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Adaptive computer-based spatial -filtering method for more accurate estimation of the

surface velocity of debris flow

APPLIED OPTICS

M. Shorif, Hiroyuki Inaba, Yasumasa Itakura, Yasuo Yoshida, and Masao Kasahara

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Outline

• Introduction

• Sensor System– Principle– Adaptive Computer-Based Method

• Simulation Results

• Velocity Estimation Results of Debris Flow

• Conclusion

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Introduction

• Spatial-filtering velocimetry– Based on image-velocity sensing– Results of computer-based is better than hardware-based

• Repeatability• Analytical flexibility

• Hardware-based spatial filter– It is difficult to change the controllable parameters

• Computer-based spatial filter– Possible to change the filter parameters– Determination of the optimum parameters is a difficult problem…

• In this paper, we concentrated on an adaptive approach of the computer-based spatial-filtering that can adjust the filter parameters (the slit width of the filter).

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Sensor SystemA. Principle

Ω=V/HΩ: image velocityV: surface velocity of flowH: distance between the flow surface and sensor

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Sensor SystemA. Principle

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Sensor SystemA. Principle

• Time-varying output signal

• Equation(1) can be simplified as follows[1]:

– I(u,v) is the Fourier transform of i(x,y)– au /20

[1]. M. S. Uddin, H. Inaba, Y. Itakura, and M. Kasahara, “Estimation of the surface velocity of debris flow with computer-based spatial filtering,” Appl. Opt. 37, 6234-6239 (1998).

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Sensor SystemA. Principle

• The central frequency of output signal

• With Ω=V/H, Eq.(4) becomes

• The maximum-entropy method (MEM)[11][12] show high accuracy for extracting the central frequency from such noisy output signals.

[11]. D. G. Childers, ed., Modern Spectrum Analysis (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1978), pp. 23-118[12]. H. Ogura and Y. Yoshida, “Spectral analysis and subtraction of noise in radar signals,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 62-71 (1981).

00 2 fu

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Sensor SystemA. Principle

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Sensor SystemB. Adaptive Computer-Based Method• The slit width should be chosen to fit to the fundamental spatial frequenc

y of the debris flow’s surface brightness distribution.

• The size of the surface pattern of figs. (a)-(c) is larger than that of figs. (d)-(f)

• It is better to adjust the slit width matched with the pattern size of the flow surface.

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Sensor SystemB. Adaptive Computer-Based Method

• We try to calculate spatial correlation length...

• From the plot of R(k), the value of k when the normalized R(k) falls to (1/e)(=0.367), is treated as the correlation length.

K=5

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Sensor SystemB. Adaptive Computer-Based Method

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Simulation Results

• Two random moving images[16] with moving velocity 1 pixel/frame ( : spatial correlation, : temporal correlation, image size: 256×64)– =0.3, =0.03– =0.5, =0.03aK bK

aK

aK

bK

bK

[16]: Y. Yoshida, H. Ogura, and Y. Sakura, “method of random image synthesis by means of computer,”, Electron. Commun. Jpn. 65-A, 1-10 (1982).

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Simulation Results

• Normal computer-based spatial-filtering– filter height = 30

– the number of slits (N) = 5

– estimated the MEM every 45 frames

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Simulation Results

• Adaptive computer-based spatial-filtering (correlation rectangle:120×30)– If L<6 → a=6– If L>A/ → a=A/ ( =5)minNminNminN

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Simulation Results

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Velocity Estimation Results of Debris Flow

• The video images of a debris flow that occurred on 14 July 1993 at the Mt. Yakedake Volcano, Japan

• Correlation rectangle: 120×50• Filter size: 450×128

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Velocity Estimation Results of Debris Flow

• Rapid temporal fluctuations in the surface– The moving average method[17] with a smoothing

window length of 5

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1),,(

[17] A. V. Oppenheim and R. W. Schafer, Discrete-time Signal Processing(Prentice-Hall, New Delhi, India, 1994), pp. 17-18

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Conclusions

• We compare adaptive computer-based spatial-filtering, normal computer-based spatial-filtering, and hardware-based spatial-filtering in this paper.

• The adaptive method can be the most accurate because of its ability to adjust the filter parameters for tuning the spatial filter to the stochastic characteristics of the flow.

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Thank you!