Abstract

A computer-based spatial-filtering velocimeter to measure the surface velocity of natural debris flow is described. This is a simple and interesting technique implemented with a spatial filter constructed as a software program that processes the video image of debris flow instead of a hardware implementation. The surface velocity of the debris flow at the Mt. Yakedake Volcano, Japan, was estimated by this computer-based spatial-filtering method, and the results were compared with those obtained by a hardware-based spatial-filtering method. Computer-based spatial filtering has the important advantage of a capability for tuning the spatial-filter parameters to the target flow.

© 1998 Optical Society of America

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  1. Y. Itakura, K. Ogawa, H. Suwa, K. Mizuhara, “Trends and fluctuations of the surface-velocity of debris flow measured by a non-contact speed sensor with a spatial filter,” in Proceedings of the International Symposium on Fluid Control and Measurement, M. Harada, ed. (Pergamon, New York, 1986), pp. 781–786.
  2. Y. Itakura, H. Suwa, “Measurement of surface velocity of debris flow by spatial filtering velocimetry,” in Proceedings of The Japan–China Symposium on Landslides and Debris Flows, (Japan Landslide Society, Tokyo, 1989), pp. 199–203.
  3. Y. Itakura, H. Inaba, M. Kasahara, “Measurement of surface velocity of natural turbulent flows by spatial filtering velocimetry,” in Proceedings of the XIII IMEKO World Congress, L. Benetazzo, S. Sartori, eds. (International Measurement Confederation Secretariat, Budapest, Hungary, 1994), pp. 2086–2091.
  4. J. T. Ator, “Image-velocity sensing with parallel-slit reticles,” J. Opt. Soc. Am 53, 1416–1422 (1963).
    [CrossRef]
  5. J. T. Ator, “Image velocity sensing by optical correlation,” Appl. Opt. 5, 1325–1331 (1966).
    [CrossRef] [PubMed]
  6. Y. Aizu, T. Asakura, “Principles and development of spatial filtering velocimetry,” Appl. Phys. B 43, 209–224 (1987).
    [CrossRef]
  7. B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
    [CrossRef]
  8. Y. Itakura, H. Suwa, M. Takeuchi, “Measurement of surface velocity of debris flows by spatial filtering velocimetry,” Trans. Soc. Instrum. Control Eng. 25, 504–506 (1989).
  9. Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Signal processing of spatial filtering velocimetry for turbulent flow,” in Proceedings of the 1989 International Symposium on Noise and Clutter Rejection in Radars and Imaging Sensors, T. Suzuki, H. Ogura, S. Fujimura, eds. (Institute of Electronics, Information and Communication Engineers, Tokyo, 1989), pp. 148–153.
  10. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 90–92.
  11. D. G. Childers, ed., Modern Spectrum Analysis (IEEE Press, Piscataway, N.J., 1978), pp. 23–118.
  12. H. Ogura, Y. Yoshida, “Spectral analysis and subtraction of noise in radar signals,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 62–71 (1981).
    [CrossRef]
  13. Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Spatial filtering velocimetry: computer simulation by the artificial random moving image and application to the measurement of the surface velocity of debris flow,” Trans. Soc. Instrum. Control Eng. 27, 1092–1098 (1991).
  14. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989), Chap. 4.
  15. A. V. Oppenheim, R. W. Schafer, Discrete Time Signal Processing, (Prentice-Hall, New Delhi, India, 1994), pp. 17–18.

1991

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Spatial filtering velocimetry: computer simulation by the artificial random moving image and application to the measurement of the surface velocity of debris flow,” Trans. Soc. Instrum. Control Eng. 27, 1092–1098 (1991).

1989

Y. Itakura, H. Suwa, M. Takeuchi, “Measurement of surface velocity of debris flows by spatial filtering velocimetry,” Trans. Soc. Instrum. Control Eng. 25, 504–506 (1989).

1987

Y. Aizu, T. Asakura, “Principles and development of spatial filtering velocimetry,” Appl. Phys. B 43, 209–224 (1987).
[CrossRef]

1981

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

H. Ogura, Y. Yoshida, “Spectral analysis and subtraction of noise in radar signals,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 62–71 (1981).
[CrossRef]

1966

1963

J. T. Ator, “Image-velocity sensing with parallel-slit reticles,” J. Opt. Soc. Am 53, 1416–1422 (1963).
[CrossRef]

Aizu, Y.

Y. Aizu, T. Asakura, “Principles and development of spatial filtering velocimetry,” Appl. Phys. B 43, 209–224 (1987).
[CrossRef]

Asakura, T.

Y. Aizu, T. Asakura, “Principles and development of spatial filtering velocimetry,” Appl. Phys. B 43, 209–224 (1987).
[CrossRef]

Ator, J. T.

J. T. Ator, “Image velocity sensing by optical correlation,” Appl. Opt. 5, 1325–1331 (1966).
[CrossRef] [PubMed]

J. T. Ator, “Image-velocity sensing with parallel-slit reticles,” J. Opt. Soc. Am 53, 1416–1422 (1963).
[CrossRef]

Horn, B. K. P.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

Inaba, H.

Y. Itakura, H. Inaba, M. Kasahara, “Measurement of surface velocity of natural turbulent flows by spatial filtering velocimetry,” in Proceedings of the XIII IMEKO World Congress, L. Benetazzo, S. Sartori, eds. (International Measurement Confederation Secretariat, Budapest, Hungary, 1994), pp. 2086–2091.

Itakura, Y.

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Spatial filtering velocimetry: computer simulation by the artificial random moving image and application to the measurement of the surface velocity of debris flow,” Trans. Soc. Instrum. Control Eng. 27, 1092–1098 (1991).

Y. Itakura, H. Suwa, M. Takeuchi, “Measurement of surface velocity of debris flows by spatial filtering velocimetry,” Trans. Soc. Instrum. Control Eng. 25, 504–506 (1989).

Y. Itakura, H. Inaba, M. Kasahara, “Measurement of surface velocity of natural turbulent flows by spatial filtering velocimetry,” in Proceedings of the XIII IMEKO World Congress, L. Benetazzo, S. Sartori, eds. (International Measurement Confederation Secretariat, Budapest, Hungary, 1994), pp. 2086–2091.

Y. Itakura, K. Ogawa, H. Suwa, K. Mizuhara, “Trends and fluctuations of the surface-velocity of debris flow measured by a non-contact speed sensor with a spatial filter,” in Proceedings of the International Symposium on Fluid Control and Measurement, M. Harada, ed. (Pergamon, New York, 1986), pp. 781–786.

Y. Itakura, H. Suwa, “Measurement of surface velocity of debris flow by spatial filtering velocimetry,” in Proceedings of The Japan–China Symposium on Landslides and Debris Flows, (Japan Landslide Society, Tokyo, 1989), pp. 199–203.

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Signal processing of spatial filtering velocimetry for turbulent flow,” in Proceedings of the 1989 International Symposium on Noise and Clutter Rejection in Radars and Imaging Sensors, T. Suzuki, H. Ogura, S. Fujimura, eds. (Institute of Electronics, Information and Communication Engineers, Tokyo, 1989), pp. 148–153.

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989), Chap. 4.

Kasahara, M.

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Spatial filtering velocimetry: computer simulation by the artificial random moving image and application to the measurement of the surface velocity of debris flow,” Trans. Soc. Instrum. Control Eng. 27, 1092–1098 (1991).

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Signal processing of spatial filtering velocimetry for turbulent flow,” in Proceedings of the 1989 International Symposium on Noise and Clutter Rejection in Radars and Imaging Sensors, T. Suzuki, H. Ogura, S. Fujimura, eds. (Institute of Electronics, Information and Communication Engineers, Tokyo, 1989), pp. 148–153.

Y. Itakura, H. Inaba, M. Kasahara, “Measurement of surface velocity of natural turbulent flows by spatial filtering velocimetry,” in Proceedings of the XIII IMEKO World Congress, L. Benetazzo, S. Sartori, eds. (International Measurement Confederation Secretariat, Budapest, Hungary, 1994), pp. 2086–2091.

Mizuhara, K.

Y. Itakura, K. Ogawa, H. Suwa, K. Mizuhara, “Trends and fluctuations of the surface-velocity of debris flow measured by a non-contact speed sensor with a spatial filter,” in Proceedings of the International Symposium on Fluid Control and Measurement, M. Harada, ed. (Pergamon, New York, 1986), pp. 781–786.

Ogawa, K.

Y. Itakura, K. Ogawa, H. Suwa, K. Mizuhara, “Trends and fluctuations of the surface-velocity of debris flow measured by a non-contact speed sensor with a spatial filter,” in Proceedings of the International Symposium on Fluid Control and Measurement, M. Harada, ed. (Pergamon, New York, 1986), pp. 781–786.

Ogura, H.

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Spatial filtering velocimetry: computer simulation by the artificial random moving image and application to the measurement of the surface velocity of debris flow,” Trans. Soc. Instrum. Control Eng. 27, 1092–1098 (1991).

H. Ogura, Y. Yoshida, “Spectral analysis and subtraction of noise in radar signals,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 62–71 (1981).
[CrossRef]

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Signal processing of spatial filtering velocimetry for turbulent flow,” in Proceedings of the 1989 International Symposium on Noise and Clutter Rejection in Radars and Imaging Sensors, T. Suzuki, H. Ogura, S. Fujimura, eds. (Institute of Electronics, Information and Communication Engineers, Tokyo, 1989), pp. 148–153.

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, Discrete Time Signal Processing, (Prentice-Hall, New Delhi, India, 1994), pp. 17–18.

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 90–92.

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, Discrete Time Signal Processing, (Prentice-Hall, New Delhi, India, 1994), pp. 17–18.

Schunck, B. G.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

Suwa, H.

Y. Itakura, H. Suwa, M. Takeuchi, “Measurement of surface velocity of debris flows by spatial filtering velocimetry,” Trans. Soc. Instrum. Control Eng. 25, 504–506 (1989).

Y. Itakura, K. Ogawa, H. Suwa, K. Mizuhara, “Trends and fluctuations of the surface-velocity of debris flow measured by a non-contact speed sensor with a spatial filter,” in Proceedings of the International Symposium on Fluid Control and Measurement, M. Harada, ed. (Pergamon, New York, 1986), pp. 781–786.

Y. Itakura, H. Suwa, “Measurement of surface velocity of debris flow by spatial filtering velocimetry,” in Proceedings of The Japan–China Symposium on Landslides and Debris Flows, (Japan Landslide Society, Tokyo, 1989), pp. 199–203.

Takeuchi, M.

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Spatial filtering velocimetry: computer simulation by the artificial random moving image and application to the measurement of the surface velocity of debris flow,” Trans. Soc. Instrum. Control Eng. 27, 1092–1098 (1991).

Y. Itakura, H. Suwa, M. Takeuchi, “Measurement of surface velocity of debris flows by spatial filtering velocimetry,” Trans. Soc. Instrum. Control Eng. 25, 504–506 (1989).

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Signal processing of spatial filtering velocimetry for turbulent flow,” in Proceedings of the 1989 International Symposium on Noise and Clutter Rejection in Radars and Imaging Sensors, T. Suzuki, H. Ogura, S. Fujimura, eds. (Institute of Electronics, Information and Communication Engineers, Tokyo, 1989), pp. 148–153.

Yoshida, Y.

H. Ogura, Y. Yoshida, “Spectral analysis and subtraction of noise in radar signals,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 62–71 (1981).
[CrossRef]

Appl. Opt.

Appl. Phys. B

Y. Aizu, T. Asakura, “Principles and development of spatial filtering velocimetry,” Appl. Phys. B 43, 209–224 (1987).
[CrossRef]

Artif. Intell.

B. K. P. Horn, B. G. Schunck, “Determining optical flow,” Artif. Intell. 17, 185–203 (1981).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

H. Ogura, Y. Yoshida, “Spectral analysis and subtraction of noise in radar signals,” IEEE Trans. Aerosp. Electron. Syst. AES-17, 62–71 (1981).
[CrossRef]

J. Opt. Soc. Am

J. T. Ator, “Image-velocity sensing with parallel-slit reticles,” J. Opt. Soc. Am 53, 1416–1422 (1963).
[CrossRef]

Trans. Soc. Instrum. Control Eng.

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Spatial filtering velocimetry: computer simulation by the artificial random moving image and application to the measurement of the surface velocity of debris flow,” Trans. Soc. Instrum. Control Eng. 27, 1092–1098 (1991).

Y. Itakura, H. Suwa, M. Takeuchi, “Measurement of surface velocity of debris flows by spatial filtering velocimetry,” Trans. Soc. Instrum. Control Eng. 25, 504–506 (1989).

Other

Y. Itakura, M. Takeuchi, M. Kasahara, H. Ogura, “Signal processing of spatial filtering velocimetry for turbulent flow,” in Proceedings of the 1989 International Symposium on Noise and Clutter Rejection in Radars and Imaging Sensors, T. Suzuki, H. Ogura, S. Fujimura, eds. (Institute of Electronics, Information and Communication Engineers, Tokyo, 1989), pp. 148–153.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 90–92.

D. G. Childers, ed., Modern Spectrum Analysis (IEEE Press, Piscataway, N.J., 1978), pp. 23–118.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989), Chap. 4.

A. V. Oppenheim, R. W. Schafer, Discrete Time Signal Processing, (Prentice-Hall, New Delhi, India, 1994), pp. 17–18.

Y. Itakura, K. Ogawa, H. Suwa, K. Mizuhara, “Trends and fluctuations of the surface-velocity of debris flow measured by a non-contact speed sensor with a spatial filter,” in Proceedings of the International Symposium on Fluid Control and Measurement, M. Harada, ed. (Pergamon, New York, 1986), pp. 781–786.

Y. Itakura, H. Suwa, “Measurement of surface velocity of debris flow by spatial filtering velocimetry,” in Proceedings of The Japan–China Symposium on Landslides and Debris Flows, (Japan Landslide Society, Tokyo, 1989), pp. 199–203.

Y. Itakura, H. Inaba, M. Kasahara, “Measurement of surface velocity of natural turbulent flows by spatial filtering velocimetry,” in Proceedings of the XIII IMEKO World Congress, L. Benetazzo, S. Sartori, eds. (International Measurement Confederation Secretariat, Budapest, Hungary, 1994), pp. 2086–2091.

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Figures (8)

Fig. 1
Fig. 1

Basic construction of spatial-filtering velocimetry system: AMP, amplifier.

Fig. 2
Fig. 2

Tripolar parallel-slit reticle.

Fig. 3
Fig. 3

Block diagram of the computer-based spatial-filtering system.

Fig. 4
Fig. 4

One frame of the digitized image of debris flow.

Fig. 5
Fig. 5

Filtering output signal for 45 image frames.

Fig. 6
Fig. 6

MEM spectrum obtained from the output signal of Fig. 5.

Fig. 7
Fig. 7

Surface velocity of the debris flow estimated with the computer-based spatial-filtering method for a filter size of (450, 128) pixels and N = 5.

Fig. 8
Fig. 8

Comparison of the estimated surface velocity of the debris flow after smoothing obtained by the computer-based method for a filter size of (450, 128) pixels and N = 5 and by the hardware-based spatial filtering method for a filter size (2, 0.9) m on the surface and N = 5.

Tables (1)

Tables Icon

Table 1 Smoothing Indices of Computer-Based Spatial-Filtering Velocimetry for Different Filter Sizes and Numbers of Parallel Slits for Smoothing-Window Lengths of 5 and 7

Equations (22)

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g t = C   - -   i x - Ω t ,   y r x ,   y d x d y ,
g t = C 4 π 2 - -   I u ,   v R - u ,   - v exp - ju Ω t d u d v ,
R u ,   v = AB   k = -   d k exp jk N π - π / 3 × sinc A u - ku 0 2 sinc Bv 2 ,
d k = 2 π k sin π k 2 cos π k 6 k 0 0 k = 0 .
g ( t ) = 2 3 π   CI ( u 0 ,   0 ) cos ( u 0 Ω t + N π - π / 3 ) , - A / 2 Ω t A / 2 Ω .
f 0 = u 0 Ω 2 π ,
V = af 0 H .
SI = 1 N s     V - V s 2 1 / 2 ,
r x ,   y = r a x + A 2 w A x w B y ,
r a x = r a x + ka ,     k = 0 ,   ± 1 ,   ± 2 ,   .
r a x = + 1     0 x a / 3 0       a / 3 x a / 2 ,     5 a / 6 x a - 1     a / 2 x 5 a / 6 .
w A x = + 1     - A / 2 x A / 2 0       otherwise ,
w B y = + 1     - B / 2 x B / 2 0       otherwise .
R u ,   v = AB   k = -   d k exp jk N π - π / 3 × sinc A u - ku 0 2 sinc Bv 2 ,
d k = 2 π k   sin π k 2 cos π k 6 k 0 0 k = 0 .
g t = CAB 4 π 2 k = -   d k exp jk N π - π / 3 × - -   I u ,   v exp - ju Ω t × sinc A u + ku 0 2 sinc Bv 2 d u d v .
sinc Bv 2     2 π B   δ v .
g t = CA 2 π k = -   d k exp jk N π - π / 3 × - I u ,   0 exp ( - ju Ω t ) sinc A u + ku 0 2 d u .
g t = CA 2 π k = -   d k exp jk u 0 Ω t + N π - π / 3 × I - ku 0 ,   0 - sinc A λ 2 exp - j λ Ω t d λ ,
- sinc A λ 2 exp - j λ Ω t d λ = 2 π A     - A / 2 π t A / 2 π 0       otherwise .
g t = C   k = -   d k I - ku 0 ,   0 exp jk u 0 Ω t + N π - π / 3 , - A / 2 Ω t A / 2 Ω .
g t = 2 3 π   CI u 0 ,   0 cos u 0 Ω t + N π - π / 3 ] , - A / 2 Ω t A / 2 Ω .

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