Abstract

Fringe inverse videogrammetry based on global pose estimation is presented to measure a three- dimensional (3D) coordinate. The main components involve an LCD screen, a tactile probe equipped with a microcamera, and a portable personal computer. The LCD is utilized to display fringes, a microcamera is installed on the tactile probe, and the 3D coordinate of the center of the probe tip can be calculated through the microcamera’s pose. Fourier fringe analysis is exploited to complete subpixel location of reference points. A convex-relaxation optimization algorithm is employed to estimate the global camera pose, which guarantees global convergence compared with bundle adjustment, a local pose estimation algorithm. The experiments demonstrate that fringe inverse videogrammetry can measure the 3D coordinate precisely.

© 2011 Optical Society of America

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References

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    [CrossRef]
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2011

2010

T. Bothe, W. Li, M. Schulte, C. Von Kopylow, R. B. Bergmann, and W. P. P. Juptner, “Vision ray calibration for the quantitative geometric description of general imaging and projection optics in metrology,” Appl. Opt. 49, 5851–5860 (2010).
[CrossRef] [PubMed]

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48, 191–204 (2010).
[CrossRef]

S. Zhang, “Recent progress on real-time 3D shape measurement using digital fringe projection technique,” Opt. Lasers Eng. 48, 149–158 (2010).
[CrossRef]

J. Salvi, S. Fernandez, T. Pribanic, and X. Liado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recog. 43, 2666–2680 (2010).
[CrossRef]

T. Luhmann, “Close range photogrammetry for industrial applications,” ISPRS J. Photogramm. Remote Sensing 65, 558–569 (2010).
[CrossRef]

2009

R. I. Hartley and F. Kahl, “Global optimization through rotation space search,” Int. J. Comput. Vis. 82, 64–79(2009).
[CrossRef]

D. Henrion and J. B. Lasserre, “GloptiPoly 3: moment, optimization and semidefinite programming,” Optim. Meth. Software 24, 761–779 (2009).
[CrossRef]

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 31, 376–383 (2009).
[CrossRef]

T. Luhmann, “Precision potential of photogrammetric 6DOF pose estimation with a single camera,” ISPRS J. Photogramm. Remote Sensing 64, 275–284 (2009).
[CrossRef]

M. I. A. Lourakis and A. A. Argyros, “SBA: A software package for generic sparse bundle adjustment,” ACM Trans. Math. Softw. 36, 1–30 (2009).
[CrossRef]

Q. Yu, G. Jiang, S. Fu, Z. Chao, Y. Shang, and X. Sun, “Fold-ray videometrics method for the deformation measurement of nonintervisible large structures,” Appl. Opt. 48, 4683–4687(2009).
[CrossRef] [PubMed]

2008

2007

I. Markovsky and S. Van Huffel, “Overview of total least-square methods,” Signal Process. 87, 2283–2302 (2007).
[CrossRef]

2006

J. Zhu, Y. Li, and S. Ye, “Design and calibration of a single-camera-based stereo vision sensor,” Opt. Eng. 45083001, 2006.
[CrossRef]

G. Schweighofer and A. Pinz, “Robust pose estimation from a planar target,” IEEE Trans. Pattern Anal. Machine Intell. 28, 2024–2030 (2006).
[CrossRef]

L. D. Wallace, N. J. Lawson, A. R. Harvey, J. D. C. Jones, and A. J. Moore, “High-speed photogrammetry system for measuring the kinematics of insect wings,” Appl. Opt. 45, 4165–4173(2006).
[CrossRef] [PubMed]

2004

2001

X. Su and W. Chen, “Fourier transform profilometry: A review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

2000

C. P. Lu, G. Hager, and E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Machine Intell. 22, 610–620 (2000).
[CrossRef]

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

1994

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[CrossRef]

1992

J. Wen, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

1987

Argyros, A. A.

M. I. A. Lourakis and A. A. Argyros, “SBA: A software package for generic sparse bundle adjustment,” ACM Trans. Math. Softw. 36, 1–30 (2009).
[CrossRef]

Bergmann, R. B.

Bothe, T.

Chao, Z.

Chen, W.

S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008).
[CrossRef] [PubMed]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: A review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: A review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

Chihara, K.

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 31, 376–383 (2009).
[CrossRef]

Clarke, T. A.

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[CrossRef]

Cohen, P.

J. Wen, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Douxchamps, D.

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 31, 376–383 (2009).
[CrossRef]

Fernandez, S.

J. Salvi, S. Fernandez, T. Pribanic, and X. Liado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recog. 43, 2666–2680 (2010).
[CrossRef]

Fu, S.

Hager, G.

C. P. Lu, G. Hager, and E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Machine Intell. 22, 610–620 (2000).
[CrossRef]

Hartley, R. I.

R. I. Hartley and F. Kahl, “Global optimization through rotation space search,” Int. J. Comput. Vis. 82, 64–79(2009).
[CrossRef]

Harvey, A. R.

Hausler, G.

Heikkila, J.

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106–1112.

Henrion, D.

D. Henrion and J. B. Lasserre, “GloptiPoly 3: moment, optimization and semidefinite programming,” Optim. Meth. Software 24, 761–779 (2009).
[CrossRef]

Herniou, M.

J. Wen, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Horn, B. K. P.

Jiang, G.

Jing, H.

Jones, J. D. C.

Juptner, W. P. P.

Kahl, F.

R. I. Hartley and F. Kahl, “Global optimization through rotation space search,” Int. J. Comput. Vis. 82, 64–79(2009).
[CrossRef]

Knauer, M. C.

Lasserre, J. B.

D. Henrion and J. B. Lasserre, “GloptiPoly 3: moment, optimization and semidefinite programming,” Optim. Meth. Software 24, 761–779 (2009).
[CrossRef]

Lawson, N. J.

Leitz, K. H.

Li, A.

Li, S.

Li, W.

Li, Y.

B. Zhang and Y. Li, “Dynamic calibration of the relative pose and error analysis in a structured light system,” J. Opt. Soc. Am. A 25, 612–622 (2008).
[CrossRef]

J. Zhu, Y. Li, and S. Ye, “Design and calibration of a single-camera-based stereo vision sensor,” Opt. Eng. 45083001, 2006.
[CrossRef]

Liado, X.

J. Salvi, S. Fernandez, T. Pribanic, and X. Liado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recog. 43, 2666–2680 (2010).
[CrossRef]

Liu, X.

Liu, Y.

Lourakis, M. I. A.

M. I. A. Lourakis and A. A. Argyros, “SBA: A software package for generic sparse bundle adjustment,” ACM Trans. Math. Softw. 36, 1–30 (2009).
[CrossRef]

Lu, C. P.

C. P. Lu, G. Hager, and E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Machine Intell. 22, 610–620 (2000).
[CrossRef]

Luhmann, T.

T. Luhmann, “Close range photogrammetry for industrial applications,” ISPRS J. Photogramm. Remote Sensing 65, 558–569 (2010).
[CrossRef]

T. Luhmann, “Precision potential of photogrammetric 6DOF pose estimation with a single camera,” ISPRS J. Photogramm. Remote Sensing 64, 275–284 (2009).
[CrossRef]

Markovsky, I.

I. Markovsky and S. Van Huffel, “Overview of total least-square methods,” Signal Process. 87, 2283–2302 (2007).
[CrossRef]

Mjolsness, E.

C. P. Lu, G. Hager, and E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Machine Intell. 22, 610–620 (2000).
[CrossRef]

Moore, A. J.

Peng, X.

Pinz, A.

G. Schweighofer and A. Pinz, “Robust pose estimation from a planar target,” IEEE Trans. Pattern Anal. Machine Intell. 28, 2024–2030 (2006).
[CrossRef]

Pribanic, T.

J. Salvi, S. Fernandez, T. Pribanic, and X. Liado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recog. 43, 2666–2680 (2010).
[CrossRef]

Richter, C.

Salvi, J.

J. Salvi, S. Fernandez, T. Pribanic, and X. Liado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recog. 43, 2666–2680 (2010).
[CrossRef]

Schulte, M.

Schweighofer, G.

G. Schweighofer and A. Pinz, “Robust pose estimation from a planar target,” IEEE Trans. Pattern Anal. Machine Intell. 28, 2024–2030 (2006).
[CrossRef]

Shang, Y.

Short, T.

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[CrossRef]

Shortis, M. R.

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[CrossRef]

Silven, O.

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106–1112.

Su, X.

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48, 191–204 (2010).
[CrossRef]

Y. Tang, X. Su, Y. Liu, and H. Jing, “3D shape measurement of the aspheric mirror by advanced phase measuring deflectometry,” Opt. Express 16, 15090–15096 (2008).
[CrossRef] [PubMed]

S. Li, W. Chen, and X. Su, “Reliability-guided phase unwrapping in wavelet-transform profilometry,” Appl. Opt. 47, 3369–3377 (2008).
[CrossRef] [PubMed]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: A review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: A review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

Sun, X.

Tang, Y.

Van Huffel, S.

I. Markovsky and S. Van Huffel, “Overview of total least-square methods,” Signal Process. 87, 2283–2302 (2007).
[CrossRef]

Von Kopylow, C.

Wallace, L. D.

Wen, J.

J. Wen, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Ye, S.

J. Zhu, Y. Li, and S. Ye, “Design and calibration of a single-camera-based stereo vision sensor,” Opt. Eng. 45083001, 2006.
[CrossRef]

Yin, Y.

Yu, Q.

Zhang, B.

Zhang, Q.

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48, 191–204 (2010).
[CrossRef]

Zhang, S.

S. Zhang, “Recent progress on real-time 3D shape measurement using digital fringe projection technique,” Opt. Lasers Eng. 48, 149–158 (2010).
[CrossRef]

Zhang, X.

Zhang, Z.

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

Zhu, J.

J. Zhu, Y. Li, and S. Ye, “Design and calibration of a single-camera-based stereo vision sensor,” Opt. Eng. 45083001, 2006.
[CrossRef]

ACM Trans. Math. Softw.

M. I. A. Lourakis and A. A. Argyros, “SBA: A software package for generic sparse bundle adjustment,” ACM Trans. Math. Softw. 36, 1–30 (2009).
[CrossRef]

Appl. Opt.

IEEE Trans. Pattern Anal. Machine Intell.

J. Wen, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

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

C. P. Lu, G. Hager, and E. Mjolsness, “Fast and globally convergent pose estimation from video images,” IEEE Trans. Pattern Anal. Machine Intell. 22, 610–620 (2000).
[CrossRef]

D. Douxchamps and K. Chihara, “High-accuracy and robust localization of large control markers for geometric camera calibration,” IEEE Trans. Pattern Anal. Machine Intell. 31, 376–383 (2009).
[CrossRef]

G. Schweighofer and A. Pinz, “Robust pose estimation from a planar target,” IEEE Trans. Pattern Anal. Machine Intell. 28, 2024–2030 (2006).
[CrossRef]

Int. J. Comput. Vis.

R. I. Hartley and F. Kahl, “Global optimization through rotation space search,” Int. J. Comput. Vis. 82, 64–79(2009).
[CrossRef]

ISPRS J. Photogramm. Remote Sensing

T. Luhmann, “Close range photogrammetry for industrial applications,” ISPRS J. Photogramm. Remote Sensing 65, 558–569 (2010).
[CrossRef]

T. Luhmann, “Precision potential of photogrammetric 6DOF pose estimation with a single camera,” ISPRS J. Photogramm. Remote Sensing 64, 275–284 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

J. Zhu, Y. Li, and S. Ye, “Design and calibration of a single-camera-based stereo vision sensor,” Opt. Eng. 45083001, 2006.
[CrossRef]

Opt. Express

Opt. Lasers Eng.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: A review,” Opt. Lasers Eng. 42, 245–261 (2004).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: A review,” Opt. Lasers Eng. 35, 263–284 (2001).
[CrossRef]

X. Su and Q. Zhang, “Dynamic 3-D shape measurement method: A review,” Opt. Lasers Eng. 48, 191–204 (2010).
[CrossRef]

S. Zhang, “Recent progress on real-time 3D shape measurement using digital fringe projection technique,” Opt. Lasers Eng. 48, 149–158 (2010).
[CrossRef]

Opt. Lett.

Optim. Meth. Software

D. Henrion and J. B. Lasserre, “GloptiPoly 3: moment, optimization and semidefinite programming,” Optim. Meth. Software 24, 761–779 (2009).
[CrossRef]

Pattern Recog.

J. Salvi, S. Fernandez, T. Pribanic, and X. Liado, “A state of the art in structured light patterns for surface profilometry,” Pattern Recog. 43, 2666–2680 (2010).
[CrossRef]

Proc. SPIE

M. R. Shortis, T. A. Clarke, and T. Short, “Comparison of some techniques for the subpixel location of discrete target images,” Proc. SPIE 2350, 239–250 (1994).
[CrossRef]

Signal Process.

I. Markovsky and S. Van Huffel, “Overview of total least-square methods,” Signal Process. 87, 2283–2302 (2007).
[CrossRef]

Other

J. Heikkila and O. Silven, “A four-step camera calibration procedure with implicit image correction,” in IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 1997), pp. 1106–1112.

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Figures (11)

Fig. 1
Fig. 1

Principle of traditional tactile probing system.

Fig. 2
Fig. 2

Schematic diagram of fringe inverse videogrammetry.

Fig. 3
Fig. 3

The process of fringe inverse videogrammetry.

Fig. 4
Fig. 4

The wrapped phase distribution in one direction.

Fig. 5
Fig. 5

Imaging model of central perspective projection.

Fig. 6
Fig. 6

The robustness of global pose estimation to noise. (a) The robustness of rotation matrix to noise. (b) The robustness of translation vector to noise.

Fig. 7
Fig. 7

The comparison of runtime.

Fig. 8
Fig. 8

(a) One of fringes used for camera calibration. (b) The reference points corresponding to (a).

Fig. 9
Fig. 9

Six fringes for probe calibration.

Fig. 10
Fig. 10

The label of measurement.

Fig. 11
Fig. 11

The repeatability of measurement results. (a) x direction, (b) y direction, (c) z direction.

Tables (2)

Tables Icon

Table 1 Results of Camera Calibration (Pixel)

Tables Icon

Table 2 Error Comparisons Using Linear Solution, Bundle Adjustment, and Global Pose Estimation/mm

Equations (20)

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

I ( x , y ) = a + b 1 cos [ 2 π x f x + φ x 0 ( x , y ) ] + b 2 cos [ 2 π y f y + φ y 0 ( x , y ) ] ,
I ( u , v ) = a ( u , v ) + b 1 ( u , v ) cos [ φ u ( u , v ) ] + b 2 ( u , v ) cos [ φ v ( u , v ) ] ,
{ u = g 0 + g 1 φ w u ( u , v ) + g 2 φ w v ( u , v ) v = j 0 + j 1 φ w u ( u , v ) + j 2 φ w v ( u , v ) .
{ u f = u r + round ( w / 2 ) + 1 + g 0 v f = v r + round ( w / 2 ) + 1 + j 0 .
λ [ x ˜ y ˜ 1 ] = K [ R T ] [ X Y 1 ] ,
δ x = k 1 r d 2 + k 2 r d 4 + k 5 r d 6 + 2 k 3 x d y d + k 4 ( r d 2 + 2 x d 2 ) δ y = k 1 r d 2 + k 2 r d 4 + k 5 r d 6 + k 3 ( r d 2 + 2 y d 2 ) + 2 k 4 x d y d ,
q i = R p i + T ,
E i s = i = 1 n [ ( u i R p i + t x R p i + t z ) 2 + ( v i R p i + t y R p i + t z ) 2 ]
E o s ( R , T ) = i = 1 n [ I V i ] [ R p i + T ] 2 V i = υ i υ i T υ i T υ i .
Δ χ ( R , T ) = [ J T J ] 1 J T χ ( R , T ) .
T opt = Λ 1 ( i = 1 n Λ i R p i ) 1 .
E o s ( R ) = i = 1 n Λ i Q i p i 2 = p i T ( i = 1 n Q i T Λ i T Λ i Q i ) p i ,
R = ( q 1 2 + q 2 2 q 3 2 q 4 2 2 ( q 2 q 3 + q 1 q 4 ) 2 ( q 2 q 4 q 1 q 3 ) 2 ( q 2 q 3 q 1 q 4 ) q 1 2 q 2 2 + q 3 2 q 4 2 2 ( q 3 q 4 + q 1 q 2 ) 2 ( q 2 q 4 + q 1 q 3 ) 2 ( q 3 q 4 q 1 q 2 ) q 1 2 q 2 2 q 3 2 q 4 2 ) .
R p i = G i e , G i = ( X i 0 2 Z i 2 Y i X i 2 Y i 2 Z i X i 0 X i Y i 2 Z i 0 2 X i Y i 2 X i 0 Y i 2 Z i Y i Z i 2 Y i 2 X i 0 Z i 0 2 X i Z i 2 Y i Z i ) .
E o s ( e ) = e T ( i = 1 n M i T Λ i T Λ i M i ) e ,
min E ( e ) Subject to     q 1 2 + q 2 2 + q 3 2 + q 4 2 = 1 , q 1 > 0.
E _ R ( % ) = R _ true R / R _ true E _ trans ( % ) = T _ true T / T _ true .
[ X c n , Y c n , Z c n ] T = R n 1 T n .
A O 0 = b , [ X c 2 X c 1 Y c 2 Y c 1 Z c 2 Z c 1 X c 3 X c 2 Y c 3 Y c 2 Z c 3 Z c 2 X c n X c ( n 1 ) Y c n Y c ( n 1 ) Z c n Z c ( n 1 ) ] = A , 1 2 [ ( X c 2 2 + Y c 2 2 + Z c 2 2 ) ( X c 1 2 + Y c 1 2 + Z c 1 2 ) ( X c 3 2 + Y c 3 2 + Z c 3 2 ) ( X c 2 2 + Y c 2 2 + Z c 2 2 ) ( X c n 2 + Y c n 2 + Z c n 2 ) ( X c ( n 1 ) 2 + Y c ( n 1 ) 2 + Z c ( n 1 ) 2 ) ] = b .
R [ X w , Y w , Z w ] T + T = [ X c , Y c , Z c ] T .

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