging 8(3), 263–269 (1989).
[Crossref] [PubMed]

Chaudhuri, S.

S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, “Detection of blood vessels in retinal images using two-dimensional matched filters,” IEEE Trans. Med. Imaging 8(3), 263–269 (1989).
[Crossref] [PubMed]

Clarke, T. A.

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Dettwiler, D.

T. M. Koller, G. Gerig, G. Szekely, and D. Dettwiler, “Multiscale detection of curvilinear structures in 2-D and 3-D image data,” in Proceedings of the Fifth International Conference on Computer Vision (Boston, MA., Jun. 1995), pp. 864–869.
[Crossref]

Fan, K. C.

L. W. Tsai, J. W. Hsieh, and K. C. Fan, “Vehicle detection using normalized color and edge map,” IEEE Trans. Image Process. 16(3), 850–864 (2007).
[Crossref] [PubMed]

Faure, E.

M. A. Luengo-Oroz, E. Faure, and J. Angulo, “Robust iris segmentation on uncalibrated noisy images using mathematical morphology,” Image Vis. Comput. 28(2), 278–284 (2010).
[Crossref]

Felberer, F.

Fischler, M. A.

M. A. Fischler, J. M. Tenenbaum, and H. C. Wolf, “Detection of roads and linear structures in low-resolution aerial imagery using a multisource knowledge integration technique,” Comput. Graph. Image Process. 15(3), 201–223 (1981).
[Crossref]

Geman, D.

D. Geman and B. Jedynak, “An active testing model for tracking roads in satellite images,” IEEE Trans. Pattern Anal. 18(1), 1–14 (1996).
[Crossref]

Geng, L. X.

G. Xu, X. T. Li, J. Su, H. D. Pan, and L. X. Geng, “Integrative evaluation of the optimal configuration for the measurement of the line segments using stereo vision,” Optik (Stuttg.) 124(11), 1015–1018 (2013).
[Crossref]

Gerig, G.

T. M. Koller, G. Gerig, G. Szekely, and D. Dettwiler, “Multiscale detection of curvilinear structures in 2-D and 3-D image data,” in Proceedings of the Fifth International Conference on Computer Vision (Boston, MA., Jun. 1995), pp. 864–869.
[Crossref]

Geusebroek, J. M.

J. van de Weijer, T. Gevers, and J. M. Geusebroek, “Edge and corner detection by photometric quasi-invariants,” IEEE Trans. Pattern Anal. 27(4), 625–630 (2005).
[Crossref]

Gevers, T.

J. van de Weijer, T. Gevers, and J. M. Geusebroek, “Edge and corner detection by photometric quasi-invariants,” IEEE Trans. Pattern Anal. 27(4), 625–630 (2005).
[Crossref]

Goldbaum, M.

S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, “Detection of blood vessels in retinal images using two-dimensional matched filters,” IEEE Trans. Med. Imaging 8(3), 263–269 (1989).
[Crossref] [PubMed]

Gong, G. H.

J. Yan, G. H. Gong, and C. Tian, “Hue-based feature detection for geometry calibration of multiprojector arrays,” Opt. Eng. 53(6), 063108 (2014).
[Crossref]

Hao, Z. B.

Hitzenberger, C. K.

Hsieh, J. W.

L. W. Tsai, J. W. Hsieh, and K. C. Fan, “Vehicle detection using normalized color and edge map,” IEEE Trans. Image Process. 16(3), 850–864 (2007).
[Crossref] [PubMed]

Hu, Z.

Z. Hu, C. Marshall, R. Bicker, and P. Taylor, “Automatic surface roughing with 3D machine vision and cooperative robot control,” Robot. Auton. Syst. 55(7), 552–560 (2007).
[Crossref]

Jedynak, B.

D. Geman and B. Jedynak, “An active testing model for tracking roads in satellite images,” IEEE Trans. Pattern Anal. 18(1), 1–14 (1996).
[Crossref]

Ju, W. P.

R. Legarda-Saenz, T. Bothe, and W. P. Ju, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

Karara, H. M.

Y. I. Abdel-Aziz and H. M. Karara, “Direct linear transformation into object space coordinates in close-range photogrammetry,” in Proceedings of the Symposium on Close-Range Photogrammetry (Falls Church, VA, USA, 1971), pp. 1–18.

Katz, N.

S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, “Detection of blood vessels in retinal images using two-dimensional matched filters,” IEEE Trans. Med. Imaging 8(3), 263–269 (1989).
[Crossref] [PubMed]

Koller, T. M.

T. M. Koller, G. Gerig, G. Szekely, and D. Dettwiler, “Multiscale detection of curvilinear structures in 2-D and 3-D image data,” in Proceedings of the Fifth International Conference on Computer Vision (Boston, MA., Jun. 1995), pp. 864–869.
[Crossref]

Kroisamer, J. S.

Laligant, O.

O. Laligant and F. Truchetet, “A nonlinear derivative scheme applied to edge detection,” IEEE Trans. Pattern Anal. 32(2), 242–257 (2010).
[Crossref]

Leandry, I.

I. Leandry, C. Breque, and V. Valle, “Calibration of a structured-light projection system: development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
[Crossref]

Legarda-Saenz, R.

R. Legarda-Saenz, T. Bothe, and W. P. Ju, “Accurate procedure for the calibration of a structured light system,” Opt. Eng. 43(2), 464–471 (2004).
[Crossref]

Lemaitre, C.

C. Lemaitre, M. Perdoch, A. Rahmoune, J. Matas, and J. Miteran, “Detection and matching of curvilinear structures,” Pattern Recognit. 44(7), 1514–1527 (2011).
[Crossref]

Li, X. T.

Lu, X.

Luengo-Oroz, M. A.

M. A. Luengo-Oroz, E. Faure, and J. Angulo, “Robust iris segmentation on uncalibrated noisy images using mathematical morphology,” Image Vis. Comput. 28(2), 278–284 (2010).
[Crossref]

Lupton, R. H.

C. Alard and R. H. Lupton, “A method for optimal image subtraction,” Astrophys. J. 503(1), 325–331 (1998).
[Crossref]

Malik, J.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. 12(7), 629–639 (1990).
[Crossref]

Marshall, C.

Z. Hu, C. Marshall, R. Bicker, and P. Taylor, “Automatic surface roughing with 3D machine vision and cooperative robot control,” Robot. Auton. Syst. 55(7), 552–560 (2007).
[Crossref]

Matas, J.

C. Lemaitre, M. Perdoch, A. Rahmoune, J. Matas, and J. Miteran, “Detection and matching of curvilinear structures,” Pattern Recognit. 44(7), 1514–1527 (2011).
[Crossref]

Milford, M. J.

M. J. Milford and G. F. Wyeth, “Mapping a suburb with a single camera using a biologically inspired SLAM system,” IEEE Trans. Robot. 24(5), 1038–1053 (2008).
[Crossref]

Miteran, J.

C. Lemaitre, M. Perdoch, A. Rahmoune, J. Matas, and J. Miteran, “Detection and matching of curvilinear structures,” Pattern Recognit. 44(7), 1514–1527 (2011).
[Crossref]

Nelson, M.

S. Chaudhuri, S. Chatterjee, N. Katz, M. Nelson, and M. Goldbaum, “Detection of blood vessels in retinal images using two-dimensional matched filters,” IEEE Trans. Med. Imaging 8(3), 263–269 (1989).
[Crossref] [PubMed]

Oliver, J.

Oliver, J. H.

Pan, H. D.

G. Xu, X. T. Li, J. Su, H. D. Pan, and L. X. Geng, “Integrative evaluation of the optimal configuration for the measurement of the line segments using stereo vision,” Optik (Stuttg.) 124(11), 1015–1018 (2013).
[Crossref]

G. Xu, X. T. Li, J. Su, H. D. Pan, and G. D. Tian, “Precision evaluation of three-dimensional feature points measurement by binocular vision,” J. Opt. Soc. Korea 15(1), 30–37 (2011).
[Crossref]

Perdoch, M.

C. Lemaitre, M. Perdoch, A. Rahmoune, J. Matas, and J. Miteran, “Detection and matching of curvilinear structures,” Pattern Recognit. 44(7), 1514–1527 (2011).
[Crossref]

Perona, P.

P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. 12(7), 629–639 (1990).
[Crossref]

Pircher, M.

Qi, L.

Rahmoune, A.

C. Lemaitre, M. Perdoch, A. Rahmoune, J. Matas, and J. Miteran, “Detection and matching of curvilinear structures,” Pattern Recognit. 44(7), 1514–1527 (2011).
[Crossref]

Shi, H.

K. Zhang, B. Xu, L. Tang, and H. Shi, “Modeling of binocular vision system for 3D reconstruction with improved genetic algorithms,” Int. J. Adv. Manuf. Technol. 29(7–8), 722–728 (2006).
[Crossref]

Shirinzadeh, B.

G. A. Al-Kindi and B. Shirinzadeh, “An evaluation of surface roughness parameters measurement using vision-based data,” Int. J. Mach. Tools Manuf. 47(3), 697–708 (2007).
[Crossref]

Short, T.

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Shortis, M. R.

M. R. Shortis, T. A. Clarke, and T. Short, “A comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[Crossref]

Steger, C.

C. Steger, “Unbiased extraction of lines with parabolic and Gaussian profiles,” Comput. Vis. Image Underst. 117(2), 97–112 (2013).

C. Steger, “An unbiased detector of curvilinear structures”, IEEE Trans. Pattern Anal. 20(2), 113–125 (1998).
[Crossref]

Su, J.

Sun, L. N.

Szekely, G.

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Z. Hu, C. Marshall, R. Bicker, and P. Taylor, “Automatic surface roughing with 3D machine vision and cooperative robot control,” Robot. Auton. Syst. 55(7), 552–560 (2007).
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J. van de Weijer, T. Gevers, and J. M. Geusebroek, “Edge and corner detection by photometric quasi-invariants,” IEEE Trans. Pattern Anal. 27(4), 625–630 (2005).
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G. J. Zhang and Z. Z. Wei, “A novel calibration approach to structured light 3D vision inspection,” Opt. Laser Technol. 34(5), 373–380 (2002).
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M. A. Fischler, J. M. Tenenbaum, and H. C. Wolf, “Detection of roads and linear structures in low-resolution aerial imagery using a multisource knowledge integration technique,” Comput. Graph. Image Process. 15(3), 201–223 (1981).
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F. Q. Zhou and G. J. Zhang, “Complete calibration of a structured light stripe vision sensor through planar target of unknown orientations,” Image Vis. Comput. 23(1), 59–67 (2005).
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K. Zhang, B. Xu, L. Tang, and H. Shi, “Modeling of binocular vision system for 3D reconstruction with improved genetic algorithms,” Int. J. Adv. Manuf. Technol. 29(7–8), 722–728 (2006).
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Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
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F. Q. Zhou and G. J. Zhang, “Complete calibration of a structured light stripe vision sensor through planar target of unknown orientations,” Image Vis. Comput. 23(1), 59–67 (2005).
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L. W. Tsai, J. W. Hsieh, and K. C. Fan, “Vehicle detection using normalized color and edge map,” IEEE Trans. Image Process. 16(3), 850–864 (2007).
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F. Q. Zhou and G. J. Zhang, “Complete calibration of a structured light stripe vision sensor through planar target of unknown orientations,” Image Vis. Comput. 23(1), 59–67 (2005).
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K. Zhang, B. Xu, L. Tang, and H. Shi, “Modeling of binocular vision system for 3D reconstruction with improved genetic algorithms,” Int. J. Adv. Manuf. Technol. 29(7–8), 722–728 (2006).
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J. Yan, G. H. Gong, and C. Tian, “Hue-based feature detection for geometry calibration of multiprojector arrays,” Opt. Eng. 53(6), 063108 (2014).
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Opt. Laser Technol. (1)

G. J. Zhang and Z. Z. Wei, “A novel calibration approach to structured light 3D vision inspection,” Opt. Laser Technol. 34(5), 373–380 (2002).
[Crossref]

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I. Leandry, C. Breque, and V. Valle, “Calibration of a structured-light projection system: development to large dimension objects,” Opt. Lasers Eng. 50(3), 373–379 (2012).
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Z. H. Zhang, “Review of single-shot 3D shape measurement by phase calculation-based fringe projection techniques,” Opt. Lasers Eng. 50(8), 1097–1106 (2012).
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S. Zhang, “Recent progresses on real-time 3D shape measurement using digital fringe projection techniques,” Opt. Lasers Eng. 48(2), 149–158 (2010).
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T. M. Koller, G. Gerig, G. Szekely, and D. Dettwiler, “Multiscale detection of curvilinear structures in 2-D and 3-D image data,” in Proceedings of the Fifth International Conference on Computer Vision (Boston, MA., Jun. 1995), pp. 864–869.
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Figures (7)

Fig. 1
Fig. 1 The normalization function h(λ1, λ2) for the eigenvalues λ1, λ2 of the Hessian matrix.
Fig. 2
Fig. 2 The calibration process of a laser plane using a height gauge and a 3D calibration board.
Fig. 3
Fig. 3 The 3D calibration points of a laser plane using a height gauge and a 3D calibration board.
Fig. 4
Fig. 4 The positive process of the translation and rotations from the original reconstructed 3D points to the 2D points in the horizontal plane. T is the translation vector, α is the first rotation angle to x axis, β is the second rotation angle to y axis.
Fig. 5
Fig. 5 The inverse process of the translation and rotations from the fitting curve in the horizontal plane to the fitting curve in the original laser plane. -β is the first rotation angle to y axis, -α is the second rotation angle to x axis, -T is the translation vector.
Fig. 6
Fig. 6 Experimental results of the first laser curve on the car model. (a) Original image, (b) Laser curve, (c) Centers extracted by the Hessian method with the thresholds of λ1 = 1 and λ2 = −2, (d) Enlarged view of Fig. 6(c), (e) Centers extracted by the sigmoid-Gaussian method, (f) Enlarged view of Fig. 6(e), (g) Forward transformation process from the 3D reconstructed centers to the 2D points in the xoy plane, (h) Inverse transformation process from the 2D curve in the xoy plane to the 3D curve in the original position.
Fig. 7
Fig. 7 Experimental results of the second laser curve on the car model. (a) Original image, (b) Laser curve, (c) Centers extracted by the Hessian method with the thresholds of λ1 = 1 and λ2 = −2, (d) Enlarged view of Fig. 6(c), (e) Centers extracted by the sigmoid-Gaussian method, (f) Enlarged view of Fig. 6(e), (g) Forward transformation process from the 3D reconstructed centers to the 2D points in the xoy plane, (h) Inverse transformation process from the 2D curve in the xoy plane to the 3D curve in the original position.

Equations (24)

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H ( x , y ) = [ I x x ( x , y ) I x y ( x , y ) I x y ( x , y ) I y y ( x , y ) ]
h 1 ( λ 1 ) = exp ( - λ 1 2 / c )
h 2 ( λ 2 ) = 1 1 + exp [ - b ( | λ 2 | a / 2 ) ]
h ( λ 1 , λ 2 ) = exp ( - λ 1 2 / c ) 1 + exp [ - b ( | λ 2 | a / 2 ) ]
a = max [ | λ 2 ( I l ( x , y ) ) | ]
I ( x + t n x , y + t n y ) = I ( x , y ) + t n x I x ( x , y ) + t n y I y ( x , y ) + 1 / 2 ( t 2 n x 2 I x x ( x , y ) + 2 t 2 n x n y I x y ( x , y ) + t 2 n y 2 I y y ( x , y ) )
t = - n x I x ( x , y ) + n y I y ( x , y ) n x 2 I x x ( x , y ) + 2 n x n y I x y ( x , y ) + n y 2 I y y ( x , y )
s i [ x i y i 1 ] = [ m 11 m 12 m 13 m 14 m 21 m 22 m 23 m 24 m 31 m 32 m 33 m 34 ] [ X i Y i Z i 1 ]
a X + b Y + c Z + d = 0
( X ( T ) Y ( T ) Z ( T ) ) = ( X Y Z ) + T
( X ( α , T ) Y ( α , T ) Z ( α , T ) ) = R x ( α ) ( X ( T ) Y ( T ) Z ( T ) )
α = a r c tan ( t y / t z )
( t x ( α ) t y ( α ) t z ( α ) ) = R x ( α ) ( t x t y t z )
( X ( α , β , T ) Y ( α , β , T ) Z ( α , β , T ) ) = R y ( β ) ( X ( α , T ) Y ( α , T ) Z ( α , T ) )
β = a r c tan ( - t y ( α ) / t z ( α ) )
{ x = x y = f ( x ) z = 0
{ x = f 1 ( y ) y = y z = 0
[ X Y Z ] = [ cos β x t x cos α f ( x ) + sin α sin β x t y - sin α f ( x ) + cos α sin β x t z ]
[ X Y Z ] = [ cos β f 1 ( y ) t x cos α y + sin α sin β f 1 ( y ) t y - sin α y + cos α sin β f 1 ( y ) t z ]
Z = 0.0167 X + 0 . 3 6 1 7 Y + 2 3 1 . 6 0 6 7
{ x = 0.0012 y 2 + 0.4597 y + 127.751 y = y z = 0
{ x = 0.0012 y 2 + 0.4597 y + 127.751 y = y z = 0
{ X = - 0.0012 y 2 + 0.4596 y + 124.3226 Y = 6.3022 × 10 - 6 y 2 + 0.9379 y - 74.7379 Z = - 1.7426 × 10 - 5 y 2 + 0.3469 y + 206.6485
{ X = - 0.0012 y 2 + 0.4596 y + 124.3226 Y = 6.3022 × 10 - 6 y 2 + 0.9379 y - 74.7379 Z = - 1.7426 × 10 - 5 y 2 + 0.3469 y + 206.6485

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