Abstract

The successful application of a recurrent neural network of the Hopfield type to the solution of the stereo image-pair reconciliation problem in stereoscopic particle image velocimetry (PIV) in the tracking mode is described. The results of applying the network to both virtual-flow and physical-flow PIV data sets are presented, and the usefulness of this novel approach to PIV stereo image analysis is demonstrated. A partner-particle image-pair density (PPID) parameter is defined as the average number of potential particle image-pair candidates in the search window in the second view corresponding to a single image pair in the first view. A quantitative assessment of the performance of the method is then made from groups of 100 synthetic flow images at various values of the PPID. The successful pairing of complementary image points is shown to vary from 100% at a PPID of 1 and to remain greater than 97% successful for PPID’s up to 5. The application of the method to a hydraulic flow is also described, with in-line stereo images presented, and the application of the neural-matching method is demonstrated for a typical data set.

© 1998 Optical Society of America

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References

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  1. I. Grant, Selected Papers on PIV, Vol. MS99 of the SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1994).
  2. I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mechan. Eng. Part C 211, 55–76 (1997).
    [CrossRef]
  3. I. Grant and A. Liu, “Method for the efficient incoherent analysis of particle image velocimetry images” (reprinted in Ref. 1), Appl. Opt. 28, 1745–1748 (1989).
  4. I. Grant and X. Pan, “An investigation of the performance of multi layer neural networks applied to the analysis of PIV images,” Exp. Fluids 19, 159–166 (1995).
    [CrossRef]
  5. I. Grant and X. Pan, “The use of neural techniques in PIV and PTV,” Meas. Sci. Technol. 8, 1399–1405 (1997).
    [CrossRef]
  6. I. Grant, Y. Zhao, Y. Tan, and J. N. Stewart, “Three component flow mapping: experiences in stereoscopic PIV and holographic velocimetry,” in Proceedings of the Fourth International Conference on Laser Anemometry, Advances and Applications (reprinted in Ref. 1) (American Society of Mechanical Engineers, New York, 1991), pp. 368–371.
  7. K. D. Hinsch, “Three-dimensional particle image velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
    [CrossRef]
  8. I. Grant, S. Fu, X. Pan, and X. Wang, “The application of an in-line, stereoscopic, PIV system to 3-component velocity measurement,” Exp. Fluids 19, 214–222 (1995).
    [CrossRef]
  9. X. Pan, “Advanced technology applied to PIV measurement,” Ph.D. dissertation (Heriot-Watt University, Edinburgh, Scotland, 1996).
  10. 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. Robotics Automat. 3, 323–344 (1987).
    [CrossRef]
  11. N. M. Nasrabadi and Y. C. Chang, “Hopfield network for stereo vision correspondence,” IEEE Trans. Neural Networks 3, 5–13 (1992).
    [CrossRef]
  12. I. Grant, X. Pan, X. Wang, and J. N. Stewart, “Correction for viewing angle applied to PIV data obtained in aerodynamic blade vortex interaction studies,” Exp. Fluids 17, 95–99 (1994).

1997 (2)

I. Grant and X. Pan, “The use of neural techniques in PIV and PTV,” Meas. Sci. Technol. 8, 1399–1405 (1997).
[CrossRef]

I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mechan. Eng. Part C 211, 55–76 (1997).
[CrossRef]

1995 (3)

I. Grant and X. Pan, “An investigation of the performance of multi layer neural networks applied to the analysis of PIV images,” Exp. Fluids 19, 159–166 (1995).
[CrossRef]

K. D. Hinsch, “Three-dimensional particle image velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
[CrossRef]

I. Grant, S. Fu, X. Pan, and X. Wang, “The application of an in-line, stereoscopic, PIV system to 3-component velocity measurement,” Exp. Fluids 19, 214–222 (1995).
[CrossRef]

1994 (1)

I. Grant, X. Pan, X. Wang, and J. N. Stewart, “Correction for viewing angle applied to PIV data obtained in aerodynamic blade vortex interaction studies,” Exp. Fluids 17, 95–99 (1994).

1992 (1)

N. M. Nasrabadi and Y. C. Chang, “Hopfield network for stereo vision correspondence,” IEEE Trans. Neural Networks 3, 5–13 (1992).
[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. Robotics Automat. 3, 323–344 (1987).
[CrossRef]

Chang, Y. C.

N. M. Nasrabadi and Y. C. Chang, “Hopfield network for stereo vision correspondence,” IEEE Trans. Neural Networks 3, 5–13 (1992).
[CrossRef]

Fu, S.

I. Grant, S. Fu, X. Pan, and X. Wang, “The application of an in-line, stereoscopic, PIV system to 3-component velocity measurement,” Exp. Fluids 19, 214–222 (1995).
[CrossRef]

Grant, I.

I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mechan. Eng. Part C 211, 55–76 (1997).
[CrossRef]

I. Grant and X. Pan, “The use of neural techniques in PIV and PTV,” Meas. Sci. Technol. 8, 1399–1405 (1997).
[CrossRef]

I. Grant and X. Pan, “An investigation of the performance of multi layer neural networks applied to the analysis of PIV images,” Exp. Fluids 19, 159–166 (1995).
[CrossRef]

I. Grant, S. Fu, X. Pan, and X. Wang, “The application of an in-line, stereoscopic, PIV system to 3-component velocity measurement,” Exp. Fluids 19, 214–222 (1995).
[CrossRef]

I. Grant, X. Pan, X. Wang, and J. N. Stewart, “Correction for viewing angle applied to PIV data obtained in aerodynamic blade vortex interaction studies,” Exp. Fluids 17, 95–99 (1994).

I. Grant, Y. Zhao, Y. Tan, and J. N. Stewart, “Three component flow mapping: experiences in stereoscopic PIV and holographic velocimetry,” in Proceedings of the Fourth International Conference on Laser Anemometry, Advances and Applications (reprinted in Ref. 1) (American Society of Mechanical Engineers, New York, 1991), pp. 368–371.

Hinsch, K. D.

K. D. Hinsch, “Three-dimensional particle image velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
[CrossRef]

Nasrabadi, N. M.

N. M. Nasrabadi and Y. C. Chang, “Hopfield network for stereo vision correspondence,” IEEE Trans. Neural Networks 3, 5–13 (1992).
[CrossRef]

Pan, X.

I. Grant and X. Pan, “The use of neural techniques in PIV and PTV,” Meas. Sci. Technol. 8, 1399–1405 (1997).
[CrossRef]

I. Grant and X. Pan, “An investigation of the performance of multi layer neural networks applied to the analysis of PIV images,” Exp. Fluids 19, 159–166 (1995).
[CrossRef]

I. Grant, S. Fu, X. Pan, and X. Wang, “The application of an in-line, stereoscopic, PIV system to 3-component velocity measurement,” Exp. Fluids 19, 214–222 (1995).
[CrossRef]

I. Grant, X. Pan, X. Wang, and J. N. Stewart, “Correction for viewing angle applied to PIV data obtained in aerodynamic blade vortex interaction studies,” Exp. Fluids 17, 95–99 (1994).

Stewart, J. N.

I. Grant, X. Pan, X. Wang, and J. N. Stewart, “Correction for viewing angle applied to PIV data obtained in aerodynamic blade vortex interaction studies,” Exp. Fluids 17, 95–99 (1994).

I. Grant, Y. Zhao, Y. Tan, and J. N. Stewart, “Three component flow mapping: experiences in stereoscopic PIV and holographic velocimetry,” in Proceedings of the Fourth International Conference on Laser Anemometry, Advances and Applications (reprinted in Ref. 1) (American Society of Mechanical Engineers, New York, 1991), pp. 368–371.

Tan, Y.

I. Grant, Y. Zhao, Y. Tan, and J. N. Stewart, “Three component flow mapping: experiences in stereoscopic PIV and holographic velocimetry,” in Proceedings of the Fourth International Conference on Laser Anemometry, Advances and Applications (reprinted in Ref. 1) (American Society of Mechanical Engineers, New York, 1991), pp. 368–371.

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. Robotics Automat. 3, 323–344 (1987).
[CrossRef]

Wang, X.

I. Grant, S. Fu, X. Pan, and X. Wang, “The application of an in-line, stereoscopic, PIV system to 3-component velocity measurement,” Exp. Fluids 19, 214–222 (1995).
[CrossRef]

I. Grant, X. Pan, X. Wang, and J. N. Stewart, “Correction for viewing angle applied to PIV data obtained in aerodynamic blade vortex interaction studies,” Exp. Fluids 17, 95–99 (1994).

Zhao, Y.

I. Grant, Y. Zhao, Y. Tan, and J. N. Stewart, “Three component flow mapping: experiences in stereoscopic PIV and holographic velocimetry,” in Proceedings of the Fourth International Conference on Laser Anemometry, Advances and Applications (reprinted in Ref. 1) (American Society of Mechanical Engineers, New York, 1991), pp. 368–371.

Exp. Fluids (3)

I. Grant and X. Pan, “An investigation of the performance of multi layer neural networks applied to the analysis of PIV images,” Exp. Fluids 19, 159–166 (1995).
[CrossRef]

I. Grant, S. Fu, X. Pan, and X. Wang, “The application of an in-line, stereoscopic, PIV system to 3-component velocity measurement,” Exp. Fluids 19, 214–222 (1995).
[CrossRef]

I. Grant, X. Pan, X. Wang, and J. N. Stewart, “Correction for viewing angle applied to PIV data obtained in aerodynamic blade vortex interaction studies,” Exp. Fluids 17, 95–99 (1994).

IEEE J. Robotics 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. Robotics Automat. 3, 323–344 (1987).
[CrossRef]

IEEE Trans. Neural Networks (1)

N. M. Nasrabadi and Y. C. Chang, “Hopfield network for stereo vision correspondence,” IEEE Trans. Neural Networks 3, 5–13 (1992).
[CrossRef]

Meas. Sci. Technol. (2)

K. D. Hinsch, “Three-dimensional particle image velocimetry,” Meas. Sci. Technol. 6, 742–753 (1995).
[CrossRef]

I. Grant and X. Pan, “The use of neural techniques in PIV and PTV,” Meas. Sci. Technol. 8, 1399–1405 (1997).
[CrossRef]

Proc. Inst. Mechan. Eng. Part C (1)

I. Grant, “Particle image velocimetry: a review,” Proc. Inst. Mechan. Eng. Part C 211, 55–76 (1997).
[CrossRef]

Other (4)

I. Grant and A. Liu, “Method for the efficient incoherent analysis of particle image velocimetry images” (reprinted in Ref. 1), Appl. Opt. 28, 1745–1748 (1989).

I. Grant, Y. Zhao, Y. Tan, and J. N. Stewart, “Three component flow mapping: experiences in stereoscopic PIV and holographic velocimetry,” in Proceedings of the Fourth International Conference on Laser Anemometry, Advances and Applications (reprinted in Ref. 1) (American Society of Mechanical Engineers, New York, 1991), pp. 368–371.

I. Grant, Selected Papers on PIV, Vol. MS99 of the SPIE Milestone Series (SPIE Press, Bellingham, Wash., 1994).

X. Pan, “Advanced technology applied to PIV measurement,” Ph.D. dissertation (Heriot-Watt University, Edinburgh, Scotland, 1996).

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Figures (10)

Fig. 1
Fig. 1

Axial stereogrammetry system applied in digital PIV hydraulic-flow studies.

Fig. 2
Fig. 2

Ray-diagram representation of the geometry of the axial stereo model.

Fig. 3
Fig. 3

Schematic representation of neuron interconnectivity in a Hopfield network.

Fig. 4
Fig. 4

Form of the sigmoidal function representing the interneuron synaptic weights.

Fig. 5
Fig. 5

Superposition of the two experimental views from the axial stereogrammetry system.

Fig. 6
Fig. 6

Example of neuron output values at the initial and the final stages of calculation.

Fig. 7
Fig. 7

Example images obtained in the flow simulation: (a) Image from the front camera. (b) Image from the back camera.

Fig. 8
Fig. 8

Image-matching success ratio as a function of the PPID.

Fig. 9
Fig. 9

Two image pairs obtained from the hydraulic-flow experiment: (a), (c) Images obtained from the front camera. (b), (d) Images obtained from the back camera.

Fig. 10
Fig. 10

Example of perspective reconstruction of the flow from experimental data: (a) Front view. (b) Side view. (c) Top view.

Equations (16)

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r B i B = R Z + d , r F i F = R Z , α 1 = α 2 = α ,
A u = b ,
A = r 31 X 1 - r 11 f r 32 X 1 - r 12 f r 33 X 1 - r 13 f r 31 Y 1 - r 21 f r 32 Y 1 - r 22 f r 33 Y 1 - r 23 f r 31 X 2 - r 11 f r 32 X 2 - r 12 f r 33 X 2 - r 13 f r 31 Y 2 - r 21 f r 32 Y 2 - r 22 f r 33 Y 2 - r 23 f , u = x w y w z w , b = t x f - t z X 1 t y f - t z Y 1 t x f - t z X 2 t y f - t z Y 2 ,
u = A T A - 1 A T b .
ν i t = j = 1 N   w ij x j t - I i ,
x i t + 1 = sgn ν i t = 1 ν i t > 0 0 ν i t < 0 x i t ν i t = 0 .
w ij = μ = 1 N   z i μ z j μ ,
x i t + 1 = f ν i t = f j = 1 N   w ij x j t - I i ,
E = - 1 2 i = 1 N j = 1 N   w ij x i x j - i = 1 N   I i x i ,
Δ E = - j = 1 N   w ij x j - I i Δ x i .
E = - i = 1 N 1 k = 1 N 2 j = 1 N 1 l = 1 N 2   c ikjl p ik p jl - i = 1 N 1 1 - k = 1 N 2   P ik 2 + k = 1 N 1 1 - i = 1 N 2   p ik 2 .
E = - 1 2 i = 1 N 1 k = 1 N 2 j = 1 N 1 l = 1 N 2 c ikjl - δ ij - δ kl p ik p jl - i = 1 N 1 k = 1 N 2   2 p ik ,
C ikjl = 2 1 + exp Δ d - θ - 1 ,
Δ d = w | Δ r ik - Δ r jl | + nw 2 | Δ α ik - Δ α jl | = w 1 Δ d 1 + nw 2 Δ d 2 .
r B = r F i B i F Z Z + d .
r B max = r F i B i F Z max Z max + d ,     r B min = r F i B i F Z min x Z min + d .

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