Abstract

A machine vision method for accurately measuring the diameters of cylindrical shafts is presented. Perspective projection and the geometrical features of cylindrical shafts are modeled in order to enable accurate measurement of shaft diameters. Some of the model parameters are determined using a shaft of known diameter. The camera model itself includes radial and tangential distortions terms. Experiments were used to measure the accuracy of the proposed method and the effect of the position of the camera relative to the shaft, as well as other factors.

© 2011 Optical Society of America

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References

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  2. J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell. 24, 1606–1617 (2002).
    [CrossRef]
  3. A. J. Tabatabai and O. R. Mitchell, “Edge location to sub-pixel values in digital imagery,” IEEE Trans. Pattern Anal. Machine Intell. 6, 188–201 (1984).
    [CrossRef]
  4. E. P. Lyvers, O. R. Mitchell, M. L. Akey, and A. P. Reeves, “Sub-pixel measurements using a moment-based edge operator,” IEEE Trans. Pattern Anal. Machine Intell. 11, 1293–1309(1989).
    [CrossRef]
  5. Y.-S. Li, T. Y. Young, and J. A. Magerl, “Sub-pixel edge detection and estimation with a microprocessor-controlled line scan camera,” IEEE Trans. Ind. Electron. 35, 105–112 (1988).
    [CrossRef]
  6. J. Ye, G. K. Fu, and U. P. Poudel, “High-accuracy edge detection with blurred edge model,” Image Vis. Comput. 23, 453–467 (2005).
    [CrossRef]
  7. A. Cantatore, A. Cigada, R. Sala, and E. Zappa, “Hyperbolic tangent algorithm for periodic effect cancellation in sub-pixel resolution edge displacement measurement,” Measurement 42, 1226–1232 (2009).
    [CrossRef]
  8. R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Automat. 3, 323–344(1987).
    [CrossRef]
  9. J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1066–1076 (2000).
    [CrossRef]
  10. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1330–1334(2000).
    [CrossRef]
  11. X. Gao, W. Ding, T. Gao, and Z. Gong, “High precision contactless object-diameter measurement using IR light source,” in Proceedings of IEEE Conference on Automation and Logistics (IEEE, 2009), pp. 915–920.
    [CrossRef]
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    [CrossRef]
  13. C. Sun, Q. You, Y. Qiu, and S. Ye, “Online machine vision method for measuring the diameter and straightness of seamless steel pipes,” Opt. Eng. 40, 2565–2571 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  18. Q. Song, D. Wu, J. Liu, C. Zhang, and J. Huang, “Instrumentation design and precision analysis of the external diameter measurement system based on CCD parallel light projection method,” Proc. SPIE 7156, 71562I (2008).
    [CrossRef]
  19. O. Faugeras, Three-Dimensional Computer Vision: a Geometric Viewpoint (MIT Press, 1993).
  20. J. More, The Levenberg-Marquardt Algorithm, Implementation and Theory (Numerical Analysis, 1977).

2009 (1)

A. Cantatore, A. Cigada, R. Sala, and E. Zappa, “Hyperbolic tangent algorithm for periodic effect cancellation in sub-pixel resolution edge displacement measurement,” Measurement 42, 1226–1232 (2009).
[CrossRef]

2008 (1)

Q. Song, D. Wu, J. Liu, C. Zhang, and J. Huang, “Instrumentation design and precision analysis of the external diameter measurement system based on CCD parallel light projection method,” Proc. SPIE 7156, 71562I (2008).
[CrossRef]

2007 (1)

Y. A. Lemeshko, Y. V. Chugui, and A. K. Yarovaya, “Precision dimensional inspection of diameters of circular reflecting cylinders,” Optoelectron. Instrument. Proc. 43, 284–291(2007).
[CrossRef]

2005 (1)

J. Ye, G. K. Fu, and U. P. Poudel, “High-accuracy edge detection with blurred edge model,” Image Vis. Comput. 23, 453–467 (2005).
[CrossRef]

2004 (1)

2002 (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell. 24, 1606–1617 (2002).
[CrossRef]

2001 (1)

C. Sun, Q. You, Y. Qiu, and S. Ye, “Online machine vision method for measuring the diameter and straightness of seamless steel pipes,” Opt. Eng. 40, 2565–2571 (2001).
[CrossRef]

2000 (2)

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1066–1076 (2000).
[CrossRef]

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

1998 (1)

1989 (1)

E. P. Lyvers, O. R. Mitchell, M. L. Akey, and A. P. Reeves, “Sub-pixel measurements using a moment-based edge operator,” IEEE Trans. Pattern Anal. Machine Intell. 11, 1293–1309(1989).
[CrossRef]

1988 (1)

Y.-S. Li, T. Y. Young, and J. A. Magerl, “Sub-pixel edge detection and estimation with a microprocessor-controlled line scan camera,” IEEE Trans. Ind. Electron. 35, 105–112 (1988).
[CrossRef]

1987 (1)

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Automat. 3, 323–344(1987).
[CrossRef]

1985 (1)

1984 (2)

K. Takesa, H. Sato, Y. Tani, and T. Sata, “Measurement of diameter using charge coupled device (CCD),” CIRP Ann. 33, 377–381 (1984).
[CrossRef]

A. J. Tabatabai and O. R. Mitchell, “Edge location to sub-pixel values in digital imagery,” IEEE Trans. Pattern Anal. Machine Intell. 6, 188–201 (1984).
[CrossRef]

Akey, M. L.

E. P. Lyvers, O. R. Mitchell, M. L. Akey, and A. P. Reeves, “Sub-pixel measurements using a moment-based edge operator,” IEEE Trans. Pattern Anal. Machine Intell. 11, 1293–1309(1989).
[CrossRef]

Butler, D. J.

Byer, R. L.

Canny, J.

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell. 24, 1606–1617 (2002).
[CrossRef]

Cantatore, A.

A. Cantatore, A. Cigada, R. Sala, and E. Zappa, “Hyperbolic tangent algorithm for periodic effect cancellation in sub-pixel resolution edge displacement measurement,” Measurement 42, 1226–1232 (2009).
[CrossRef]

Chugui, Y. V.

Y. A. Lemeshko, Y. V. Chugui, and A. K. Yarovaya, “Precision dimensional inspection of diameters of circular reflecting cylinders,” Optoelectron. Instrument. Proc. 43, 284–291(2007).
[CrossRef]

Cigada, A.

A. Cantatore, A. Cigada, R. Sala, and E. Zappa, “Hyperbolic tangent algorithm for periodic effect cancellation in sub-pixel resolution edge displacement measurement,” Measurement 42, 1226–1232 (2009).
[CrossRef]

Ding, W.

X. Gao, W. Ding, T. Gao, and Z. Gong, “High precision contactless object-diameter measurement using IR light source,” in Proceedings of IEEE Conference on Automation and Logistics (IEEE, 2009), pp. 915–920.
[CrossRef]

Faugeras, O.

O. Faugeras, Three-Dimensional Computer Vision: a Geometric Viewpoint (MIT Press, 1993).

Fejer, M. M.

Forbes, G. W.

Fu, G. K.

J. Ye, G. K. Fu, and U. P. Poudel, “High-accuracy edge detection with blurred edge model,” Image Vis. Comput. 23, 453–467 (2005).
[CrossRef]

Gao, T.

X. Gao, W. Ding, T. Gao, and Z. Gong, “High precision contactless object-diameter measurement using IR light source,” in Proceedings of IEEE Conference on Automation and Logistics (IEEE, 2009), pp. 915–920.
[CrossRef]

Gao, X.

X. Gao, W. Ding, T. Gao, and Z. Gong, “High precision contactless object-diameter measurement using IR light source,” in Proceedings of IEEE Conference on Automation and Logistics (IEEE, 2009), pp. 915–920.
[CrossRef]

Gong, Z.

X. Gao, W. Ding, T. Gao, and Z. Gong, “High precision contactless object-diameter measurement using IR light source,” in Proceedings of IEEE Conference on Automation and Logistics (IEEE, 2009), pp. 915–920.
[CrossRef]

Heikkila, J.

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1066–1076 (2000).
[CrossRef]

Huang, J.

Q. Song, D. Wu, J. Liu, C. Zhang, and J. Huang, “Instrumentation design and precision analysis of the external diameter measurement system based on CCD parallel light projection method,” Proc. SPIE 7156, 71562I (2008).
[CrossRef]

Lemeshko, Y. A.

Y. A. Lemeshko, Y. V. Chugui, and A. K. Yarovaya, “Precision dimensional inspection of diameters of circular reflecting cylinders,” Optoelectron. Instrument. Proc. 43, 284–291(2007).
[CrossRef]

Li, Y.-S.

Y.-S. Li, T. Y. Young, and J. A. Magerl, “Sub-pixel edge detection and estimation with a microprocessor-controlled line scan camera,” IEEE Trans. Ind. Electron. 35, 105–112 (1988).
[CrossRef]

Liu, J.

Q. Song, D. Wu, J. Liu, C. Zhang, and J. Huang, “Instrumentation design and precision analysis of the external diameter measurement system based on CCD parallel light projection method,” Proc. SPIE 7156, 71562I (2008).
[CrossRef]

Lyvers, E. P.

E. P. Lyvers, O. R. Mitchell, M. L. Akey, and A. P. Reeves, “Sub-pixel measurements using a moment-based edge operator,” IEEE Trans. Pattern Anal. Machine Intell. 11, 1293–1309(1989).
[CrossRef]

Magel, G. A.

Magerl, J. A.

Y.-S. Li, T. Y. Young, and J. A. Magerl, “Sub-pixel edge detection and estimation with a microprocessor-controlled line scan camera,” IEEE Trans. Ind. Electron. 35, 105–112 (1988).
[CrossRef]

Mitchell, O. R.

E. P. Lyvers, O. R. Mitchell, M. L. Akey, and A. P. Reeves, “Sub-pixel measurements using a moment-based edge operator,” IEEE Trans. Pattern Anal. Machine Intell. 11, 1293–1309(1989).
[CrossRef]

A. J. Tabatabai and O. R. Mitchell, “Edge location to sub-pixel values in digital imagery,” IEEE Trans. Pattern Anal. Machine Intell. 6, 188–201 (1984).
[CrossRef]

More, J.

J. More, The Levenberg-Marquardt Algorithm, Implementation and Theory (Numerical Analysis, 1977).

Poudel, U. P.

J. Ye, G. K. Fu, and U. P. Poudel, “High-accuracy edge detection with blurred edge model,” Image Vis. Comput. 23, 453–467 (2005).
[CrossRef]

Qiu, Y.

C. Sun, Q. You, Y. Qiu, and S. Ye, “Online machine vision method for measuring the diameter and straightness of seamless steel pipes,” Opt. Eng. 40, 2565–2571 (2001).
[CrossRef]

Reeves, A. P.

E. P. Lyvers, O. R. Mitchell, M. L. Akey, and A. P. Reeves, “Sub-pixel measurements using a moment-based edge operator,” IEEE Trans. Pattern Anal. Machine Intell. 11, 1293–1309(1989).
[CrossRef]

Sala, R.

A. Cantatore, A. Cigada, R. Sala, and E. Zappa, “Hyperbolic tangent algorithm for periodic effect cancellation in sub-pixel resolution edge displacement measurement,” Measurement 42, 1226–1232 (2009).
[CrossRef]

Sasaki, O.

Sata, T.

K. Takesa, H. Sato, Y. Tani, and T. Sata, “Measurement of diameter using charge coupled device (CCD),” CIRP Ann. 33, 377–381 (1984).
[CrossRef]

Sato, H.

K. Takesa, H. Sato, Y. Tani, and T. Sata, “Measurement of diameter using charge coupled device (CCD),” CIRP Ann. 33, 377–381 (1984).
[CrossRef]

Smith, S. M.

S. M. Smith, Feature Based Image Sequence Understanding (Oxford University, 1992).

Song, Q.

Q. Song, D. Wu, J. Liu, C. Zhang, and J. Huang, “Instrumentation design and precision analysis of the external diameter measurement system based on CCD parallel light projection method,” Proc. SPIE 7156, 71562I (2008).
[CrossRef]

Sun, C.

C. Sun, Q. You, Y. Qiu, and S. Ye, “Online machine vision method for measuring the diameter and straightness of seamless steel pipes,” Opt. Eng. 40, 2565–2571 (2001).
[CrossRef]

Suzuki, T.

Tabatabai, A. J.

A. J. Tabatabai and O. R. Mitchell, “Edge location to sub-pixel values in digital imagery,” IEEE Trans. Pattern Anal. Machine Intell. 6, 188–201 (1984).
[CrossRef]

Takesa, K.

K. Takesa, H. Sato, Y. Tani, and T. Sata, “Measurement of diameter using charge coupled device (CCD),” CIRP Ann. 33, 377–381 (1984).
[CrossRef]

Tani, Y.

K. Takesa, H. Sato, Y. Tani, and T. Sata, “Measurement of diameter using charge coupled device (CCD),” CIRP Ann. 33, 377–381 (1984).
[CrossRef]

Tsai, R. Y.

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Automat. 3, 323–344(1987).
[CrossRef]

Wu, D.

Q. Song, D. Wu, J. Liu, C. Zhang, and J. Huang, “Instrumentation design and precision analysis of the external diameter measurement system based on CCD parallel light projection method,” Proc. SPIE 7156, 71562I (2008).
[CrossRef]

Xu, Y.

Yarovaya, A. K.

Y. A. Lemeshko, Y. V. Chugui, and A. K. Yarovaya, “Precision dimensional inspection of diameters of circular reflecting cylinders,” Optoelectron. Instrument. Proc. 43, 284–291(2007).
[CrossRef]

Ye, J.

J. Ye, G. K. Fu, and U. P. Poudel, “High-accuracy edge detection with blurred edge model,” Image Vis. Comput. 23, 453–467 (2005).
[CrossRef]

Ye, S.

C. Sun, Q. You, Y. Qiu, and S. Ye, “Online machine vision method for measuring the diameter and straightness of seamless steel pipes,” Opt. Eng. 40, 2565–2571 (2001).
[CrossRef]

You, Q.

C. Sun, Q. You, Y. Qiu, and S. Ye, “Online machine vision method for measuring the diameter and straightness of seamless steel pipes,” Opt. Eng. 40, 2565–2571 (2001).
[CrossRef]

Young, T. Y.

Y.-S. Li, T. Y. Young, and J. A. Magerl, “Sub-pixel edge detection and estimation with a microprocessor-controlled line scan camera,” IEEE Trans. Ind. Electron. 35, 105–112 (1988).
[CrossRef]

Zappa, E.

A. Cantatore, A. Cigada, R. Sala, and E. Zappa, “Hyperbolic tangent algorithm for periodic effect cancellation in sub-pixel resolution edge displacement measurement,” Measurement 42, 1226–1232 (2009).
[CrossRef]

Zhang, C.

Q. Song, D. Wu, J. Liu, C. Zhang, and J. Huang, “Instrumentation design and precision analysis of the external diameter measurement system based on CCD parallel light projection method,” Proc. SPIE 7156, 71562I (2008).
[CrossRef]

Zhang, Z.

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

Appl. Opt. (3)

CIRP Ann. (1)

K. Takesa, H. Sato, Y. Tani, and T. Sata, “Measurement of diameter using charge coupled device (CCD),” CIRP Ann. 33, 377–381 (1984).
[CrossRef]

IEEE J. Robot. Automat. (1)

R. Y. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses,” IEEE J. Robot. Automat. 3, 323–344(1987).
[CrossRef]

IEEE Trans. Ind. Electron. (1)

Y.-S. Li, T. Y. Young, and J. A. Magerl, “Sub-pixel edge detection and estimation with a microprocessor-controlled line scan camera,” IEEE Trans. Ind. Electron. 35, 105–112 (1988).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (5)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell. 24, 1606–1617 (2002).
[CrossRef]

A. J. Tabatabai and O. R. Mitchell, “Edge location to sub-pixel values in digital imagery,” IEEE Trans. Pattern Anal. Machine Intell. 6, 188–201 (1984).
[CrossRef]

E. P. Lyvers, O. R. Mitchell, M. L. Akey, and A. P. Reeves, “Sub-pixel measurements using a moment-based edge operator,” IEEE Trans. Pattern Anal. Machine Intell. 11, 1293–1309(1989).
[CrossRef]

J. Heikkila, “Geometric camera calibration using circular control points,” IEEE Trans. Pattern Anal. Machine Intell. 22, 1066–1076 (2000).
[CrossRef]

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

Image Vis. Comput. (1)

J. Ye, G. K. Fu, and U. P. Poudel, “High-accuracy edge detection with blurred edge model,” Image Vis. Comput. 23, 453–467 (2005).
[CrossRef]

Measurement (1)

A. Cantatore, A. Cigada, R. Sala, and E. Zappa, “Hyperbolic tangent algorithm for periodic effect cancellation in sub-pixel resolution edge displacement measurement,” Measurement 42, 1226–1232 (2009).
[CrossRef]

Opt. Eng. (1)

C. Sun, Q. You, Y. Qiu, and S. Ye, “Online machine vision method for measuring the diameter and straightness of seamless steel pipes,” Opt. Eng. 40, 2565–2571 (2001).
[CrossRef]

Optoelectron. Instrument. Proc. (1)

Y. A. Lemeshko, Y. V. Chugui, and A. K. Yarovaya, “Precision dimensional inspection of diameters of circular reflecting cylinders,” Optoelectron. Instrument. Proc. 43, 284–291(2007).
[CrossRef]

Proc. SPIE (1)

Q. Song, D. Wu, J. Liu, C. Zhang, and J. Huang, “Instrumentation design and precision analysis of the external diameter measurement system based on CCD parallel light projection method,” Proc. SPIE 7156, 71562I (2008).
[CrossRef]

Other (4)

O. Faugeras, Three-Dimensional Computer Vision: a Geometric Viewpoint (MIT Press, 1993).

J. More, The Levenberg-Marquardt Algorithm, Implementation and Theory (Numerical Analysis, 1977).

S. M. Smith, Feature Based Image Sequence Understanding (Oxford University, 1992).

X. Gao, W. Ding, T. Gao, and Z. Gong, “High precision contactless object-diameter measurement using IR light source,” in Proceedings of IEEE Conference on Automation and Logistics (IEEE, 2009), pp. 915–920.
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Imaging model of a shaft.

Fig. 2
Fig. 2

Section plane perpendicular to X w axis.

Fig. 3
Fig. 3

Experimental facilities for the static experiment.

Fig. 4
Fig. 4

Camera at three different positions: a 1 , a 2 , a 3 .

Fig. 5
Fig. 5

Illumination with and without coverings.

Fig. 6
Fig. 6

Error for the parameters calibrated with one, five, and nine segments.

Fig. 7
Fig. 7

Cases for a short distance d 1 matched with a short focal length f 1 and a long distance d 2 matched with a long focal length f 2 .

Fig. 8
Fig. 8

Experimental facilities for the dynamic experiment.

Fig. 9
Fig. 9

Error under spindle speeds of 400, 900, and 1200 r / min .

Fig. 10
Fig. 10

Measurement error using multiple images.

Tables (3)

Tables Icon

Table 1 Comparison of the Measured Diameters

Tables Icon

Table 2 Error from the Spindle Rotation

Tables Icon

Table 3 Comparison of Calibration Models in Zhang [10], Heikkila [9], and This Article

Equations (15)

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

[ x c y c z c ] = F ( A , x p , y p ) .
[ x c y c z c ] = R [ x w y w z w ] + t ,
[ x y ] = d d z w [ x w y w ] ,
D ^ = 2 d y 2 + d 2 | y | .
b 1 Δ T y Δ T y b 2 = b 1 2 + d 2 b 2 2 + d 2 ,
Δ T y = b 2 b 1 2 + d 2 + b 1 b 2 2 + d 2 b 1 2 + d 2 + b 2 2 + d 2 .
D ^ = 2 d y 2 + d 2 | y Δ T y | .
D = 1 2 n i = 1 2 n D ^ i ( x p i , y p i , R , t ) ,
t = R ( 0 , 0 , d ) T .
L 1 :     y = k 1 x + b 1 , z = 1 , L 2 :     y = k 2 x + b 2 , z = 1 .
m 1 = k 1 b 1 , n 1 = 1 b 1 , m 2 = k 2 b 2 , n 2 = 1 b 2 , m x = n 1 n 2 m 1 n 2 m 2 n 1 , n x = m 1 m 2 m 2 n 1 m 1 n 2 .
{ ( m z , n z , 1 ) T ( m x , n x , 1 ) = 0 | m z m 1 + n z n 1 + 1 | m z 2 + n z 2 + 1 m 1 2 + n 1 2 + 1 = | m z m 2 + n z n 2 + 1 | m z 2 + n z 2 + 1 m 2 2 + n 2 2 + 1 .
d = D 0 / 2 sin ( α / 2 ) ,
α = arccos | m 1 m 2 + n 1 n 2 + 1 | m 1 2 + n 1 2 + 1 m 2 2 + n 2 2 + 1 .
i = 1 m j = 1 2 n D 0 i D ^ 0 i j ( x p i j , y p i j , θ , ψ , φ , d ) 2 ,

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