Abstract

Triangulation laser range scanning, which has been wildly used in various applications, can reconstruct the 3D geometric of the object with high precision by processing the image of laser stripe. The unbiased line extractor proposed by Steger is one of the most commonly used algorithms in laser stripe center extraction for its precision and robustness. Therefore, it is of great significance to assess the statistical performance of the Steger method when it is applied on laser stripe with Gaussian intensity profile. In this paper, a statistical behavior analysis for the laser stripe center extractor based on Steger method has been carried out. Relationships between center extraction precision, image quality and stripe characteristics have been examined analytically. Optimal scale of Gaussian smoothing kernel can be determined for each laser stripe image to achieve the highest precision according to the derived formula. Flexible three-step noise estimation procedure has been proposed to evaluate the center extraction precision of a typical triangulation laser scanning system by simply referring to the acquired images. The validity of our analysis has been verified by experiments on both artificial and natural images.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Cui and X. Zhu, “A generalized reference-plane-based calibration method in optical triangular profilometry,” Opt. Express17(23), 20735–20746 (2009).
    [CrossRef] [PubMed]
  2. Z. Zhang and L. Yuan, “Building a 3D scanner system based on monocular vision,” Appl. Opt.51(11), 1638–1644 (2012).
    [CrossRef] [PubMed]
  3. Y. Zhang, S. Wang, X. Zhang, F. Xie, and J. Wang, “Freight train gauge-exceeding detection based on three-dimensional stereo vision measurement,” Mach. Vis. Appl.24(3), 461–475 (2012).
  4. L. Marc, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J. Shade, and D. Fulk, “The digital Michelangelo project: 3D scanning of large statues,” in Proceedings of the 27th annual Conference on Computer Graphics and Interactive Techniques, ACM Press/Addison-Wesley Publishing Co., 131–144, (2000).
  5. C. Steger, “An unbiased detector of curvilinear structures,” IEEE Trans. Pattern Anal. Mach. Intell.20(2), 113–125 (1998).
    [CrossRef]
  6. C. Steger, “Unbiased Extraction of Curvilinear Structures from 2D and 3D Images,” Dissertation, Fakultät für Informatik, Technische Universität München, 1998.
  7. F. Zhou, G. Zhang, and J. Jiang, “Constructing feature points for calibrating a structured light vision sensor by viewing a plane from unknown orientations,” Opt. Lasers Eng.43(10), 1056–1070 (2005).
    [CrossRef]
  8. R. Yang, S. Cheng, W. Yang, and Y. Chen, “Robust and accurate surface measurement using structured light,” IEEE Trans. Instrum. Meas.57(6), 1275–1280 (2008).
    [CrossRef]
  9. R. D. Wedowski, G. A. Atkinson, M. L. Smith, and L. N. Smith, “A system for the dynamic industrial inspection of specular freeform surfaces,” Opt. Lasers Eng.50(5), 632–644 (2012).
    [CrossRef]
  10. C. Steger, “Unbiased extraction of lines with parabolic and Gaussian profiles,” Comput. Vis. Image Underst.117(2), 97–112 (2013).
  11. F. Bouchara and S. Ramdani, “Statistical behavior of edge detectors,” Signal Image Video Process.1(3), 273–285 (2007).
    [CrossRef]
  12. K. Astrom and A. Heyden, “Stochastic modeling and analysis of sub-pixel edge detection,” in Proceedings of the 13th International Conference on Pattern Recognition, (1996), 86–90.
    [CrossRef]
  13. C. Steger, “Analytical and empirical performance evaluation of sub-pixel line and edge detection,” in Empirical Evaluation Methods in Computer Vision, K.W. Bowyer and P. J. Phillips, ed. (IEEE Computer Society Press, 1998).
  14. R. B. Fisher and D. K. Naidu, “A comparison of algorithms for sub-pixel peak detection,” in Advances in Image Processing, Multimedia and Machine Vision, J. Sanz, ed. (Springer-Verlag, Heidelberg, 1996).
  15. J. Forest, J. Salvi, E. Cabruja, and C. Pous, “Laser stripe peak detector for 3D scanners. A FIR filter approach,” in Proceedings of the 17th International Conference on Pattern Recognition, (2004), 646–649.
    [CrossRef]
  16. T.-S. Chen, C.-C. Chang, and M.-S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process.7(10), 1485–1488 (1998).
    [CrossRef] [PubMed]
  17. J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process.12(11), 1338–1351 (2003).
    [CrossRef] [PubMed]

2013

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

2012

R. D. Wedowski, G. A. Atkinson, M. L. Smith, and L. N. Smith, “A system for the dynamic industrial inspection of specular freeform surfaces,” Opt. Lasers Eng.50(5), 632–644 (2012).
[CrossRef]

Y. Zhang, S. Wang, X. Zhang, F. Xie, and J. Wang, “Freight train gauge-exceeding detection based on three-dimensional stereo vision measurement,” Mach. Vis. Appl.24(3), 461–475 (2012).

Z. Zhang and L. Yuan, “Building a 3D scanner system based on monocular vision,” Appl. Opt.51(11), 1638–1644 (2012).
[CrossRef] [PubMed]

2009

2008

R. Yang, S. Cheng, W. Yang, and Y. Chen, “Robust and accurate surface measurement using structured light,” IEEE Trans. Instrum. Meas.57(6), 1275–1280 (2008).
[CrossRef]

2007

F. Bouchara and S. Ramdani, “Statistical behavior of edge detectors,” Signal Image Video Process.1(3), 273–285 (2007).
[CrossRef]

2005

F. Zhou, G. Zhang, and J. Jiang, “Constructing feature points for calibrating a structured light vision sensor by viewing a plane from unknown orientations,” Opt. Lasers Eng.43(10), 1056–1070 (2005).
[CrossRef]

2003

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process.12(11), 1338–1351 (2003).
[CrossRef] [PubMed]

1998

T.-S. Chen, C.-C. Chang, and M.-S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process.7(10), 1485–1488 (1998).
[CrossRef] [PubMed]

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

Astrom, K.

K. Astrom and A. Heyden, “Stochastic modeling and analysis of sub-pixel edge detection,” in Proceedings of the 13th International Conference on Pattern Recognition, (1996), 86–90.
[CrossRef]

Atkinson, G. A.

R. D. Wedowski, G. A. Atkinson, M. L. Smith, and L. N. Smith, “A system for the dynamic industrial inspection of specular freeform surfaces,” Opt. Lasers Eng.50(5), 632–644 (2012).
[CrossRef]

Bouchara, F.

F. Bouchara and S. Ramdani, “Statistical behavior of edge detectors,” Signal Image Video Process.1(3), 273–285 (2007).
[CrossRef]

Cabruja, E.

J. Forest, J. Salvi, E. Cabruja, and C. Pous, “Laser stripe peak detector for 3D scanners. A FIR filter approach,” in Proceedings of the 17th International Conference on Pattern Recognition, (2004), 646–649.
[CrossRef]

Chang, C.-C.

T.-S. Chen, C.-C. Chang, and M.-S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process.7(10), 1485–1488 (1998).
[CrossRef] [PubMed]

Chen, T.-S.

T.-S. Chen, C.-C. Chang, and M.-S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process.7(10), 1485–1488 (1998).
[CrossRef] [PubMed]

Chen, Y.

R. Yang, S. Cheng, W. Yang, and Y. Chen, “Robust and accurate surface measurement using structured light,” IEEE Trans. Instrum. Meas.57(6), 1275–1280 (2008).
[CrossRef]

Cheng, S.

R. Yang, S. Cheng, W. Yang, and Y. Chen, “Robust and accurate surface measurement using structured light,” IEEE Trans. Instrum. Meas.57(6), 1275–1280 (2008).
[CrossRef]

Cui, S.

Forest, J.

J. Forest, J. Salvi, E. Cabruja, and C. Pous, “Laser stripe peak detector for 3D scanners. A FIR filter approach,” in Proceedings of the 17th International Conference on Pattern Recognition, (2004), 646–649.
[CrossRef]

Heyden, A.

K. Astrom and A. Heyden, “Stochastic modeling and analysis of sub-pixel edge detection,” in Proceedings of the 13th International Conference on Pattern Recognition, (1996), 86–90.
[CrossRef]

Hwang, M.-S.

T.-S. Chen, C.-C. Chang, and M.-S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process.7(10), 1485–1488 (1998).
[CrossRef] [PubMed]

Jiang, J.

F. Zhou, G. Zhang, and J. Jiang, “Constructing feature points for calibrating a structured light vision sensor by viewing a plane from unknown orientations,” Opt. Lasers Eng.43(10), 1056–1070 (2005).
[CrossRef]

Portilla, J.

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process.12(11), 1338–1351 (2003).
[CrossRef] [PubMed]

Pous, C.

J. Forest, J. Salvi, E. Cabruja, and C. Pous, “Laser stripe peak detector for 3D scanners. A FIR filter approach,” in Proceedings of the 17th International Conference on Pattern Recognition, (2004), 646–649.
[CrossRef]

Ramdani, S.

F. Bouchara and S. Ramdani, “Statistical behavior of edge detectors,” Signal Image Video Process.1(3), 273–285 (2007).
[CrossRef]

Salvi, J.

J. Forest, J. Salvi, E. Cabruja, and C. Pous, “Laser stripe peak detector for 3D scanners. A FIR filter approach,” in Proceedings of the 17th International Conference on Pattern Recognition, (2004), 646–649.
[CrossRef]

Simoncelli, E. P.

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process.12(11), 1338–1351 (2003).
[CrossRef] [PubMed]

Smith, L. N.

R. D. Wedowski, G. A. Atkinson, M. L. Smith, and L. N. Smith, “A system for the dynamic industrial inspection of specular freeform surfaces,” Opt. Lasers Eng.50(5), 632–644 (2012).
[CrossRef]

Smith, M. L.

R. D. Wedowski, G. A. Atkinson, M. L. Smith, and L. N. Smith, “A system for the dynamic industrial inspection of specular freeform surfaces,” Opt. Lasers Eng.50(5), 632–644 (2012).
[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. Mach. Intell.20(2), 113–125 (1998).
[CrossRef]

Strela, V.

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process.12(11), 1338–1351 (2003).
[CrossRef] [PubMed]

Wainwright, M. J.

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process.12(11), 1338–1351 (2003).
[CrossRef] [PubMed]

Wang, J.

Y. Zhang, S. Wang, X. Zhang, F. Xie, and J. Wang, “Freight train gauge-exceeding detection based on three-dimensional stereo vision measurement,” Mach. Vis. Appl.24(3), 461–475 (2012).

Wang, S.

Y. Zhang, S. Wang, X. Zhang, F. Xie, and J. Wang, “Freight train gauge-exceeding detection based on three-dimensional stereo vision measurement,” Mach. Vis. Appl.24(3), 461–475 (2012).

Wedowski, R. D.

R. D. Wedowski, G. A. Atkinson, M. L. Smith, and L. N. Smith, “A system for the dynamic industrial inspection of specular freeform surfaces,” Opt. Lasers Eng.50(5), 632–644 (2012).
[CrossRef]

Xie, F.

Y. Zhang, S. Wang, X. Zhang, F. Xie, and J. Wang, “Freight train gauge-exceeding detection based on three-dimensional stereo vision measurement,” Mach. Vis. Appl.24(3), 461–475 (2012).

Yang, R.

R. Yang, S. Cheng, W. Yang, and Y. Chen, “Robust and accurate surface measurement using structured light,” IEEE Trans. Instrum. Meas.57(6), 1275–1280 (2008).
[CrossRef]

Yang, W.

R. Yang, S. Cheng, W. Yang, and Y. Chen, “Robust and accurate surface measurement using structured light,” IEEE Trans. Instrum. Meas.57(6), 1275–1280 (2008).
[CrossRef]

Yuan, L.

Zhang, G.

F. Zhou, G. Zhang, and J. Jiang, “Constructing feature points for calibrating a structured light vision sensor by viewing a plane from unknown orientations,” Opt. Lasers Eng.43(10), 1056–1070 (2005).
[CrossRef]

Zhang, X.

Y. Zhang, S. Wang, X. Zhang, F. Xie, and J. Wang, “Freight train gauge-exceeding detection based on three-dimensional stereo vision measurement,” Mach. Vis. Appl.24(3), 461–475 (2012).

Zhang, Y.

Y. Zhang, S. Wang, X. Zhang, F. Xie, and J. Wang, “Freight train gauge-exceeding detection based on three-dimensional stereo vision measurement,” Mach. Vis. Appl.24(3), 461–475 (2012).

Zhang, Z.

Zhou, F.

F. Zhou, G. Zhang, and J. Jiang, “Constructing feature points for calibrating a structured light vision sensor by viewing a plane from unknown orientations,” Opt. Lasers Eng.43(10), 1056–1070 (2005).
[CrossRef]

Zhu, X.

Appl. Opt.

Comput. Vis. Image Underst.

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

IEEE Trans. Image Process.

T.-S. Chen, C.-C. Chang, and M.-S. Hwang, “A virtual image cryptosystem based upon vector quantization,” IEEE Trans. Image Process.7(10), 1485–1488 (1998).
[CrossRef] [PubMed]

J. Portilla, V. Strela, M. J. Wainwright, and E. P. Simoncelli, “Image denoising using scale mixtures of Gaussians in the wavelet domain,” IEEE Trans. Image Process.12(11), 1338–1351 (2003).
[CrossRef] [PubMed]

IEEE Trans. Instrum. Meas.

R. Yang, S. Cheng, W. Yang, and Y. Chen, “Robust and accurate surface measurement using structured light,” IEEE Trans. Instrum. Meas.57(6), 1275–1280 (2008).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

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

Mach. Vis. Appl.

Y. Zhang, S. Wang, X. Zhang, F. Xie, and J. Wang, “Freight train gauge-exceeding detection based on three-dimensional stereo vision measurement,” Mach. Vis. Appl.24(3), 461–475 (2012).

Opt. Express

Opt. Lasers Eng.

F. Zhou, G. Zhang, and J. Jiang, “Constructing feature points for calibrating a structured light vision sensor by viewing a plane from unknown orientations,” Opt. Lasers Eng.43(10), 1056–1070 (2005).
[CrossRef]

R. D. Wedowski, G. A. Atkinson, M. L. Smith, and L. N. Smith, “A system for the dynamic industrial inspection of specular freeform surfaces,” Opt. Lasers Eng.50(5), 632–644 (2012).
[CrossRef]

Signal Image Video Process.

F. Bouchara and S. Ramdani, “Statistical behavior of edge detectors,” Signal Image Video Process.1(3), 273–285 (2007).
[CrossRef]

Other

K. Astrom and A. Heyden, “Stochastic modeling and analysis of sub-pixel edge detection,” in Proceedings of the 13th International Conference on Pattern Recognition, (1996), 86–90.
[CrossRef]

C. Steger, “Analytical and empirical performance evaluation of sub-pixel line and edge detection,” in Empirical Evaluation Methods in Computer Vision, K.W. Bowyer and P. J. Phillips, ed. (IEEE Computer Society Press, 1998).

R. B. Fisher and D. K. Naidu, “A comparison of algorithms for sub-pixel peak detection,” in Advances in Image Processing, Multimedia and Machine Vision, J. Sanz, ed. (Springer-Verlag, Heidelberg, 1996).

J. Forest, J. Salvi, E. Cabruja, and C. Pous, “Laser stripe peak detector for 3D scanners. A FIR filter approach,” in Proceedings of the 17th International Conference on Pattern Recognition, (2004), 646–649.
[CrossRef]

L. Marc, K. Pulli, B. Curless, S. Rusinkiewicz, D. Koller, L. Pereira, M. Ginzton, S. Anderson, J. Davis, J. Ginsberg, J. Shade, and D. Fulk, “The digital Michelangelo project: 3D scanning of large statues,” in Proceedings of the 27th annual Conference on Computer Graphics and Interactive Techniques, ACM Press/Addison-Wesley Publishing Co., 131–144, (2000).

C. Steger, “Unbiased Extraction of Curvilinear Structures from 2D and 3D Images,” Dissertation, Fakultät für Informatik, Technische Universität München, 1998.

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 (4)

Fig. 1
Fig. 1

Laser stripe profile model: (a) zero-order; (b) first-order; and (c) second-order.

Fig. 2
Fig. 2

Laser stripe line-width estimation and Gaussian curve fitting.

Fig. 3
Fig. 3

Synthetic image experiments: (a) synthetic image with Gaussian white noise; (b) center position distribution; (c) extracted and predicted variance with respect to different image SNR (A = 100, σw = 5).

Fig. 4
Fig. 4

Real experiments: (a) system setup; (b) estimated and real distribution of the extracted center positions.

Tables (1)

Tables Icon

Table 1 Comparison of estimated and actual precision in real image tests (CL = 99.9%)

Equations (8)

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

f w (x)=Aexp( x 2 2 σ w 2 )+h(x),
f(x,y)=i(x,y)+n(x,y).
N(μ, σ l )= 1 2π σ l exp[ (xμ) 2 2 σ l 2 ],
r x (x,y)= r f,x (x,y)+ r n,x (x,y)=0 ,
σ r n,x 2 = σ n 2 8π σ 4 ,
r w (x,σ,A, σ w )= f w (x) g σ (x)= f w (x) [ 1 2π σ exp( x 2 2 σ 2 )] = A σ w ( σ w 2 + σ 2 ) 1 2 ( x 2 ( σ w 2 + σ 2 ) 2 1 ( σ w 2 + σ 2 ) )exp( x 2 2( σ w 2 + σ 2 ) )
r f,xx ( 0,0 )= A σ w ( σ w 2 + σ 2 ) 3 2 ,
σ l 2 = σ r n,x 2 r f,xx (0,0) 2 = σ n 2 ( σ 2 + σ w 2 ) 3 8π A 2 σ 4 σ w 2 = ( σ 2 + σ w 2 ) 3 8π σ 4 σ w 2 1 SNR .

Metrics