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Debris flow velocity estimation: A comparison between gradient-based method and cross-correlation method

Image Processing: Algorithms and Systems (Proceedings of SPIE Volumn4667) San Jose, CA, 2002; pp. 130-138

M. Shorif Uddin, H. Inaba, Y. Yoshida, and Y. Itakura

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Outline

Introduction Methods

Gradient-based method Cross-correlation method

Computer Simulation Debris Flow Velocity Estimation Conclusion

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Introduction

The surface velocity of debris flow is important to prevent disaster.

Some proposed methods Spatial-filtering method

Drawback: only 1D average velocity Gradient-based method (spatio-temporal deri

vative space method) Cross-correlation method

Gradient-based method and Cross-correlation method can estimate the field with detailed local variations.

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MethodsI. Gradient-based Method

f(x, y, t) is the brightness of a pixel whose spatial coordinates are (x,y) at time t.

(i,j: x, y, t)

(u,v) is the velocity of f(x, y, t)

t

ff

y

ff

x

ff tyx

,,

dxdydttyxftyxfS jiij ),,(),,(

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,),(xyyyxx

xxytxyxt

xyyyxx

yyxtxyyt

SSS

SSSS

SSS

SSSSvu

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MethodsI. Gradient-based Method

But the gradient-based method behaves poorly in the estimation of large motion…

Multiscale smoothing operation

The operation with a window Image area reduced by Image velocity reduced by s

ssw 2s

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MethodsI. Gradient-based Method (Multiscale Smoothing)

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MethodsII. Cross-correlation Method

The largest correlation value → the best match of the block

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Computer SimulationSynthetic Random Image

Image size: 128×64, moving velocity:(5, 0) (pixels/frame)

: spatial correlation, : temporal correlationaK bK

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=0.05

=0.05

Computer SimulationSynthetic Random Image

aK bK

aK

aK=0.05

=0.60

=0.30

=0.05

=0.30

=0.60

aK aKaK

bKbKbKbK

I II III IV

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Computer Simulationfor Gradient-based Method

Γ= 4 pixels × 4 pixels × 2 frames

aK=0.05

=0.05

=0.05

=0.60

=0.30

=0.05

=0.30

=0.60

aKaK

aK aK

bK

bK

bK

bK

I II

III IV

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Computer Simulationfor Cross-correlation Method

Block size: 8×8, search range:16×16

=0.05

=0.05

=0.30

=0.05

=0.05

=0.60

=0.30

=0.60

aKI II

III IV

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Computer SimulationDiscussion

When ↑, the accuracy of estimation↓ Computation time

Gradient-base method: Γ=m pixels × n pixels × 2 frames, the number of smoothing size = N, approximately needs multiplications

Cross-correlation method: block size p×q pixels, search range 2p×2q, needs 3× (p×q) ×(2p×2q) multiplications

For gradient-based method, (m×n)=(4×4) and N=8. For cross-correlation method, (p×q)=(8×8).

The number of multiplications of cross-correlation method is 4 times greater than that of gradient-based method.

)(6 22 nmN

bK

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Debris Flow Velocity Estimation

Debris flow occurred on 14 July 1993 at the Mt. Yakedake Volcano, Japan. (640×480 pixels)

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Debris Flow Velocity Estimation

Cross-correlation method,Mean:11.59 pixels/frameMode:12.00 pixels/frame

Gradient-based method,Mean:11.30 pixels/frameMode:13.50 pixels/frame

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Conclusions

We compared the performance of gradient-base method and cross-correlation method.

We performed a computer simulation with synthetic images and found that the accuracy of the cross-correlation method is higher than that of the gradient-based method.

The velocity field estimation results of a debris flow have been presented.