Abstract

We describe and characterize an experimental system to perform shape measurements on deformable objects using high-speed close-range photogrammetry. The eventual application is to extract the kinematics of several marked points on an insect wing during tethered and hovering flight. We investigate the performance of the system with a small number of views and determine an empirical relation between the mean pixel error of the optimization routine and the position error. Velocity and acceleration are calculated by numerical differencing, and their relation to the position errors is verified. For a field of view of 40mm×40mm, a rms accuracy of 30  μm in position, 150mm/s in velocity, and 750m/s 2 in acceleration at 5000  frames∕s is achieved. This accuracy is sufficient to measure the kinematics of hoverfly flight.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. B. Atkinson, ed., Close Range Photogrammetry and Machine Vision (Whittles, 1996).
  2. L. Zeng, H. Matsumoto, S. Sunada, and K. Kawachi, "High-resolution method for measuring the torsional deformation of a dragonfly wing by combining a displacement probe with an acousto-optic deflector," Opt. Eng. 35, 507-513 (1996).
    [CrossRef]
  3. L. Zeng, H. Matsumoto, and K. Kawachi, "A fringe shadow method for measuring flapping angle and torsional angle of a dragonfly wing," Meas. Sci. Technol. 7, 776-781 (1996).
    [CrossRef]
  4. L. Zeng, H. Matsumoto, and K. Kawachi, "Divergent-ray projection method for measuring the flapping angle, lag angle and torsional angle of a bumblebee wing," Opt. Eng. 35, 3135-3139 (1996).
    [CrossRef]
  5. A. P. Wilmot and C. P. Ellington, "Measuring the angle of attack of beating insect wings: robust three-dimensional reconstruction from two-dimensional images," J. Exp. Biol. 200, 2693-2704 (1997).
  6. D. Song, H. Wang, L. Zeng, and C. Yin, "Measuring the camber deformation of a dragonfly wing using projected comb fringe," Rev. Sci. Instrum. 72, 2450-2454 (2001).
    [CrossRef]
  7. H. Wang, L. Zeng, and C. Yin, "Measuring the body position, attitude and wing deformation of a free-flight dragonfly by combining a comb fringe pattern with sign points on the wing," Meas. Sci. Technol. 13, 903-908 (2002).
    [CrossRef]
  8. S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
    [CrossRef]
  9. R. I. Hartley, "Euclidean reconstruction from uncalibrated views," in Proceedings of the DARPA-ESPRIT workshop on Applications of Invariants in Computer Vision (Springer-Verlag, 1993), pp. 187-202.
  10. A. Watt and M. Watt, Advanced Animation and Rendering Techniques Theory and Practice (ACM, 1992).
  11. D. C. Brown, "Close range camera calibration," Photogramm. Eng. 37, 855-866 (1971).
  12. B. Triggs, P. McLauchlan, R. Hartley, and A. Fiztgibbon, "Bundle adjustment--a modern synthesis," in Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298-372.
  13. B. Girod, G. Greiner, and H. Niemann, eds., Principles of 3D Image Analysis and Synthesis (Kluwer Academic, 2000).
  14. N. J. Lawson and J. Wu, "Three-dimensional particle image velocimetry: error analysis of stereoscopic techniques," Meas. Sci. Technol. 8, 894-900 (1997).
    [CrossRef]

2002 (2)

H. Wang, L. Zeng, and C. Yin, "Measuring the body position, attitude and wing deformation of a free-flight dragonfly by combining a comb fringe pattern with sign points on the wing," Meas. Sci. Technol. 13, 903-908 (2002).
[CrossRef]

S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
[CrossRef]

2001 (1)

D. Song, H. Wang, L. Zeng, and C. Yin, "Measuring the camber deformation of a dragonfly wing using projected comb fringe," Rev. Sci. Instrum. 72, 2450-2454 (2001).
[CrossRef]

1997 (2)

A. P. Wilmot and C. P. Ellington, "Measuring the angle of attack of beating insect wings: robust three-dimensional reconstruction from two-dimensional images," J. Exp. Biol. 200, 2693-2704 (1997).

N. J. Lawson and J. Wu, "Three-dimensional particle image velocimetry: error analysis of stereoscopic techniques," Meas. Sci. Technol. 8, 894-900 (1997).
[CrossRef]

1996 (3)

L. Zeng, H. Matsumoto, S. Sunada, and K. Kawachi, "High-resolution method for measuring the torsional deformation of a dragonfly wing by combining a displacement probe with an acousto-optic deflector," Opt. Eng. 35, 507-513 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, and K. Kawachi, "A fringe shadow method for measuring flapping angle and torsional angle of a dragonfly wing," Meas. Sci. Technol. 7, 776-781 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, and K. Kawachi, "Divergent-ray projection method for measuring the flapping angle, lag angle and torsional angle of a bumblebee wing," Opt. Eng. 35, 3135-3139 (1996).
[CrossRef]

1971 (1)

D. C. Brown, "Close range camera calibration," Photogramm. Eng. 37, 855-866 (1971).

Atkinson, K. B.

K. B. Atkinson, ed., Close Range Photogrammetry and Machine Vision (Whittles, 1996).

Brown, D. C.

D. C. Brown, "Close range camera calibration," Photogramm. Eng. 37, 855-866 (1971).

Ellington, C. P.

A. P. Wilmot and C. P. Ellington, "Measuring the angle of attack of beating insect wings: robust three-dimensional reconstruction from two-dimensional images," J. Exp. Biol. 200, 2693-2704 (1997).

Fiztgibbon, A.

B. Triggs, P. McLauchlan, R. Hartley, and A. Fiztgibbon, "Bundle adjustment--a modern synthesis," in Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298-372.

Girod, B.

B. Girod, G. Greiner, and H. Niemann, eds., Principles of 3D Image Analysis and Synthesis (Kluwer Academic, 2000).

Greiner, G.

B. Girod, G. Greiner, and H. Niemann, eds., Principles of 3D Image Analysis and Synthesis (Kluwer Academic, 2000).

Hartley, R.

B. Triggs, P. McLauchlan, R. Hartley, and A. Fiztgibbon, "Bundle adjustment--a modern synthesis," in Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298-372.

Hartley, R. I.

R. I. Hartley, "Euclidean reconstruction from uncalibrated views," in Proceedings of the DARPA-ESPRIT workshop on Applications of Invariants in Computer Vision (Springer-Verlag, 1993), pp. 187-202.

Kawachi, K.

S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
[CrossRef]

L. Zeng, H. Matsumoto, and K. Kawachi, "Divergent-ray projection method for measuring the flapping angle, lag angle and torsional angle of a bumblebee wing," Opt. Eng. 35, 3135-3139 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, S. Sunada, and K. Kawachi, "High-resolution method for measuring the torsional deformation of a dragonfly wing by combining a displacement probe with an acousto-optic deflector," Opt. Eng. 35, 507-513 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, and K. Kawachi, "A fringe shadow method for measuring flapping angle and torsional angle of a dragonfly wing," Meas. Sci. Technol. 7, 776-781 (1996).
[CrossRef]

Lawson, N. J.

N. J. Lawson and J. Wu, "Three-dimensional particle image velocimetry: error analysis of stereoscopic techniques," Meas. Sci. Technol. 8, 894-900 (1997).
[CrossRef]

Matsumoto, H.

L. Zeng, H. Matsumoto, S. Sunada, and K. Kawachi, "High-resolution method for measuring the torsional deformation of a dragonfly wing by combining a displacement probe with an acousto-optic deflector," Opt. Eng. 35, 507-513 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, and K. Kawachi, "A fringe shadow method for measuring flapping angle and torsional angle of a dragonfly wing," Meas. Sci. Technol. 7, 776-781 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, and K. Kawachi, "Divergent-ray projection method for measuring the flapping angle, lag angle and torsional angle of a bumblebee wing," Opt. Eng. 35, 3135-3139 (1996).
[CrossRef]

McLauchlan, P.

B. Triggs, P. McLauchlan, R. Hartley, and A. Fiztgibbon, "Bundle adjustment--a modern synthesis," in Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298-372.

Meng, X.

S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
[CrossRef]

Niemann, H.

B. Girod, G. Greiner, and H. Niemann, eds., Principles of 3D Image Analysis and Synthesis (Kluwer Academic, 2000).

Song, D.

S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
[CrossRef]

D. Song, H. Wang, L. Zeng, and C. Yin, "Measuring the camber deformation of a dragonfly wing using projected comb fringe," Rev. Sci. Instrum. 72, 2450-2454 (2001).
[CrossRef]

Sunada, S.

S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
[CrossRef]

L. Zeng, H. Matsumoto, S. Sunada, and K. Kawachi, "High-resolution method for measuring the torsional deformation of a dragonfly wing by combining a displacement probe with an acousto-optic deflector," Opt. Eng. 35, 507-513 (1996).
[CrossRef]

Triggs, B.

B. Triggs, P. McLauchlan, R. Hartley, and A. Fiztgibbon, "Bundle adjustment--a modern synthesis," in Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298-372.

Wang, H.

S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
[CrossRef]

H. Wang, L. Zeng, and C. Yin, "Measuring the body position, attitude and wing deformation of a free-flight dragonfly by combining a comb fringe pattern with sign points on the wing," Meas. Sci. Technol. 13, 903-908 (2002).
[CrossRef]

D. Song, H. Wang, L. Zeng, and C. Yin, "Measuring the camber deformation of a dragonfly wing using projected comb fringe," Rev. Sci. Instrum. 72, 2450-2454 (2001).
[CrossRef]

Watt, A.

A. Watt and M. Watt, Advanced Animation and Rendering Techniques Theory and Practice (ACM, 1992).

Watt, M.

A. Watt and M. Watt, Advanced Animation and Rendering Techniques Theory and Practice (ACM, 1992).

Wilmot, A. P.

A. P. Wilmot and C. P. Ellington, "Measuring the angle of attack of beating insect wings: robust three-dimensional reconstruction from two-dimensional images," J. Exp. Biol. 200, 2693-2704 (1997).

Wu, J.

N. J. Lawson and J. Wu, "Three-dimensional particle image velocimetry: error analysis of stereoscopic techniques," Meas. Sci. Technol. 8, 894-900 (1997).
[CrossRef]

Yin, C.

H. Wang, L. Zeng, and C. Yin, "Measuring the body position, attitude and wing deformation of a free-flight dragonfly by combining a comb fringe pattern with sign points on the wing," Meas. Sci. Technol. 13, 903-908 (2002).
[CrossRef]

D. Song, H. Wang, L. Zeng, and C. Yin, "Measuring the camber deformation of a dragonfly wing using projected comb fringe," Rev. Sci. Instrum. 72, 2450-2454 (2001).
[CrossRef]

Zeng, L.

H. Wang, L. Zeng, and C. Yin, "Measuring the body position, attitude and wing deformation of a free-flight dragonfly by combining a comb fringe pattern with sign points on the wing," Meas. Sci. Technol. 13, 903-908 (2002).
[CrossRef]

S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
[CrossRef]

D. Song, H. Wang, L. Zeng, and C. Yin, "Measuring the camber deformation of a dragonfly wing using projected comb fringe," Rev. Sci. Instrum. 72, 2450-2454 (2001).
[CrossRef]

L. Zeng, H. Matsumoto, S. Sunada, and K. Kawachi, "High-resolution method for measuring the torsional deformation of a dragonfly wing by combining a displacement probe with an acousto-optic deflector," Opt. Eng. 35, 507-513 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, and K. Kawachi, "Divergent-ray projection method for measuring the flapping angle, lag angle and torsional angle of a bumblebee wing," Opt. Eng. 35, 3135-3139 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, and K. Kawachi, "A fringe shadow method for measuring flapping angle and torsional angle of a dragonfly wing," Meas. Sci. Technol. 7, 776-781 (1996).
[CrossRef]

J. Exp. Biol. (1)

A. P. Wilmot and C. P. Ellington, "Measuring the angle of attack of beating insect wings: robust three-dimensional reconstruction from two-dimensional images," J. Exp. Biol. 200, 2693-2704 (1997).

JSME Int. J. (1)

S. Sunada, D. Song, X. Meng, H. Wang, L. Zeng, and K. Kawachi, "Optical measurement of the deformation, motion and generated force of the wings of a moth, Mythima separata (Walker)," JSME Int. J. , Ser. B 45, 836-842 (2002).
[CrossRef]

Meas. Sci. Technol. (3)

L. Zeng, H. Matsumoto, and K. Kawachi, "A fringe shadow method for measuring flapping angle and torsional angle of a dragonfly wing," Meas. Sci. Technol. 7, 776-781 (1996).
[CrossRef]

H. Wang, L. Zeng, and C. Yin, "Measuring the body position, attitude and wing deformation of a free-flight dragonfly by combining a comb fringe pattern with sign points on the wing," Meas. Sci. Technol. 13, 903-908 (2002).
[CrossRef]

N. J. Lawson and J. Wu, "Three-dimensional particle image velocimetry: error analysis of stereoscopic techniques," Meas. Sci. Technol. 8, 894-900 (1997).
[CrossRef]

Opt. Eng. (2)

L. Zeng, H. Matsumoto, and K. Kawachi, "Divergent-ray projection method for measuring the flapping angle, lag angle and torsional angle of a bumblebee wing," Opt. Eng. 35, 3135-3139 (1996).
[CrossRef]

L. Zeng, H. Matsumoto, S. Sunada, and K. Kawachi, "High-resolution method for measuring the torsional deformation of a dragonfly wing by combining a displacement probe with an acousto-optic deflector," Opt. Eng. 35, 507-513 (1996).
[CrossRef]

Photogramm. Eng. (1)

D. C. Brown, "Close range camera calibration," Photogramm. Eng. 37, 855-866 (1971).

Rev. Sci. Instrum. (1)

D. Song, H. Wang, L. Zeng, and C. Yin, "Measuring the camber deformation of a dragonfly wing using projected comb fringe," Rev. Sci. Instrum. 72, 2450-2454 (2001).
[CrossRef]

Other (5)

R. I. Hartley, "Euclidean reconstruction from uncalibrated views," in Proceedings of the DARPA-ESPRIT workshop on Applications of Invariants in Computer Vision (Springer-Verlag, 1993), pp. 187-202.

A. Watt and M. Watt, Advanced Animation and Rendering Techniques Theory and Practice (ACM, 1992).

K. B. Atkinson, ed., Close Range Photogrammetry and Machine Vision (Whittles, 1996).

B. Triggs, P. McLauchlan, R. Hartley, and A. Fiztgibbon, "Bundle adjustment--a modern synthesis," in Vision Algorithms: Theory and Practice, Vol. 1883 of Lecture Notes in Computer Science, B. Triggs, A. Zisserman, and R. Szeliski, eds. (Springer, 2000), pp. 298-372.

B. Girod, G. Greiner, and H. Niemann, eds., Principles of 3D Image Analysis and Synthesis (Kluwer Academic, 2000).

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 (7)

Fig. 1
Fig. 1

Central perspective of projection model for camera i, viewing point j.

Fig. 2
Fig. 2

Schematic of experimental setup with laser illumination.

Fig. 3
Fig. 3

(a) Standard deviation of error for X (circles), Y (squares), and Z (triangles) directions. The solid curve shows empirical error based on MPE and the number of views. (b) MPE (squares) with ±1 standard deviation (SD) error bars. The solid curve shows an empirical curve 0.1 × (1−1∕N).

Fig. 4
Fig. 4

Calibration target spot Z height measured with white-light interferometer (squares), looking edge on to 26 × 6 measurement points. Static photogrammetry measurement (circles) calculated from four views.

Fig. 5
Fig. 5

Error between measured and nominal spot positions on Mylar calibration target, laser-illuminated dynamic photogrammetry using 14 images. (a) X, (b) Y, and (c) Z directions.

Fig. 6
Fig. 6

Error in (a) angular velocity and (b) normalized acceleration (angular velocity squared) relative to the nominal angular velocity of the Mylar calibration target, laser-illuminated dynamic photogrammetry using 14 images. Error in (c) angular velocity and (d) normalized acceleration relative to the nominal angular velocity after least-squares circle fit to spot trajectories.

Fig. 7
Fig. 7

Example image of a housefly wing taken under laser illumination.

Tables (2)

Tables Icon

Table 1 Standard Deviation of Errors in Position ( X , Y , Z ) Relative to the Nominal Calibration Target Position for a Mylar Target Mounted to an Optical Chopper

Tables Icon

Table 2 Standard Deviation of Errors in Position ( X , Y , Z ) Relative to the Mean Position for a Housefly Wing and Relative to the Nominal Position for a Glass Calibration Target

Equations (11)

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

x i , j = M i X O j , i = 1 , , m , j = 1 , , n ,
x i , j = z i m i , 11 X O j + m i , 12 Y O j + m i , 13 Z O j + m i , 14 m i , 31 XO j + m i , 32 Y O j + m i , 33 Z O j + m i , 34 ,
y i , j = z i m i , 21 X O j + m i , 22 Y O j + m i , 23 Z O j + m i , 24 m i , 31 X O j + m i , 32 Y O j + m i , 33 Z O j + m i , 34 .
K i = [ f x s f x p x 0 f y p y 0 0 1 ] ,
Δ x r = ( x / r ) ( k 1 r 3 + k 2 r 5 + k 3 r 7 + ) ,
Δ y r = ( y / r ) ( k 1 r 3 + k 2 r 5 + k 3 r 7 + ) ,
Δ x d = p 2 ( r 2 + 2 x 2 ) + 2 p 1 x y ,
Δ y d = p 1 ( r 2 + 2 y 2 ) + 2 p 2 x y ,
x i , j = f i ( C i , M i , X Oj ) ,
J T J δ = J T L ,
MPE = 1 m n i = 1 m j = 1 n L 2 .

Metrics