Abstract

The calibration of computer vision systems that contain the camera and the projector usually utilizes markers of the well-designed patterns to calculate the system parameters. Undesirably, the noise and radial distortion exist universally, which decreases the calibration accuracy and consequently decreases the measurement accuracy of the related technology. In this paper, a method is proposed to remove the noise and radial distortion by registering the captured pattern with an ideal pattern. After the optimal modeled pattern is obtained by registration, the degree of freedom of the total calibration markers is reduced to one and both the noise and radial distortion are removed successfully. The accuracy improvement in a structured light scanning system is over 1024 order of magnitude in the sense of mean square errors. Most importantly, the proposed method can be readily adopted by the computer vision techniques that use projectors or cameras.

© 2015 Optical Society of America

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References

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  1. A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express 18(8), 8338–8352 (2010).
    [Crossref] [PubMed]
  2. S. Moon, S. W. Lee, and Z. Chen, “Reference spectrum extraction and fixed-pattern noise removal in optical coherence tomography,” Opt. Express 18(24), 24395–24404 (2010).
    [Crossref] [PubMed]
  3. F. Pan, W. Xiao, S. Liu, F. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19(5), 3862–3869 (2011).
    [Crossref] [PubMed]
  4. C. T. Lin, C. C. Wei, and M. I. Chao, “Phase noise suppression of optical OFDM signals in 60-GHz RoF transmission system,” Opt. Express 19(11), 10423–10428 (2011).
    [Crossref] [PubMed]
  5. N. Brauckmann, M. Kues, P. Gross, and C. Fallnich, “Noise reduction of supercontinua via optical feedback,” Opt. Express 19(16), 14763–14778 (2011).
    [Crossref] [PubMed]
  6. M. Szkulmowski, I. Gorczynska, D. Szlag, M. Sylwestrzak, A. Kowalczyk, and M. Wojtkowski, “Efficient reduction of speckle noise in optical coherence tomography,” Opt. Express 20(2), 1337–1359 (2012).
    [Crossref] [PubMed]
  7. Y. Wang, P. Meng, D. Wang, L. Rong, and S. Panezai, “Speckle noise suppression in digital holography by angular diversity with phase-only spatial light modulator,” Opt. Express 21(17), 19568–19578 (2013).
    [Crossref] [PubMed]
  8. S. M. Jung, S. M. Yang, K. H. Mun, and S. K. Han, “Optical beat interference noise reduction by using out-of-band RF clipping tone signal in remotely fed OFDMA-PON link,” Opt. Express 22(15), 18246–18253 (2014).
    [Crossref] [PubMed]
  9. J. F. Barrera, A. Vélez, and R. Torroba, “Experimental scrambling and noise reduction applied to the optical encryption of QR codes,” Opt. Express 22(17), 20268–20277 (2014).
    [Crossref] [PubMed]
  10. P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. A. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22(21), 25768–25775 (2014).
    [Crossref] [PubMed]
  11. Z. Wang, “A one-shot-projection method for measurement of specular surfaces,” Opt. Express 23(3), 1912–1929 (2015).
    [Crossref] [PubMed]
  12. Z. Z. Wang, X. Y. Huang, R. G. Yang, and Y. M. Zhang, “Measurement of mirror surfaces using specular reflection and analytical computation,” Mach Vision Appl. 24(2), 289–304 (2013).
    [Crossref]
  13. Z. Z. Wang, “Robust measurement of the diffuse surface by phase shift profilometry,” J. Opt. 16(10), 105407 (2014).
    [Crossref]
  14. K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
    [Crossref] [PubMed]
  15. C. Guan, L. G. Hassebrook, D. L. Lau, and V. G. Yalla, “Improved composite-pattern structured light profilometry by means of postprocessing,” Opt. Eng. 47(9), 097203 (2008).
  16. C. Je, S. W. Lee, and R. H. Park, “Colour-stripe permutation pattern for rapid structured-light range imaging,” Opt. Commun. 285(9), 2320–2331 (2012).
    [Crossref]
  17. C. Je, K. H. Lee, and S. W. Lee, “Multi-projector color structured-light vision,” Signal Process. Image Commun. 28(9), 1046–1058 (2013).
    [Crossref]
  18. L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express 19(13), 12809–12814 (2011).
    [Crossref] [PubMed]
  19. W. Jang, C. Je, Y. Seo, and S. W. Lee, “Stuctured-light stereo: Comparative analysis and integration of structured-light and active stereo for measuring dynamic shape,” Opt. Lasers Eng. 51(11), 1255–1264 (2013).
    [Crossref]
  20. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. on PAMI 22(11), 1330–1334 (2000).
    [Crossref]
  21. Z. Z. Wang, “Monitoring of GMAW weld pool from the reflected laser lines for real time control,” IEEE Trans, on Ind, Inform 10(4), 2073–2083 (2014).
  22. D. C. Brown, “Decentering distortion of lenses,” Photogramm. Eng. 32(3), 444–462 (1966).
  23. R. Cucchiara, C. Grana, A. Pratzi, and R. Vezzani, “A hough transform-based method for radial lens distortion correction,” ICIAP 1, 182–187 (2003).
  24. J. P. Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” Proc. SPIE 7266, 726611 (2008).
    [Crossref]
  25. A. K. Geetha and S. Murali, “Automatic rectification of perspective distortion from a single image using plane homography,” IJCSA 3(5), 47–58 (2013).
    [Crossref]

2015 (1)

2014 (5)

2013 (5)

C. Je, K. H. Lee, and S. W. Lee, “Multi-projector color structured-light vision,” Signal Process. Image Commun. 28(9), 1046–1058 (2013).
[Crossref]

W. Jang, C. Je, Y. Seo, and S. W. Lee, “Stuctured-light stereo: Comparative analysis and integration of structured-light and active stereo for measuring dynamic shape,” Opt. Lasers Eng. 51(11), 1255–1264 (2013).
[Crossref]

A. K. Geetha and S. Murali, “Automatic rectification of perspective distortion from a single image using plane homography,” IJCSA 3(5), 47–58 (2013).
[Crossref]

Z. Z. Wang, X. Y. Huang, R. G. Yang, and Y. M. Zhang, “Measurement of mirror surfaces using specular reflection and analytical computation,” Mach Vision Appl. 24(2), 289–304 (2013).
[Crossref]

Y. Wang, P. Meng, D. Wang, L. Rong, and S. Panezai, “Speckle noise suppression in digital holography by angular diversity with phase-only spatial light modulator,” Opt. Express 21(17), 19568–19578 (2013).
[Crossref] [PubMed]

2012 (2)

M. Szkulmowski, I. Gorczynska, D. Szlag, M. Sylwestrzak, A. Kowalczyk, and M. Wojtkowski, “Efficient reduction of speckle noise in optical coherence tomography,” Opt. Express 20(2), 1337–1359 (2012).
[Crossref] [PubMed]

C. Je, S. W. Lee, and R. H. Park, “Colour-stripe permutation pattern for rapid structured-light range imaging,” Opt. Commun. 285(9), 2320–2331 (2012).
[Crossref]

2011 (4)

2010 (3)

2008 (2)

C. Guan, L. G. Hassebrook, D. L. Lau, and V. G. Yalla, “Improved composite-pattern structured light profilometry by means of postprocessing,” Opt. Eng. 47(9), 097203 (2008).

J. P. Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” Proc. SPIE 7266, 726611 (2008).
[Crossref]

2003 (1)

R. Cucchiara, C. Grana, A. Pratzi, and R. Vezzani, “A hough transform-based method for radial lens distortion correction,” ICIAP 1, 182–187 (2003).

2000 (1)

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

1966 (1)

D. C. Brown, “Decentering distortion of lenses,” Photogramm. Eng. 32(3), 444–462 (1966).

Asundi, A. K.

Barrera, J. F.

Bianco, V.

Bizheva, K.

Brauckmann, N.

Brown, D. C.

D. C. Brown, “Decentering distortion of lenses,” Photogramm. Eng. 32(3), 444–462 (1966).

Chao, M. I.

Chen, Z.

Clausi, D. A.

Cucchiara, R.

R. Cucchiara, C. Grana, A. Pratzi, and R. Vezzani, “A hough transform-based method for radial lens distortion correction,” ICIAP 1, 182–187 (2003).

Fallnich, C.

Ferraro, P.

Geetha, A. K.

A. K. Geetha and S. Murali, “Automatic rectification of perspective distortion from a single image using plane homography,” IJCSA 3(5), 47–58 (2013).
[Crossref]

Geldenhuys, R.

J. P. Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” Proc. SPIE 7266, 726611 (2008).
[Crossref]

Gorczynska, I.

Grana, C.

R. Cucchiara, C. Grana, A. Pratzi, and R. Vezzani, “A hough transform-based method for radial lens distortion correction,” ICIAP 1, 182–187 (2003).

Gross, P.

Guan, C.

C. Guan, L. G. Hassebrook, D. L. Lau, and V. G. Yalla, “Improved composite-pattern structured light profilometry by means of postprocessing,” Opt. Eng. 47(9), 097203 (2008).

Han, S. K.

Hao, Q.

Hassebrook, L. G.

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref] [PubMed]

C. Guan, L. G. Hassebrook, D. L. Lau, and V. G. Yalla, “Improved composite-pattern structured light profilometry by means of postprocessing,” Opt. Eng. 47(9), 097203 (2008).

Huang, L.

Huang, X. Y.

Z. Z. Wang, X. Y. Huang, R. G. Yang, and Y. M. Zhang, “Measurement of mirror surfaces using specular reflection and analytical computation,” Mach Vision Appl. 24(2), 289–304 (2013).
[Crossref]

Jang, W.

W. Jang, C. Je, Y. Seo, and S. W. Lee, “Stuctured-light stereo: Comparative analysis and integration of structured-light and active stereo for measuring dynamic shape,” Opt. Lasers Eng. 51(11), 1255–1264 (2013).
[Crossref]

Javidi, B.

Je, C.

W. Jang, C. Je, Y. Seo, and S. W. Lee, “Stuctured-light stereo: Comparative analysis and integration of structured-light and active stereo for measuring dynamic shape,” Opt. Lasers Eng. 51(11), 1255–1264 (2013).
[Crossref]

C. Je, K. H. Lee, and S. W. Lee, “Multi-projector color structured-light vision,” Signal Process. Image Commun. 28(9), 1046–1058 (2013).
[Crossref]

C. Je, S. W. Lee, and R. H. Park, “Colour-stripe permutation pattern for rapid structured-light range imaging,” Opt. Commun. 285(9), 2320–2331 (2012).
[Crossref]

Jung, S. M.

Kowalczyk, A.

Kues, M.

Lau, D. L.

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref] [PubMed]

C. Guan, L. G. Hassebrook, D. L. Lau, and V. G. Yalla, “Improved composite-pattern structured light profilometry by means of postprocessing,” Opt. Eng. 47(9), 097203 (2008).

Lee, K. H.

C. Je, K. H. Lee, and S. W. Lee, “Multi-projector color structured-light vision,” Signal Process. Image Commun. 28(9), 1046–1058 (2013).
[Crossref]

Lee, S. W.

C. Je, K. H. Lee, and S. W. Lee, “Multi-projector color structured-light vision,” Signal Process. Image Commun. 28(9), 1046–1058 (2013).
[Crossref]

W. Jang, C. Je, Y. Seo, and S. W. Lee, “Stuctured-light stereo: Comparative analysis and integration of structured-light and active stereo for measuring dynamic shape,” Opt. Lasers Eng. 51(11), 1255–1264 (2013).
[Crossref]

C. Je, S. W. Lee, and R. H. Park, “Colour-stripe permutation pattern for rapid structured-light range imaging,” Opt. Commun. 285(9), 2320–2331 (2012).
[Crossref]

S. Moon, S. W. Lee, and Z. Chen, “Reference spectrum extraction and fixed-pattern noise removal in optical coherence tomography,” Opt. Express 18(24), 24395–24404 (2010).
[Crossref] [PubMed]

Leuschner, F. W.

J. P. Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” Proc. SPIE 7266, 726611 (2008).
[Crossref]

Li, R.

Lin, C. T.

Liu, K.

Liu, S.

Memmolo, P.

Meng, P.

Mishra, A.

Moon, S.

Mun, K. H.

Murali, S.

A. K. Geetha and S. Murali, “Automatic rectification of perspective distortion from a single image using plane homography,” IJCSA 3(5), 47–58 (2013).
[Crossref]

Netti, P. A.

Ng, C. S.

Pan, F.

Panezai, S.

Park, R. H.

C. Je, S. W. Lee, and R. H. Park, “Colour-stripe permutation pattern for rapid structured-light range imaging,” Opt. Commun. 285(9), 2320–2331 (2012).
[Crossref]

Paturzo, M.

Pratzi, A.

R. Cucchiara, C. Grana, A. Pratzi, and R. Vezzani, “A hough transform-based method for radial lens distortion correction,” ICIAP 1, 182–187 (2003).

Rong, L.

Seo, Y.

W. Jang, C. Je, Y. Seo, and S. W. Lee, “Stuctured-light stereo: Comparative analysis and integration of structured-light and active stereo for measuring dynamic shape,” Opt. Lasers Eng. 51(11), 1255–1264 (2013).
[Crossref]

Sylwestrzak, M.

Szkulmowski, M.

Szlag, D.

Torroba, R.

Vélez, A.

Vezzani, R.

R. Cucchiara, C. Grana, A. Pratzi, and R. Vezzani, “A hough transform-based method for radial lens distortion correction,” ICIAP 1, 182–187 (2003).

Villiers, J. P.

J. P. Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” Proc. SPIE 7266, 726611 (2008).
[Crossref]

Wang, D.

Wang, F.

Wang, Y.

Wang, Z.

Wang, Z. Z.

Z. Z. Wang, “Monitoring of GMAW weld pool from the reflected laser lines for real time control,” IEEE Trans, on Ind, Inform 10(4), 2073–2083 (2014).

Z. Z. Wang, “Robust measurement of the diffuse surface by phase shift profilometry,” J. Opt. 16(10), 105407 (2014).
[Crossref]

Z. Z. Wang, X. Y. Huang, R. G. Yang, and Y. M. Zhang, “Measurement of mirror surfaces using specular reflection and analytical computation,” Mach Vision Appl. 24(2), 289–304 (2013).
[Crossref]

Wei, C. C.

Wojtkowski, M.

Wong, A.

Xiao, W.

Yalla, V. G.

C. Guan, L. G. Hassebrook, D. L. Lau, and V. G. Yalla, “Improved composite-pattern structured light profilometry by means of postprocessing,” Opt. Eng. 47(9), 097203 (2008).

Yang, R. G.

Z. Z. Wang, X. Y. Huang, R. G. Yang, and Y. M. Zhang, “Measurement of mirror surfaces using specular reflection and analytical computation,” Mach Vision Appl. 24(2), 289–304 (2013).
[Crossref]

Yang, S. M.

Zhang, Y. M.

Z. Z. Wang, X. Y. Huang, R. G. Yang, and Y. M. Zhang, “Measurement of mirror surfaces using specular reflection and analytical computation,” Mach Vision Appl. 24(2), 289–304 (2013).
[Crossref]

Zhang, Z. Y.

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

ICIAP (1)

R. Cucchiara, C. Grana, A. Pratzi, and R. Vezzani, “A hough transform-based method for radial lens distortion correction,” ICIAP 1, 182–187 (2003).

IEEE Trans, on Ind, Inform (1)

Z. Z. Wang, “Monitoring of GMAW weld pool from the reflected laser lines for real time control,” IEEE Trans, on Ind, Inform 10(4), 2073–2083 (2014).

IEEE Trans. on PAMI (1)

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

IJCSA (1)

A. K. Geetha and S. Murali, “Automatic rectification of perspective distortion from a single image using plane homography,” IJCSA 3(5), 47–58 (2013).
[Crossref]

J. Opt. (1)

Z. Z. Wang, “Robust measurement of the diffuse surface by phase shift profilometry,” J. Opt. 16(10), 105407 (2014).
[Crossref]

Mach Vision Appl. (1)

Z. Z. Wang, X. Y. Huang, R. G. Yang, and Y. M. Zhang, “Measurement of mirror surfaces using specular reflection and analytical computation,” Mach Vision Appl. 24(2), 289–304 (2013).
[Crossref]

Opt. Commun. (1)

C. Je, S. W. Lee, and R. H. Park, “Colour-stripe permutation pattern for rapid structured-light range imaging,” Opt. Commun. 285(9), 2320–2331 (2012).
[Crossref]

Opt. Eng. (1)

C. Guan, L. G. Hassebrook, D. L. Lau, and V. G. Yalla, “Improved composite-pattern structured light profilometry by means of postprocessing,” Opt. Eng. 47(9), 097203 (2008).

Opt. Express (13)

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-D shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref] [PubMed]

L. Huang, C. S. Ng, and A. K. Asundi, “Dynamic three-dimensional sensing for specular surface with monoscopic fringe reflectometry,” Opt. Express 19(13), 12809–12814 (2011).
[Crossref] [PubMed]

A. Wong, A. Mishra, K. Bizheva, and D. A. Clausi, “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express 18(8), 8338–8352 (2010).
[Crossref] [PubMed]

S. Moon, S. W. Lee, and Z. Chen, “Reference spectrum extraction and fixed-pattern noise removal in optical coherence tomography,” Opt. Express 18(24), 24395–24404 (2010).
[Crossref] [PubMed]

F. Pan, W. Xiao, S. Liu, F. Wang, L. Rong, and R. Li, “Coherent noise reduction in digital holographic phase contrast microscopy by slightly shifting object,” Opt. Express 19(5), 3862–3869 (2011).
[Crossref] [PubMed]

C. T. Lin, C. C. Wei, and M. I. Chao, “Phase noise suppression of optical OFDM signals in 60-GHz RoF transmission system,” Opt. Express 19(11), 10423–10428 (2011).
[Crossref] [PubMed]

N. Brauckmann, M. Kues, P. Gross, and C. Fallnich, “Noise reduction of supercontinua via optical feedback,” Opt. Express 19(16), 14763–14778 (2011).
[Crossref] [PubMed]

M. Szkulmowski, I. Gorczynska, D. Szlag, M. Sylwestrzak, A. Kowalczyk, and M. Wojtkowski, “Efficient reduction of speckle noise in optical coherence tomography,” Opt. Express 20(2), 1337–1359 (2012).
[Crossref] [PubMed]

Y. Wang, P. Meng, D. Wang, L. Rong, and S. Panezai, “Speckle noise suppression in digital holography by angular diversity with phase-only spatial light modulator,” Opt. Express 21(17), 19568–19578 (2013).
[Crossref] [PubMed]

S. M. Jung, S. M. Yang, K. H. Mun, and S. K. Han, “Optical beat interference noise reduction by using out-of-band RF clipping tone signal in remotely fed OFDMA-PON link,” Opt. Express 22(15), 18246–18253 (2014).
[Crossref] [PubMed]

J. F. Barrera, A. Vélez, and R. Torroba, “Experimental scrambling and noise reduction applied to the optical encryption of QR codes,” Opt. Express 22(17), 20268–20277 (2014).
[Crossref] [PubMed]

P. Memmolo, V. Bianco, M. Paturzo, B. Javidi, P. A. Netti, and P. Ferraro, “Encoding multiple holograms for speckle-noise reduction in optical display,” Opt. Express 22(21), 25768–25775 (2014).
[Crossref] [PubMed]

Z. Wang, “A one-shot-projection method for measurement of specular surfaces,” Opt. Express 23(3), 1912–1929 (2015).
[Crossref] [PubMed]

Opt. Lasers Eng. (1)

W. Jang, C. Je, Y. Seo, and S. W. Lee, “Stuctured-light stereo: Comparative analysis and integration of structured-light and active stereo for measuring dynamic shape,” Opt. Lasers Eng. 51(11), 1255–1264 (2013).
[Crossref]

Photogramm. Eng. (1)

D. C. Brown, “Decentering distortion of lenses,” Photogramm. Eng. 32(3), 444–462 (1966).

Proc. SPIE (1)

J. P. Villiers, F. W. Leuschner, and R. Geldenhuys, “Centi-pixel accurate real-time inverse distortion correction,” Proc. SPIE 7266, 726611 (2008).
[Crossref]

Signal Process. Image Commun. (1)

C. Je, K. H. Lee, and S. W. Lee, “Multi-projector color structured-light vision,” Signal Process. Image Commun. 28(9), 1046–1058 (2013).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 The developed structured light system.
Fig. 2
Fig. 2 Illustration of pattern and noise; (a) Designed pattern; (b) Captured pattern; (c) plot of the x coordinate differences in pixels; (d) plot of the y coordinate differences in pixels. (The y axis label is mm and x axis label is index number for (c) and (d)).
Fig. 3
Fig. 3 Results of modeling the pattern (Fig. 2(b)) by the proposed 3D pattern modeling method without center searching (a) Modeled and original x coordinates; (b) Modeled and original y coordinates; (c) x coordinate differences after modeling; (d) y coordinate differences after modeling; (The y axis label is pixel and x axis label is index number).
Fig. 4
Fig. 4 Results of modeling the pattern (Fig. 2(b)) with center searching by the proposed 3D pattern modeling method with center searching (a) Modeled xcoordinate versus original xcoordinate; (b) Modeled ycoordinate versus original y coordinate; (The y axis label is in mm and x axis label is index number).
Fig. 5
Fig. 5 Results of modeling the a set of corner points by the proposed 3D pattern modeling method without center searching (a) Captured calibration pattern with a set of detected corners; (b) Modeled points against the original points; (c) Modeledxcoordinates against originalxcoordinates; (d) Modeled y coordinates against originaly coordinates; (The y axis label is pixel and x axis label is index number for (c) and (d)).
Fig. 6
Fig. 6 Results of modeling the a set of corner points by the proposed 3D pattern modeling method with center searching (a) Modeled x coordinates against original x coordinates; (b) Modeled y coordinates against original y coordinates; (c)-(d) Modeled points against the original points; (The y axis label is pixel and x axis label is index number for (a) and(b)).
Fig. 7
Fig. 7 Results of modeling the another set of corner points by the proposed 3D pattern modeling method without center searching (a) Captured calibration pattern with a set of detected corners; (b) Modeled points against the original points; (c) Modeledx coordinates against original xcoordinates; (d) Modeled y coordinates against originaly coordinates; (The y axis label is pixel and x axis label is index number for (c) and (d)).
Fig. 8
Fig. 8 Results of modeling the another set of corner points by the proposed 3D pattern modeling method with center searching (a) Modeledxcoordinates against originalx coordinates; (b) Modeledy coordinates against original y coordinates; (c)-(d) Modeled points against the original points; (The y axis label is pixel and x axis label is index number for (a) and(b)).
Fig. 9
Fig. 9 Results of modeling the corner points by the proposed 2D pattern modeling method (a) Modeledxcoordinates against original xcoordinates; (b) Modeled ycoordinates against originalycoordinates; (c) Modeled points against the original points; (d) Modeled points overlaying on the original pattern (The y axis label is pixel and x axis label is index number for (a) and(b)).
Fig. 10
Fig. 10 Results of modeling the corner points by the proposed 3D pattern modeling method with center searching (a) Modeledxcoordinates against originalxcoordinates; (b) Modeledycoordinates against original ycoordinates; (c) Modeled points against the original points; (d) Modeled points overlaying on the original pattern (The y axis label is pixel and x axis label is index number for (a) and (b)).
Fig. 11
Fig. 11 Results of modeling the corner points on different captured camera calibration patterns by the proposed 3D pattern modeling method with center searching (a) Modeled points overlaying on the original pattern 1; (b) Modeled points overlaying on the original pattern 2; (c) Modeled points overlaying on the original pattern 3; (d) Modeled points overlaying on the original pattern 4.
Fig. 12
Fig. 12 Results of modeling the SNF laser points (a) Modeledx coordinates against originalxcoordinates; (b) Modeledycoordinates against original ycoordinates; (c) Modeled points against the original points; (d) Modeled points overlaying on the original laser pattern (The y axis label is pixel and x axis label is index number for (a) and (b)).

Tables (1)

Tables Icon

Table 1 Comparison of the proposed methods

Equations (40)

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x x c x i x c = y y c y i y c = z z c z i z c = t i   
d i m = ( x i m x 0 m ) 2 + ( y i m y 0 m ) 2 + ( z i m z 0 m ) 2    
d i p = ( x i p x 0 p ) 2 + ( y i p y 0 p ) 2 + ( z i p z 0 p ) 2  
d= d i =| d i m d i p |
P ¯ =arg min P d
[ x ¯ i p y ¯ i p z ¯ i p 1 ]=ω[ a 11 a 12 a 21 a 22 a 13 a 14 a 23 a 24 a 31 a 32 a 41 a 42 a 33 a 34 a 43 a 44 ][ x i m y i m z i m 1 ]
d r = i=1 44 ( x ¯ i p x i p ) 2 + ( y ¯ i p y i p ) 2 + ( z ¯ i p z i p ) 2  
A ¯ =arg min A d r
A=[ a 11 a 12 a 21 a 22 a 13 a 14 a 23 a 24 a 31 a 32 a 41 a 42 a 33 a 34 a 43 a 44 ]
[ ω x i 2 ω y i 2 ω ]=| h 11 h 12 h 13 h 21 h 22 h 23 h 31 h 32 h 33 |[ x i 1 y i 1 1 ]
z i 2 =( 1 a 2 x i 2 b 2 y i 2 )/ c 2
z i 2 =( H 31 x i 1 + H 32 y i 1 + H 33 )/ω
H 31 = a 2 h 11 b 2 h 21 c 2
H 32 = a 2 h 12 b 2 h 22 c 2
H 33 = ω a 2 h 13 b 2 h 23 c 2
 [ ω x i 2 ω y i 2 ω z i 2 ω ]=[ h 11 h 12 h 13 h 21 h 22 h 23 H 31 H 32 H 33 h 31 h 32 h 33 ][ x i 1 y i 1 1 ]
 [ x i 1 y i 1 1 ]= D 1 B T [ ω x i 2 ω y i 2 ω z i 2 ω ]= [ h 11 ' h 12 ' h 13 ' h 14 ' h 21 ' h 22 ' h 23 ' h 24 ' h 31 ' h 32 ' h 33 ' h 34 ' ] [ ω x i 2 ω y i 2 ω z i 2 ω ]
x i 1 = h 11 ' ω x i 2 + h 12 ' ω y i 2 + h 13 ' ω z i 2 + h 14 ' ω
y i 1 = h 21 ' ω x i 2 + h 22 ' ω y i 2 + h 23 ' ω z i 2 + h 24 ' ω
z i 1 =( 1 a 1 x i 1 b 1 y i 1 )/ c 1
z i 1 = H 31 ' ω x i 2 + H 32 ' ω y i 2 + H 33 ' ω z i 2 + H 34 ' ω
H 31 ' = h 11 ' a 1 c 1
H 32 ' = h 12 ' a 1 c 1
H 33 ' = h 13 ' a 1 c 1
H 34 ' = 1 ω c 1 h 14 ' a 1 c 1  
[ x i 1 y i 1 z i 1 1 ]=[ h 11 ' h 12 ' h 13 ' h 14 ' h 21 ' h 22 ' h 23 ' h 24 ' H 31 ' H 32 ' H 33 ' H 34 ' h 31 ' h 32 ' h 33 ' h 34 ' ][ ω x i 2 ω y i 2 ω z i 2 ω ]
A=[ h 11 ' h 12 ' h 13 ' h 14 ' h 21 ' h 22 ' h 23 ' h 24 ' H 31 ' H 32 ' H 33 ' H 34 ' h 31 ' h 32 ' h 33 ' h 34 ' ]
[ x i y i z i 1 ]= A 1  [ ω 1 x i 1 ω 1 y i 1 ω 1 z i 1 ω 1 ]
[ x i y i z i 1 ]= A 2  [ ω 2 x i 2 ω 2 y i 2 ω 2 z i 2 ω 2 ] 
 [ x i 1 y i 1 z i 1 1 ]= A 1 1 A 2 [ ω 2 x i 2 / ω 1 ω 2 y i 2 / ω 1 ω 2 z i 2 / ω 1 ω 2 / ω 1 ]
 A= A 1 1 A 2
  x e = 1 N i=1 N ( X m i X o i ) 2
  y e = 1 N i=1 N ( Y m i Y o i ) 2
d i m = ( x i m x 0 m ) 2 + ( y i m y 0 m ) 2    
d i p = ( x i p x 0 p ) 2 + ( y i p y 0 p ) 2  
[ x ¯ i p y ¯ i p 1 ]=ω[ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ][ x i m y i m 1 ]
d r = i=1 44 ( x ¯ i p x i p ) 2 + ( y ¯ i p y i p ) 2  
A ¯ =arg min A d r
A=[ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ]
[ E x E y E z ]=[ 1 N i=1 N ( X r i X o i ) 2 1 N i=1 N ( Y r i Y o i ) 2 1 N i=1 N ( Z r i Z o i ) 2 ] 

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