Abstract

We present an effective method for reconstructing and measuring the three-dimensional (3D) structures of diamond crowns based on stereo vision. To reach high measurement accuracy, the influences of 3D measurement errors are analyzed in detail. Then, a method to accurately extract the linear features of diamond edges based on virtual motion control is described. Depending on the obtained linear features, the 3D structure of a diamond crown can be reconstructed with least squares error. The validity of the proposed method is verified by experiments. The results show that the proposed method can be used to measure the 3D structures of diamond crowns with satisfactory accuracy and efficiency, and it also can be used to extract linear features and measure other similar artificial objects that can be represented by line segments.

© 2009 Optical Society of America

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  1. D. G. Goebel, “Generalized integrating sphere theory,” Appl. Opt. 6, 125-128 (1967).
    [CrossRef] [PubMed]
  2. A. Ducharme, A. Daniels, E. Grann, and G. Boreman, “Design of an integrating sphere as a uniform illumination source,” IEEE Trans. Educ. 40, 131-134 (1997).
    [CrossRef]
  3. A. Wozniak and M. Dobosz, “Factors influencing probing accuracy of a coordinate measuring machine,” IEEE Trans. Instrum. Meas. 54, 2540-2548 (2005).
    [CrossRef]
  4. H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
    [CrossRef]
  5. S. Komatsu, H. Suhara, and H. Ohzu, “Laser scanning microscope with a differential heterodyne optical probe,” Appl. Opt. 29, 4244-4249 (1990).
    [CrossRef] [PubMed]
  6. Y. S. Chen and B. T. Chen, “Measuring of a three-dimensional surface by use of a spatial distance computation,” Appl. Opt. 42, 1958-1972 (2003).
    [CrossRef] [PubMed]
  7. Z. Y. Wang, H. Du, S. Park, and H. M. Xie, “Three-dimensional shape measurement with a fast and accurate approach,” Appl. Opt. 48, 1052-1061 (2009).
    [CrossRef]
  8. P. Graebling, A. Lallement, D. Y. Zhou, and E. Hirsch, “Optical high-precision three-dimensional vision-based quality control of manufactured parts by use of synthetic images and knowledge for image-data evaluation and interpretation,” Appl. Opt. 41, 2627-2643 (2002).
    [CrossRef] [PubMed]
  9. R. Anchini, C. Liguori, V. Paciello, and A. Paolillo, “A comparison between stereo-vision techniques for the reconstruction of 3-D coordinates of objects,” IEEE Trans. Instrum. Meas. 55, 1459-1466 (2006).
    [CrossRef]
  10. S. Malassiotis and M. G. Strintzis, “Stereo vision system for precision dimensional inspection of 3D holes,” Mach. Vis. Appl. 15, 101-113 (2003).
    [CrossRef]
  11. C. Y. Lin, “A new approach to automatic reconstruction of a 3-D world using active stereo vision,” Comput. Vision Image Understand. 85, 117-143 (2002).
    [CrossRef]
  12. C. C. Chang, S. Chatterjee, and P. R. Kube, “A quantization error analysis for convergent stereo,” in IEEE International Conference on Image Processing (IEEE, 1994), Vol. 2, pp. 735-739.
  13. W. S. Kim, A. I. Ansar, R. D. Steele, and R. C. Steinke, “Performance analysis and validation of a stereo vision system,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2005), Vol. 2, pp. 1409-1416.
    [CrossRef]
  14. J. Illingworth and J. Kittler, “A survey of the Hough transform,” Comput. Vision Graph. Image Process. , 44, 87-116(1988).
    [CrossRef]
  15. J. Prakash, M. B. Meenavathi, and K. Rajesh, “Linear feature extraction using combined approach of Hough transform, Eigen values and Raster scan algorithms,” in IEEE Intelligent Sensing and Information Processing (IEEE, 2006), pp. 65-70.
  16. R. O. Duda and P. E. Hart, “Use of the Hough transform to detect lines and curves in pictures,” Commun. ACM 15, 11-15 (1972).
    [CrossRef]
  17. I. Weiss, “Line fitting in a noisy image,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 325-329 (1989).
    [CrossRef]
  18. H. Qjidaa and L. Radouane, “Robust line fitting in a noisy image by the method of moments,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1216-1223 (1999).
    [CrossRef]
  19. Y. J. Zhang, Z. X. Zhang, and J. Q. Zhang, “Automatic measurement of industrial sheetmetal parts with CAD data and non-metric image sequence,” Comput. Vision Image Understand. 102, 52-59 (2006).
    [CrossRef]
  20. S. H. Park, K. M. Lee, and S. U. Lee, “A line feature matching technique based on an eigenvector approach,” Comput. Vis. Image Underst. 77, 263-283 (2000).
    [CrossRef]
  21. V. P. Onana, E. Trouvé, G. Mauris, J. P. Rudant, and E. Tonyé, “Detection of linear features in synthetic-aperture radar images by use of the localized Radon transform and prior information,” Appl. Opt. 43, 264-273 (2004).
    [CrossRef] [PubMed]
  22. M. Kass, W. Andrew, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321-331 (1988).
    [CrossRef]
  23. Y. Anthony, Jr., K. Satyanad, and K. Arun, “A geometric snake model for segmentation of medical imagery,” IEEE Trans. Med. Imaging 16, 199-209 (1997).
    [CrossRef]
  24. Z. Y. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell. 22, 1330-1334(2000).
    [CrossRef]
  25. R. Y. Tsai, “An efficient and accurate camera calibration technique for 3D machine vision,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1986), pp. 364-374.
  26. R. Y. Tsai, “Metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Automat. 3, 323-344 (1987).
    [CrossRef]

2009 (1)

Z. Y. Wang, H. Du, S. Park, and H. M. Xie, “Three-dimensional shape measurement with a fast and accurate approach,” Appl. Opt. 48, 1052-1061 (2009).
[CrossRef]

2006 (3)

J. Prakash, M. B. Meenavathi, and K. Rajesh, “Linear feature extraction using combined approach of Hough transform, Eigen values and Raster scan algorithms,” in IEEE Intelligent Sensing and Information Processing (IEEE, 2006), pp. 65-70.

R. Anchini, C. Liguori, V. Paciello, and A. Paolillo, “A comparison between stereo-vision techniques for the reconstruction of 3-D coordinates of objects,” IEEE Trans. Instrum. Meas. 55, 1459-1466 (2006).
[CrossRef]

Y. J. Zhang, Z. X. Zhang, and J. Q. Zhang, “Automatic measurement of industrial sheetmetal parts with CAD data and non-metric image sequence,” Comput. Vision Image Understand. 102, 52-59 (2006).
[CrossRef]

2005 (2)

A. Wozniak and M. Dobosz, “Factors influencing probing accuracy of a coordinate measuring machine,” IEEE Trans. Instrum. Meas. 54, 2540-2548 (2005).
[CrossRef]

W. S. Kim, A. I. Ansar, R. D. Steele, and R. C. Steinke, “Performance analysis and validation of a stereo vision system,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2005), Vol. 2, pp. 1409-1416.
[CrossRef]

2004 (1)

V. P. Onana, E. Trouvé, G. Mauris, J. P. Rudant, and E. Tonyé, “Detection of linear features in synthetic-aperture radar images by use of the localized Radon transform and prior information,” Appl. Opt. 43, 264-273 (2004).
[CrossRef] [PubMed]

2003 (2)

Y. S. Chen and B. T. Chen, “Measuring of a three-dimensional surface by use of a spatial distance computation,” Appl. Opt. 42, 1958-1972 (2003).
[CrossRef] [PubMed]

S. Malassiotis and M. G. Strintzis, “Stereo vision system for precision dimensional inspection of 3D holes,” Mach. Vis. Appl. 15, 101-113 (2003).
[CrossRef]

2002 (2)

C. Y. Lin, “A new approach to automatic reconstruction of a 3-D world using active stereo vision,” Comput. Vision Image Understand. 85, 117-143 (2002).
[CrossRef]

P. Graebling, A. Lallement, D. Y. Zhou, and E. Hirsch, “Optical high-precision three-dimensional vision-based quality control of manufactured parts by use of synthetic images and knowledge for image-data evaluation and interpretation,” Appl. Opt. 41, 2627-2643 (2002).
[CrossRef] [PubMed]

2001 (1)

H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
[CrossRef]

2000 (2)

S. H. Park, K. M. Lee, and S. U. Lee, “A line feature matching technique based on an eigenvector approach,” Comput. Vis. Image Underst. 77, 263-283 (2000).
[CrossRef]

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

1999 (1)

H. Qjidaa and L. Radouane, “Robust line fitting in a noisy image by the method of moments,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1216-1223 (1999).
[CrossRef]

1997 (2)

Y. Anthony, Jr., K. Satyanad, and K. Arun, “A geometric snake model for segmentation of medical imagery,” IEEE Trans. Med. Imaging 16, 199-209 (1997).
[CrossRef]

A. Ducharme, A. Daniels, E. Grann, and G. Boreman, “Design of an integrating sphere as a uniform illumination source,” IEEE Trans. Educ. 40, 131-134 (1997).
[CrossRef]

1994 (1)

C. C. Chang, S. Chatterjee, and P. R. Kube, “A quantization error analysis for convergent stereo,” in IEEE International Conference on Image Processing (IEEE, 1994), Vol. 2, pp. 735-739.

1990 (1)

S. Komatsu, H. Suhara, and H. Ohzu, “Laser scanning microscope with a differential heterodyne optical probe,” Appl. Opt. 29, 4244-4249 (1990).
[CrossRef] [PubMed]

1989 (1)

I. Weiss, “Line fitting in a noisy image,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 325-329 (1989).
[CrossRef]

1988 (2)

J. Illingworth and J. Kittler, “A survey of the Hough transform,” Comput. Vision Graph. Image Process. , 44, 87-116(1988).
[CrossRef]

M. Kass, W. Andrew, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321-331 (1988).
[CrossRef]

1987 (1)

R. Y. Tsai, “Metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Automat. 3, 323-344 (1987).
[CrossRef]

1986 (1)

R. Y. Tsai, “An efficient and accurate camera calibration technique for 3D machine vision,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1986), pp. 364-374.

1972 (1)

R. O. Duda and P. E. Hart, “Use of the Hough transform to detect lines and curves in pictures,” Commun. ACM 15, 11-15 (1972).
[CrossRef]

1967 (1)

D. G. Goebel, “Generalized integrating sphere theory,” Appl. Opt. 6, 125-128 (1967).
[CrossRef] [PubMed]

Anchini, R.

R. Anchini, C. Liguori, V. Paciello, and A. Paolillo, “A comparison between stereo-vision techniques for the reconstruction of 3-D coordinates of objects,” IEEE Trans. Instrum. Meas. 55, 1459-1466 (2006).
[CrossRef]

Andrew, W.

M. Kass, W. Andrew, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321-331 (1988).
[CrossRef]

Ansar, A. I.

W. S. Kim, A. I. Ansar, R. D. Steele, and R. C. Steinke, “Performance analysis and validation of a stereo vision system,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2005), Vol. 2, pp. 1409-1416.
[CrossRef]

Anthony, Y.

Y. Anthony, Jr., K. Satyanad, and K. Arun, “A geometric snake model for segmentation of medical imagery,” IEEE Trans. Med. Imaging 16, 199-209 (1997).
[CrossRef]

Arun, K.

Y. Anthony, Jr., K. Satyanad, and K. Arun, “A geometric snake model for segmentation of medical imagery,” IEEE Trans. Med. Imaging 16, 199-209 (1997).
[CrossRef]

Boreman, G.

A. Ducharme, A. Daniels, E. Grann, and G. Boreman, “Design of an integrating sphere as a uniform illumination source,” IEEE Trans. Educ. 40, 131-134 (1997).
[CrossRef]

Chang, C. C.

C. C. Chang, S. Chatterjee, and P. R. Kube, “A quantization error analysis for convergent stereo,” in IEEE International Conference on Image Processing (IEEE, 1994), Vol. 2, pp. 735-739.

Chatterjee, S.

C. C. Chang, S. Chatterjee, and P. R. Kube, “A quantization error analysis for convergent stereo,” in IEEE International Conference on Image Processing (IEEE, 1994), Vol. 2, pp. 735-739.

Chen, B. T.

Y. S. Chen and B. T. Chen, “Measuring of a three-dimensional surface by use of a spatial distance computation,” Appl. Opt. 42, 1958-1972 (2003).
[CrossRef] [PubMed]

Chen, Y. S.

Y. S. Chen and B. T. Chen, “Measuring of a three-dimensional surface by use of a spatial distance computation,” Appl. Opt. 42, 1958-1972 (2003).
[CrossRef] [PubMed]

Chu, S. C.

H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
[CrossRef]

Costen, F.

H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
[CrossRef]

Daniels, A.

A. Ducharme, A. Daniels, E. Grann, and G. Boreman, “Design of an integrating sphere as a uniform illumination source,” IEEE Trans. Educ. 40, 131-134 (1997).
[CrossRef]

Dobosz, M.

A. Wozniak and M. Dobosz, “Factors influencing probing accuracy of a coordinate measuring machine,” IEEE Trans. Instrum. Meas. 54, 2540-2548 (2005).
[CrossRef]

Du, H.

Z. Y. Wang, H. Du, S. Park, and H. M. Xie, “Three-dimensional shape measurement with a fast and accurate approach,” Appl. Opt. 48, 1052-1061 (2009).
[CrossRef]

Ducharme, A.

A. Ducharme, A. Daniels, E. Grann, and G. Boreman, “Design of an integrating sphere as a uniform illumination source,” IEEE Trans. Educ. 40, 131-134 (1997).
[CrossRef]

Duda, R. O.

R. O. Duda and P. E. Hart, “Use of the Hough transform to detect lines and curves in pictures,” Commun. ACM 15, 11-15 (1972).
[CrossRef]

Goebel, D. G.

D. G. Goebel, “Generalized integrating sphere theory,” Appl. Opt. 6, 125-128 (1967).
[CrossRef] [PubMed]

Graebling, P.

P. Graebling, A. Lallement, D. Y. Zhou, and E. Hirsch, “Optical high-precision three-dimensional vision-based quality control of manufactured parts by use of synthetic images and knowledge for image-data evaluation and interpretation,” Appl. Opt. 41, 2627-2643 (2002).
[CrossRef] [PubMed]

Grann, E.

A. Ducharme, A. Daniels, E. Grann, and G. Boreman, “Design of an integrating sphere as a uniform illumination source,” IEEE Trans. Educ. 40, 131-134 (1997).
[CrossRef]

Hart, P. E.

R. O. Duda and P. E. Hart, “Use of the Hough transform to detect lines and curves in pictures,” Commun. ACM 15, 11-15 (1972).
[CrossRef]

Hirsch, E.

P. Graebling, A. Lallement, D. Y. Zhou, and E. Hirsch, “Optical high-precision three-dimensional vision-based quality control of manufactured parts by use of synthetic images and knowledge for image-data evaluation and interpretation,” Appl. Opt. 41, 2627-2643 (2002).
[CrossRef] [PubMed]

Iizuka, K.

H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
[CrossRef]

Illingworth, J.

J. Illingworth and J. Kittler, “A survey of the Hough transform,” Comput. Vision Graph. Image Process. , 44, 87-116(1988).
[CrossRef]

Kass, M.

M. Kass, W. Andrew, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321-331 (1988).
[CrossRef]

Kim, W. S.

W. S. Kim, A. I. Ansar, R. D. Steele, and R. C. Steinke, “Performance analysis and validation of a stereo vision system,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2005), Vol. 2, pp. 1409-1416.
[CrossRef]

Kittler, J.

J. Illingworth and J. Kittler, “A survey of the Hough transform,” Comput. Vision Graph. Image Process. , 44, 87-116(1988).
[CrossRef]

Komatsu, S.

S. Komatsu, H. Suhara, and H. Ohzu, “Laser scanning microscope with a differential heterodyne optical probe,” Appl. Opt. 29, 4244-4249 (1990).
[CrossRef] [PubMed]

Kube, P. R.

C. C. Chang, S. Chatterjee, and P. R. Kube, “A quantization error analysis for convergent stereo,” in IEEE International Conference on Image Processing (IEEE, 1994), Vol. 2, pp. 735-739.

Lallement, A.

P. Graebling, A. Lallement, D. Y. Zhou, and E. Hirsch, “Optical high-precision three-dimensional vision-based quality control of manufactured parts by use of synthetic images and knowledge for image-data evaluation and interpretation,” Appl. Opt. 41, 2627-2643 (2002).
[CrossRef] [PubMed]

Lee, K. M.

S. H. Park, K. M. Lee, and S. U. Lee, “A line feature matching technique based on an eigenvector approach,” Comput. Vis. Image Underst. 77, 263-283 (2000).
[CrossRef]

Lee, S. U.

S. H. Park, K. M. Lee, and S. U. Lee, “A line feature matching technique based on an eigenvector approach,” Comput. Vis. Image Underst. 77, 263-283 (2000).
[CrossRef]

Liguori, C.

R. Anchini, C. Liguori, V. Paciello, and A. Paolillo, “A comparison between stereo-vision techniques for the reconstruction of 3-D coordinates of objects,” IEEE Trans. Instrum. Meas. 55, 1459-1466 (2006).
[CrossRef]

Lin, C. Y.

C. Y. Lin, “A new approach to automatic reconstruction of a 3-D world using active stereo vision,” Comput. Vision Image Understand. 85, 117-143 (2002).
[CrossRef]

Malassiotis, S.

S. Malassiotis and M. G. Strintzis, “Stereo vision system for precision dimensional inspection of 3D holes,” Mach. Vis. Appl. 15, 101-113 (2003).
[CrossRef]

Mauris, G.

V. P. Onana, E. Trouvé, G. Mauris, J. P. Rudant, and E. Tonyé, “Detection of linear features in synthetic-aperture radar images by use of the localized Radon transform and prior information,” Appl. Opt. 43, 264-273 (2004).
[CrossRef] [PubMed]

Meenavathi, M. B.

J. Prakash, M. B. Meenavathi, and K. Rajesh, “Linear feature extraction using combined approach of Hough transform, Eigen values and Raster scan algorithms,” in IEEE Intelligent Sensing and Information Processing (IEEE, 2006), pp. 65-70.

Ohzu, H.

S. Komatsu, H. Suhara, and H. Ohzu, “Laser scanning microscope with a differential heterodyne optical probe,” Appl. Opt. 29, 4244-4249 (1990).
[CrossRef] [PubMed]

Onana, V. P.

V. P. Onana, E. Trouvé, G. Mauris, J. P. Rudant, and E. Tonyé, “Detection of linear features in synthetic-aperture radar images by use of the localized Radon transform and prior information,” Appl. Opt. 43, 264-273 (2004).
[CrossRef] [PubMed]

Paciello, V.

R. Anchini, C. Liguori, V. Paciello, and A. Paolillo, “A comparison between stereo-vision techniques for the reconstruction of 3-D coordinates of objects,” IEEE Trans. Instrum. Meas. 55, 1459-1466 (2006).
[CrossRef]

Paolillo, A.

R. Anchini, C. Liguori, V. Paciello, and A. Paolillo, “A comparison between stereo-vision techniques for the reconstruction of 3-D coordinates of objects,” IEEE Trans. Instrum. Meas. 55, 1459-1466 (2006).
[CrossRef]

Park, S.

Z. Y. Wang, H. Du, S. Park, and H. M. Xie, “Three-dimensional shape measurement with a fast and accurate approach,” Appl. Opt. 48, 1052-1061 (2009).
[CrossRef]

Park, S. H.

S. H. Park, K. M. Lee, and S. U. Lee, “A line feature matching technique based on an eigenvector approach,” Comput. Vis. Image Underst. 77, 263-283 (2000).
[CrossRef]

Prakash, J.

J. Prakash, M. B. Meenavathi, and K. Rajesh, “Linear feature extraction using combined approach of Hough transform, Eigen values and Raster scan algorithms,” in IEEE Intelligent Sensing and Information Processing (IEEE, 2006), pp. 65-70.

Qjidaa, H.

H. Qjidaa and L. Radouane, “Robust line fitting in a noisy image by the method of moments,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1216-1223 (1999).
[CrossRef]

Radouane, L.

H. Qjidaa and L. Radouane, “Robust line fitting in a noisy image by the method of moments,” IEEE Trans. Pattern Anal. Mach. Intell. 21, 1216-1223 (1999).
[CrossRef]

Rajesh, K.

J. Prakash, M. B. Meenavathi, and K. Rajesh, “Linear feature extraction using combined approach of Hough transform, Eigen values and Raster scan algorithms,” in IEEE Intelligent Sensing and Information Processing (IEEE, 2006), pp. 65-70.

Rudant, J. P.

V. P. Onana, E. Trouvé, G. Mauris, J. P. Rudant, and E. Tonyé, “Detection of linear features in synthetic-aperture radar images by use of the localized Radon transform and prior information,” Appl. Opt. 43, 264-273 (2004).
[CrossRef] [PubMed]

Satyanad, K.

Y. Anthony, Jr., K. Satyanad, and K. Arun, “A geometric snake model for segmentation of medical imagery,” IEEE Trans. Med. Imaging 16, 199-209 (1997).
[CrossRef]

Shimotahira, H.

H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
[CrossRef]

Steele, R. D.

W. S. Kim, A. I. Ansar, R. D. Steele, and R. C. Steinke, “Performance analysis and validation of a stereo vision system,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2005), Vol. 2, pp. 1409-1416.
[CrossRef]

Steinke, R. C.

W. S. Kim, A. I. Ansar, R. D. Steele, and R. C. Steinke, “Performance analysis and validation of a stereo vision system,” in IEEE International Conference on Systems, Man and Cybernetics (IEEE, 2005), Vol. 2, pp. 1409-1416.
[CrossRef]

Strintzis, M. G.

S. Malassiotis and M. G. Strintzis, “Stereo vision system for precision dimensional inspection of 3D holes,” Mach. Vis. Appl. 15, 101-113 (2003).
[CrossRef]

Suhara, H.

S. Komatsu, H. Suhara, and H. Ohzu, “Laser scanning microscope with a differential heterodyne optical probe,” Appl. Opt. 29, 4244-4249 (1990).
[CrossRef] [PubMed]

Terzopoulos, D.

M. Kass, W. Andrew, and D. Terzopoulos, “Snakes: active contour models,” Int. J. Comput. Vis. 1, 321-331 (1988).
[CrossRef]

Tonyé, E.

V. P. Onana, E. Trouvé, G. Mauris, J. P. Rudant, and E. Tonyé, “Detection of linear features in synthetic-aperture radar images by use of the localized Radon transform and prior information,” Appl. Opt. 43, 264-273 (2004).
[CrossRef] [PubMed]

Trouvé, E.

V. P. Onana, E. Trouvé, G. Mauris, J. P. Rudant, and E. Tonyé, “Detection of linear features in synthetic-aperture radar images by use of the localized Radon transform and prior information,” Appl. Opt. 43, 264-273 (2004).
[CrossRef] [PubMed]

Tsai, R. Y.

R. Y. Tsai, “Metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Automat. 3, 323-344 (1987).
[CrossRef]

R. Y. Tsai, “An efficient and accurate camera calibration technique for 3D machine vision,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 1986), pp. 364-374.

Wah, C.

H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
[CrossRef]

Wang, Z. Y.

Z. Y. Wang, H. Du, S. Park, and H. M. Xie, “Three-dimensional shape measurement with a fast and accurate approach,” Appl. Opt. 48, 1052-1061 (2009).
[CrossRef]

Weiss, I.

I. Weiss, “Line fitting in a noisy image,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 325-329 (1989).
[CrossRef]

Wozniak, A.

A. Wozniak and M. Dobosz, “Factors influencing probing accuracy of a coordinate measuring machine,” IEEE Trans. Instrum. Meas. 54, 2540-2548 (2005).
[CrossRef]

Xie, H. M.

Z. Y. Wang, H. Du, S. Park, and H. M. Xie, “Three-dimensional shape measurement with a fast and accurate approach,” Appl. Opt. 48, 1052-1061 (2009).
[CrossRef]

Yoshikuni, Y.

H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
[CrossRef]

Zhang, J. Q.

Y. J. Zhang, Z. X. Zhang, and J. Q. Zhang, “Automatic measurement of industrial sheetmetal parts with CAD data and non-metric image sequence,” Comput. Vision Image Understand. 102, 52-59 (2006).
[CrossRef]

Zhang, Y. J.

Y. J. Zhang, Z. X. Zhang, and J. Q. Zhang, “Automatic measurement of industrial sheetmetal parts with CAD data and non-metric image sequence,” Comput. Vision Image Understand. 102, 52-59 (2006).
[CrossRef]

Zhang, Z. X.

Y. J. Zhang, Z. X. Zhang, and J. Q. Zhang, “Automatic measurement of industrial sheetmetal parts with CAD data and non-metric image sequence,” Comput. Vision Image Understand. 102, 52-59 (2006).
[CrossRef]

Zhang, Z. Y.

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

Zhou, D. Y.

P. Graebling, A. Lallement, D. Y. Zhou, and E. Hirsch, “Optical high-precision three-dimensional vision-based quality control of manufactured parts by use of synthetic images and knowledge for image-data evaluation and interpretation,” Appl. Opt. 41, 2627-2643 (2002).
[CrossRef] [PubMed]

Appl. Opt. (7)

H. Shimotahira, K. Iizuka, S. C. Chu, C. Wah, F. Costen, and Y. Yoshikuni, “Three-dimensional laser microvision,” Appl. Opt. 40, 1784-1794 (2001).
[CrossRef]

S. Komatsu, H. Suhara, and H. Ohzu, “Laser scanning microscope with a differential heterodyne optical probe,” Appl. Opt. 29, 4244-4249 (1990).
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Figures (28)

Fig. 1
Fig. 1

(a) Schematic side view of a standard round diamond. (b) Schematic bottom view (or crown pattern) of a standard round diamond.

Fig. 2
Fig. 2

Schematic structure of the proposed image acquisition system.

Fig. 3
Fig. 3

Schematic ideal model of the principle of stereo vision measurement.

Fig. 4
Fig. 4

Two diamond images automatically segmented from the original images acquired by the stereo vision system.

Fig. 5
Fig. 5

Edges detected by the Canny method with a threshold of [ 0.068 , 0.13 ] .

Fig. 6
Fig. 6

Line detection results using the standard Hough transform method.

Fig. 7
Fig. 7

(a) Azimuth angle θ e . (b) Simulant standard crown pattern.

Fig. 8
Fig. 8

Virtual girder truss model (VGTM).

Fig. 9
Fig. 9

Schematic attraction distribution on a beam.

Fig. 10
Fig. 10

Schematic force status on joint ( P i ).

Fig. 11
Fig. 11

Flow chart of the virtual control system.

Fig. 12
Fig. 12

Equivalent forces on the end points of a beam.

Fig. 13
Fig. 13

Geometric representation of the beam ( P i j , P ( i + 1 ) k ).

Fig. 14
Fig. 14

3D line determined by two images.

Fig. 15
Fig. 15

Developed image acquisition system.

Fig. 16
Fig. 16

Main flow chart of the presented method for 3D diamond crown measurement.

Fig. 17
Fig. 17

Two diamond images segmented from the original images acquired by (a) left CCD and (b) right CCD.

Fig. 18
Fig. 18

Gradient modulus of the diamond images.

Fig. 19
Fig. 19

Response of the circular correlation integral about θ in a period.

Fig. 20
Fig. 20

Initial virtual joint force distribution in the rough feature extraction procedure. Random errors (the maximum is 40 pixels) are added to the initial positions of some virtual joints in (b).

Fig. 21
Fig. 21

Control response of the total absolute joint force in the rough linear feature extraction procedure.

Fig. 22
Fig. 22

Control response of the total absolute joint displacement in the rough linear feature extraction procedure.

Fig. 23
Fig. 23

Final positions and force distribution of virtual joints in the rough linear feature extraction procedure.

Fig. 24
Fig. 24

Control response of the total absolute beam end point force in the refined feature extraction procedure.

Fig. 25
Fig. 25

Control response of the total absolute beam end point displacement in the refined feature extraction procedure.

Fig. 26
Fig. 26

Reconstruction (in the original images) of the diamond crown patterns according to the obtained linear features of desired diamond edges.

Fig. 27
Fig. 27

3D reconstruction of the diamond crown.

Fig. 28
Fig. 28

Measurement results of the crown angles (“*” shows the measurement results, “⋄” shows the real angles, and “∘” shows the standard angle).

Equations (36)

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U K X , U K ( R X R t ) ,
K = [ f 1 a 1 f 1 c 1 u 0 0 f 1 b 1 v 0 0 0 1 ] , K = [ f 2 a 2 f 2 c 2 u 0 0 f 2 b 2 v 0 0 0 1 ] ,
R = Rot ( z , φ ) Rot ( y , θ ) Rot ( x , ψ ) ,
u = f 1 x z + u 0 , v = f 1 y z + v 0 , u = f 2 x z c ψ y s ψ z 0 c ψ + y 0 s ψ + u 0 , v = f 2 ( y c ψ + z s ψ y 0 c ψ z 0 s ψ ) z c ψ y s ψ z 0 c ψ + y 0 s ψ + v 0 ,
x = u u 0 2 f 1 z + z f 1 c ψ + z ( v v 0 ) s ψ f 1 Z 0 2 f 1 f 2 ( u u 0 ) , y = v v 0 f 1 z , z = f 1 f 2 Y 0 + ( v v 0 ) f 1 Z 0 ( v v 0 ) f 1 c ψ + ( v v 0 ) ( v v 0 ) s ψ ( v v 0 ) f 2 c ψ + f 1 f 2 s ψ ,
Δ x 1 Y 0 Δ u + ( Y 0 c ψ Z 0 s ψ ) Δ u 2 f s ψ , Δ y 1 Y 0 Δ v f s ψ , Δ z 1 Z 0 Δ v f s ψ ,
Δ x 2 ( Y 0 c ψ Z 0 s ψ ) [ ( y y 0 ) Δ φ ( z z 0 ) Δ θ Δ x 0 ] 2 Y 0 , Δ y 2 0 , Δ z 2 Z 0 [ x s ψ Δ φ + x c ψ Δ θ + ( y c ψ z s ψ + Y 0 ) Δ ψ ] Y 0 Z 0 ( s ψ Δ y 0 c ψ Δ z 0 ) Y 0 ,
Δ x 31 ( u u 0 ) Y 0 2 f f s ψ Δ f 1 + Y 0 c ψ Z 0 s ψ 2 f f s ψ ( u u 0 ) Δ f 2 , Δ y 31 ( v v 0 ) Y 0 f f s ψ Δ f 1 , Δ z 31 ( v v 0 ) Z 0 f f s ψ Δ f 2 ,
Δ x 32 Y 0 ( u u 0 ) Δ a 1 + Y 0 ( v v 0 ) Δ c 1 + Y 0 Δ u 0 2 f s ψ ( Y 0 c ψ Z 0 s ψ ) 2 f s ψ [ ( u u 0 ) Δ a 2 + ( v v 0 ) Δ c 2 + Δ u 0 ] , Δ y 32 Y 0 f s ψ [ ( v v 0 ) Δ b 1 + Δ v 0 ] , Δ z 32 Z 0 f s ψ [ ( v v 0 ) Δ b 2 + Δ v 0 ] ,
Δ x = Δ x 1 + Δ x 2 + Δ x 31 + Δ x 32 , Δ y = Δ y 1 + Δ y 2 + Δ y 31 + Δ y 32 , Δ z = Δ z 1 + Δ z 2 + Δ z 31 + Δ z 32 ,
Δ x Y 0 Δ u + ( Y 0 c ψ Z 0 s ψ ) Δ u 2 f s ψ + ( Y 0 c ψ Z 0 s ψ ) ( y Δ φ z Δ θ ) 2 Y 0 + ( u u 0 ) Y 0 2 f 2 s ψ Δ f 1 + Y 0 c ψ Z 0 s ψ 2 f 2 s ψ ( u u 0 ) Δ f 2 Y 0 u Δ a 1 + Y 0 v Δ c 1 2 f s ψ ( Y 0 c ψ Z 0 s ψ ) 2 f s ψ ( u Δ a 2 + v Δ c 2 ) + Δ A 0 , Δ y Y 0 Δ v f s ψ + ( v v 0 ) Y 0 f 2 s ψ Δ f 1 Y 0 f s ψ v Δ b 1 + Δ B 0 , Δ z Z 0 Δ v f s ψ Z 0 [ x s ψ Δ φ + x c ψ Δ θ ( y c ψ + z s ψ ) Δ ψ ] Y 0 ( v v 0 ) Z 0 f 2 s ψ Δ f 2 + Z 0 f s ψ v Δ b 2 + Δ C 0 , ( v v 0 ) Z 0 f 2 s ψ Δ f 2 + Z 0 f s ψ v Δ b 2 + Δ C 0 ,
A ( r , θ ) = 0 π / 4 [ k = 0 7 I D ( r , τ + k π 4 ) ] I S ( r , τ + θ ) d τ ,
A θ ( θ ) = R 0 R A ( r , θ ) d r ,
R = [ 1 π X = 1 N Y = 1 N I ( X , Y ) ] 1 2 ,
A ( X , Y ) = | I ( X , Y ) sin [ γ ( X , Y ) β ] | ,
W = 1 + cos ( k 1 N C 1 π ) 2 W v + W 0 ,
f ( x ) = W W A ( x , y ) D ( x , y ) d y ,
F i j = 1 L α L ( 1 α ) L f ( x ) ( L x ) d x , F ( i + 1 ) k = 1 L α L ( 1 α ) L f ( x ) x d x ,
F i j = 1 L α L ( 1 α ) L W W A ( x , y ) y ( L x ) d y d x , F ( i + 1 ) k = 1 L α L ( 1 α ) L W W A ( x , y ) y x d y d x .
F i j = 1 L α L ( 1 α ) L W W A ( x , y ) ( y L x L Δ y ) ( L x ) d y d x .
Δ y = Δ X i sin β i j + Δ Y i cos β i j ,
F i j = 1 L α L ( 1 α ) L W W A ( x , y ) y ( L x ) d y d x + ( Δ X i sin β i j Δ Y i cos β i j ) L 2 α L ( 1 α ) L W W A ( x , y ) ( L x ) 2 d y d x .
F i = F i 1 + F i 2 + F i 3 + F i 4 ,
j = 1 4 F X i j ( Δ X i , Δ Y i ) = 0 , j = 1 4 F Y i j ( Δ X i , Δ Y i ) = 0 ,
F sum = i = 1 J | F i | ,
S sum = i = 1 J | S i | ,
F i j = 1 L α L ( 1 α ) L W W A ( x , y ) ( y L x L Δ y i j x L Δ y ( i + 1 ) k ) ( L x ) d y d x , F ( i + 1 ) k = 1 L α L ( 1 α ) L W W A ( x , y ) ( y L x L Δ y i j x L Δ y ( i + 1 ) k ) ) x d y d x .
1 L α L ( 1 α ) L W W A ( x , y ) ( y L x L Δ y i j x L Δ y ( i + 1 ) k ) ( L x ) d y d x = 0 , 1 L α L ( 1 α ) L W W A ( x , y ) ( y L x L Δ y i j x L Δ y ( i + 1 ) k ) ) x d y d x = 0.
Δ Y i j = Δ y i j cos β i j , Δ X i j = Δ y i j sin β i j , Δ Y ( i + 1 ) k = Δ y ( i + 1 ) k cos β i j , Δ X ( i + 1 ) k = Δ y ( i + 1 ) k sin β i j .
S = 1 N i = 1 N w i D 2 ( p i , L ( φ , b ) ) ,
S = 1 N i = 1 N w i ( y i x i φ b ) 2 .
S φ | S = min = 0 and   S b | S = min = 0 or { i = 1 N w i x i ( y i x i φ b ) = 0 i = 1 N w i ( y i x i φ b ) = 0 .
φ = Δ y ( i + 1 ) k Δ y i j L , b = Δ y i j .
i = 1 N w i x i ( y i L x i L Δ y i j x i Δ y ( i + 1 ) k L ) = 0 , i = 1 N w i ( y i L x i L Δ y i j x i Δ y ( i + 1 ) k L ) = 0.
A = 1 K i = 1 K ( E i · n | E i | ) 2 ,
B = 1 4 K i = 1 2 K ( P i x n x + P i y n y + P i z n z n z d ) 2 + 1 4 K i = 1 2 K ( Q i x n x + Q i y n y + Q i z n z n z d ) 2 ,

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