Abstract

To accurately measure the attitude angles (pitch, roll, and yaw) of a rigid object that rotates in a space, we propose a high-precision rotation angle measurement method based on monocular vision. This method combines camera self-calibration, multiview geometry, and 3D measurement. This monocular vision measuring system consists of an area scan CCD, a prime lens, and a spots array target, which are fixed on the measured object. We can calculate the rotation angle according to the rebuilt rotating spots array target by using this monocular vision measuring system. The measurement precision of rotation angle can reach 1 arc sec in this paper’s experiments. This method has high measurement precision and good stability. Therefore we can widely use this method in machinery manufacturing, engineering measurement, aerospace, and the military.

© 2014 Optical Society of America

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  1. H. Bing-hua, Z. Hu-long, and Y. Hui, “Measurement of aircraft attitude angles based on vanishing point theory,” J. Opt. A 33, 779–783 (2012).
  2. X. Dai, O. Sasaki, J. E. Greivenkamp, and T. Suzuki, “High accuracy wide range rotation angle measurement by the use of two parallel interference patterns,” Appl. Opt. 36, 6190–6195 (1997).
    [CrossRef]
  3. A. N. Khoroshun and D. N. Artsishevskii, “Determining small angles of beam splitter rotation in optical vortex shearing interferometer,” Tech. Phys. Lett. 36, 382–385 (2010).
    [CrossRef]
  4. W. Wenqian, L. Guodong, P. Zhaobang, and C. Shizhe, “Measurement of two-dimensional small angle by means of matrix CCD,” Semicond. Optoelectron. 25, 134–138 (2004).
  5. W. Wei, S. Wang, X. Zhang, and Z. Tang, “Estimation of image rotation angle using interpolation-related spectral signatures with application to blind detection of image forgery,” IEEE Trans. Inf. Forensics Security 5, 507–517 (2010).
    [CrossRef]
  6. J. Apolinar Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131–138 (2005).
    [CrossRef]
  7. L. Lichun, Y. Qifeng, L. Zhihui, and L. Jianbing, “High-accuracy measurement of rotation angle based on image,” Acta Opt. Sin. 25, 491–496 (2005).
  8. W. Li, J. Jin, X. Li, and B. Li, “Method of rotation angle measurement in machine vision based on calibration pattern with spot array,” Appl. Opt. 49, 1001–1006 (2010).
    [CrossRef]
  9. P. Sturm and B. Triggs, “A factorization based algorithm for multi-image projective structure and motion,” in Proceedings of Fourth European Conference on Computer Vision (ECCV, 1996), pp. 709–720.
  10. T. Morita and T. Kanade, “A sequential factorization method for recovering shape and motion from image streams,” IEEE Trans. Patt. Anal. Mac Intel. 19, 858–867 (1997).
  11. W. Yuanbin, Z. Bin, and Y. Tianshun, “A linear and direct method for projective reconstruction,” in IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS, 2009), pp. 111–115.
  12. C. Xiao, L. Jianxun, and Z. Zhenfu, “Three-dimensional projective invariants of points from multiple images,” Opt. Eng. 47, 117203 (2008).
    [CrossRef]
  13. M. Pollefeys, R. Koch, and L. Van Gool, “Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters,” Int. J. Comput. Vis. 32, 7–25 (1999).
    [CrossRef]
  14. J. Jin and X. Li, “Efficient camera self-calibration method based on the absolute dual quadric,” J. Opt. Soc. Am. A 30, 287–292 (2013).
    [CrossRef]
  15. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000), pp. 585–587.
  16. M. E. Ragab and K. H. Wong, “Rotation within camera projection matrix using Euler angles, quaternions, and angle-axes,” Int. J. Robot. Autom. 24, 312–318 (2009).

2013 (1)

2012 (1)

H. Bing-hua, Z. Hu-long, and Y. Hui, “Measurement of aircraft attitude angles based on vanishing point theory,” J. Opt. A 33, 779–783 (2012).

2010 (3)

W. Li, J. Jin, X. Li, and B. Li, “Method of rotation angle measurement in machine vision based on calibration pattern with spot array,” Appl. Opt. 49, 1001–1006 (2010).
[CrossRef]

W. Wei, S. Wang, X. Zhang, and Z. Tang, “Estimation of image rotation angle using interpolation-related spectral signatures with application to blind detection of image forgery,” IEEE Trans. Inf. Forensics Security 5, 507–517 (2010).
[CrossRef]

A. N. Khoroshun and D. N. Artsishevskii, “Determining small angles of beam splitter rotation in optical vortex shearing interferometer,” Tech. Phys. Lett. 36, 382–385 (2010).
[CrossRef]

2009 (1)

M. E. Ragab and K. H. Wong, “Rotation within camera projection matrix using Euler angles, quaternions, and angle-axes,” Int. J. Robot. Autom. 24, 312–318 (2009).

2008 (1)

C. Xiao, L. Jianxun, and Z. Zhenfu, “Three-dimensional projective invariants of points from multiple images,” Opt. Eng. 47, 117203 (2008).
[CrossRef]

2005 (2)

J. Apolinar Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131–138 (2005).
[CrossRef]

L. Lichun, Y. Qifeng, L. Zhihui, and L. Jianbing, “High-accuracy measurement of rotation angle based on image,” Acta Opt. Sin. 25, 491–496 (2005).

2004 (1)

W. Wenqian, L. Guodong, P. Zhaobang, and C. Shizhe, “Measurement of two-dimensional small angle by means of matrix CCD,” Semicond. Optoelectron. 25, 134–138 (2004).

1999 (1)

M. Pollefeys, R. Koch, and L. Van Gool, “Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters,” Int. J. Comput. Vis. 32, 7–25 (1999).
[CrossRef]

1997 (2)

T. Morita and T. Kanade, “A sequential factorization method for recovering shape and motion from image streams,” IEEE Trans. Patt. Anal. Mac Intel. 19, 858–867 (1997).

X. Dai, O. Sasaki, J. E. Greivenkamp, and T. Suzuki, “High accuracy wide range rotation angle measurement by the use of two parallel interference patterns,” Appl. Opt. 36, 6190–6195 (1997).
[CrossRef]

Apolinar Muñoz-Rodríguez, J.

J. Apolinar Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131–138 (2005).
[CrossRef]

Artsishevskii, D. N.

A. N. Khoroshun and D. N. Artsishevskii, “Determining small angles of beam splitter rotation in optical vortex shearing interferometer,” Tech. Phys. Lett. 36, 382–385 (2010).
[CrossRef]

Asundi, A.

J. Apolinar Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131–138 (2005).
[CrossRef]

Bin, Z.

W. Yuanbin, Z. Bin, and Y. Tianshun, “A linear and direct method for projective reconstruction,” in IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS, 2009), pp. 111–115.

Bing-hua, H.

H. Bing-hua, Z. Hu-long, and Y. Hui, “Measurement of aircraft attitude angles based on vanishing point theory,” J. Opt. A 33, 779–783 (2012).

Dai, X.

Greivenkamp, J. E.

Guodong, L.

W. Wenqian, L. Guodong, P. Zhaobang, and C. Shizhe, “Measurement of two-dimensional small angle by means of matrix CCD,” Semicond. Optoelectron. 25, 134–138 (2004).

Hartley, R.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000), pp. 585–587.

Hui, Y.

H. Bing-hua, Z. Hu-long, and Y. Hui, “Measurement of aircraft attitude angles based on vanishing point theory,” J. Opt. A 33, 779–783 (2012).

Hu-long, Z.

H. Bing-hua, Z. Hu-long, and Y. Hui, “Measurement of aircraft attitude angles based on vanishing point theory,” J. Opt. A 33, 779–783 (2012).

Jianbing, L.

L. Lichun, Y. Qifeng, L. Zhihui, and L. Jianbing, “High-accuracy measurement of rotation angle based on image,” Acta Opt. Sin. 25, 491–496 (2005).

Jianxun, L.

C. Xiao, L. Jianxun, and Z. Zhenfu, “Three-dimensional projective invariants of points from multiple images,” Opt. Eng. 47, 117203 (2008).
[CrossRef]

Jin, J.

Kanade, T.

T. Morita and T. Kanade, “A sequential factorization method for recovering shape and motion from image streams,” IEEE Trans. Patt. Anal. Mac Intel. 19, 858–867 (1997).

Khoroshun, A. N.

A. N. Khoroshun and D. N. Artsishevskii, “Determining small angles of beam splitter rotation in optical vortex shearing interferometer,” Tech. Phys. Lett. 36, 382–385 (2010).
[CrossRef]

Koch, R.

M. Pollefeys, R. Koch, and L. Van Gool, “Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters,” Int. J. Comput. Vis. 32, 7–25 (1999).
[CrossRef]

Li, B.

Li, W.

Li, X.

Lichun, L.

L. Lichun, Y. Qifeng, L. Zhihui, and L. Jianbing, “High-accuracy measurement of rotation angle based on image,” Acta Opt. Sin. 25, 491–496 (2005).

Morita, T.

T. Morita and T. Kanade, “A sequential factorization method for recovering shape and motion from image streams,” IEEE Trans. Patt. Anal. Mac Intel. 19, 858–867 (1997).

Pollefeys, M.

M. Pollefeys, R. Koch, and L. Van Gool, “Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters,” Int. J. Comput. Vis. 32, 7–25 (1999).
[CrossRef]

Qifeng, Y.

L. Lichun, Y. Qifeng, L. Zhihui, and L. Jianbing, “High-accuracy measurement of rotation angle based on image,” Acta Opt. Sin. 25, 491–496 (2005).

Ragab, M. E.

M. E. Ragab and K. H. Wong, “Rotation within camera projection matrix using Euler angles, quaternions, and angle-axes,” Int. J. Robot. Autom. 24, 312–318 (2009).

Rodriguez-Vera, R.

J. Apolinar Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131–138 (2005).
[CrossRef]

Sasaki, O.

Shizhe, C.

W. Wenqian, L. Guodong, P. Zhaobang, and C. Shizhe, “Measurement of two-dimensional small angle by means of matrix CCD,” Semicond. Optoelectron. 25, 134–138 (2004).

Sturm, P.

P. Sturm and B. Triggs, “A factorization based algorithm for multi-image projective structure and motion,” in Proceedings of Fourth European Conference on Computer Vision (ECCV, 1996), pp. 709–720.

Suzuki, T.

Tang, Z.

W. Wei, S. Wang, X. Zhang, and Z. Tang, “Estimation of image rotation angle using interpolation-related spectral signatures with application to blind detection of image forgery,” IEEE Trans. Inf. Forensics Security 5, 507–517 (2010).
[CrossRef]

Tianshun, Y.

W. Yuanbin, Z. Bin, and Y. Tianshun, “A linear and direct method for projective reconstruction,” in IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS, 2009), pp. 111–115.

Triggs, B.

P. Sturm and B. Triggs, “A factorization based algorithm for multi-image projective structure and motion,” in Proceedings of Fourth European Conference on Computer Vision (ECCV, 1996), pp. 709–720.

Van Gool, L.

M. Pollefeys, R. Koch, and L. Van Gool, “Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters,” Int. J. Comput. Vis. 32, 7–25 (1999).
[CrossRef]

Wang, S.

W. Wei, S. Wang, X. Zhang, and Z. Tang, “Estimation of image rotation angle using interpolation-related spectral signatures with application to blind detection of image forgery,” IEEE Trans. Inf. Forensics Security 5, 507–517 (2010).
[CrossRef]

Wei, W.

W. Wei, S. Wang, X. Zhang, and Z. Tang, “Estimation of image rotation angle using interpolation-related spectral signatures with application to blind detection of image forgery,” IEEE Trans. Inf. Forensics Security 5, 507–517 (2010).
[CrossRef]

Wenqian, W.

W. Wenqian, L. Guodong, P. Zhaobang, and C. Shizhe, “Measurement of two-dimensional small angle by means of matrix CCD,” Semicond. Optoelectron. 25, 134–138 (2004).

Wong, K. H.

M. E. Ragab and K. H. Wong, “Rotation within camera projection matrix using Euler angles, quaternions, and angle-axes,” Int. J. Robot. Autom. 24, 312–318 (2009).

Xiao, C.

C. Xiao, L. Jianxun, and Z. Zhenfu, “Three-dimensional projective invariants of points from multiple images,” Opt. Eng. 47, 117203 (2008).
[CrossRef]

Yuanbin, W.

W. Yuanbin, Z. Bin, and Y. Tianshun, “A linear and direct method for projective reconstruction,” in IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS, 2009), pp. 111–115.

Zhang, X.

W. Wei, S. Wang, X. Zhang, and Z. Tang, “Estimation of image rotation angle using interpolation-related spectral signatures with application to blind detection of image forgery,” IEEE Trans. Inf. Forensics Security 5, 507–517 (2010).
[CrossRef]

Zhaobang, P.

W. Wenqian, L. Guodong, P. Zhaobang, and C. Shizhe, “Measurement of two-dimensional small angle by means of matrix CCD,” Semicond. Optoelectron. 25, 134–138 (2004).

Zhenfu, Z.

C. Xiao, L. Jianxun, and Z. Zhenfu, “Three-dimensional projective invariants of points from multiple images,” Opt. Eng. 47, 117203 (2008).
[CrossRef]

Zhihui, L.

L. Lichun, Y. Qifeng, L. Zhihui, and L. Jianbing, “High-accuracy measurement of rotation angle based on image,” Acta Opt. Sin. 25, 491–496 (2005).

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000), pp. 585–587.

Acta Opt. Sin. (1)

L. Lichun, Y. Qifeng, L. Zhihui, and L. Jianbing, “High-accuracy measurement of rotation angle based on image,” Acta Opt. Sin. 25, 491–496 (2005).

Appl. Opt. (2)

IEEE Trans. Inf. Forensics Security (1)

W. Wei, S. Wang, X. Zhang, and Z. Tang, “Estimation of image rotation angle using interpolation-related spectral signatures with application to blind detection of image forgery,” IEEE Trans. Inf. Forensics Security 5, 507–517 (2010).
[CrossRef]

IEEE Trans. Patt. Anal. Mac Intel. (1)

T. Morita and T. Kanade, “A sequential factorization method for recovering shape and motion from image streams,” IEEE Trans. Patt. Anal. Mac Intel. 19, 858–867 (1997).

Int. J. Comput. Vis. (1)

M. Pollefeys, R. Koch, and L. Van Gool, “Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters,” Int. J. Comput. Vis. 32, 7–25 (1999).
[CrossRef]

Int. J. Robot. Autom. (1)

M. E. Ragab and K. H. Wong, “Rotation within camera projection matrix using Euler angles, quaternions, and angle-axes,” Int. J. Robot. Autom. 24, 312–318 (2009).

J. Opt. A (1)

H. Bing-hua, Z. Hu-long, and Y. Hui, “Measurement of aircraft attitude angles based on vanishing point theory,” J. Opt. A 33, 779–783 (2012).

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

C. Xiao, L. Jianxun, and Z. Zhenfu, “Three-dimensional projective invariants of points from multiple images,” Opt. Eng. 47, 117203 (2008).
[CrossRef]

Opt. Laser Technol. (1)

J. Apolinar Muñoz-Rodríguez, A. Asundi, and R. Rodriguez-Vera, “Recognition of a light line pattern by Hu moments for 3-D reconstruction of a rotated object,” Opt. Laser Technol. 37, 131–138 (2005).
[CrossRef]

Semicond. Optoelectron. (1)

W. Wenqian, L. Guodong, P. Zhaobang, and C. Shizhe, “Measurement of two-dimensional small angle by means of matrix CCD,” Semicond. Optoelectron. 25, 134–138 (2004).

Tech. Phys. Lett. (1)

A. N. Khoroshun and D. N. Artsishevskii, “Determining small angles of beam splitter rotation in optical vortex shearing interferometer,” Tech. Phys. Lett. 36, 382–385 (2010).
[CrossRef]

Other (3)

W. Yuanbin, Z. Bin, and Y. Tianshun, “A linear and direct method for projective reconstruction,” in IEEE International Conference on Intelligent Computing and Intelligent Systems (ICIS, 2009), pp. 111–115.

P. Sturm and B. Triggs, “A factorization based algorithm for multi-image projective structure and motion,” in Proceedings of Fourth European Conference on Computer Vision (ECCV, 1996), pp. 709–720.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision (Cambridge University, 2000), pp. 585–587.

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Figures (9)

Fig. 1.
Fig. 1.

Camera imaging model.

Fig. 2.
Fig. 2.

Sketch map of monocular vision measuring system.

Fig. 3.
Fig. 3.

Sketch map of the rigid object rotating in a space.

Fig. 4.
Fig. 4.

Rigid object clockwise rotates the angle of α around axis x.

Fig. 5.
Fig. 5.

Schematic of the spots array target.

Fig. 6.
Fig. 6.

Linear relationship between added random error and rotation angle measurement error.

Fig. 7.
Fig. 7.

Error of the rotation angle measurement from 0° to 360°.

Fig. 8.
Fig. 8.

Error of the rotation angle measurement from 0° to 5arcmin.

Fig. 9.
Fig. 9.

Comparative experiment of rotation angle measurement by the same CCD camera in Position 1 and Position 2.

Tables (3)

Tables Icon

Table 1. Measurement and Comparative Errors of Large Rotation Angles

Tables Icon

Table 2. Measurement and Comparative Errors of Small Rotation Angles

Tables Icon

Table 3. Standard Deviation of Measurement Errors by Different Methods

Equations (31)

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

λjixji=PiXj=K[Ri|ti]Xj,
[λ11x11λ21x21λn1xn1λ12x12λ22x22λn2xn2λ15x15λ25x25λn5xn5]=[P1P2P5][X1X2Xn].
W=PX
W=PpXp=PpHH1Xp.
Pe=PpH,
Xe=H1Xp,
PpiH=αiK[Ri|ti],
PpiHa=αiKRi.
HaTPpiT=αiRiTKT,
PpiMPpiT=PpiHaHaTPpiT=αi2KRiRiTKT=αi2KKT=αi2ω.
Dabi=c=14d=14PpaciPpbdiMcd(a,b=1,2,3).
{Dab1α12ωab=0Dab2α22ωab=0Dab5α52ωab=0(a,b=1,2,3;ba),
[Ppa11Ppb11Ppa41Ppb41ωab0Ppa15Ppb15Ppa45Ppb450ωab][M11M44α12α52]=Am=0.
M=U[σ10000σ20000σ30000σ4]VT,
M=U[σ10000σ20000σ300000]VT.
M=HaHaT=U[σ10000σ20000σ300000][σ10000σ20000σ300000]VT.
Ha=Ua[σ1000σ2000σ3].
M=HaQQTHaT.
PpiHaQ=αiKRi.
PpiH=αiK[100001000010]
Q=αi(PpiHa)1K,
Ppihb=[000].
[xyz]=[1000cosαsinα0sinαcosα][xyz]=Rα[xyz].
[xyz]=[cosβ0sinβ010sinβ0cosβ][xyz]=Rβ[xyz],
[xyz]=[cosγsinγ0sinγcosγ0001][xyz]=Rγ[xyz].
[xyz]=RαRβRγ[xyz]=R[xyz],
R=[cosβcosγcosβsinγsinβsinαsinβcosγcosαsinγsinαsinβsinγ+cosαcosγsinαcosβcosαsinβcosγ+sinαsinγcosαsinβsinγsinαcosγcosαcosβ].
X=RX,
R=XXT(XXT)1,
{α={arctan(R23/R33)arctan(R23/R33)+sign(R23)·πR330R33<0β=arcsin(R13)γ={arctan(R12/R11)arctan(R12/R11)+sign(R12)·πR110R11<0
Δθ=θmθth,

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