1. 1 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

2. 2 Outline  Introduction  Methods Gradient-based method Cross-correlation method  Computer Simulation  Debris Flow Velocity Estimation  Conclusion

3. 3 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 derivative space method) Cross-correlation method  Gradient-based method and Cross- correlation method can estimate the field with detailed local variations.

4. 4 Methods I. 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)

5. 5 Methods I. 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

6. 6 Methods I. Gradient-based Method (Multiscale Smoothing)

7. 7 Methods II. Cross-correlation Method  The largest correlation value → the best match of the block

8. 8 Computer Simulation Synthetic Random Image  Image size: 128×64, moving velocity:(5, 0) (pixels/frame)  : spatial correlation, : temporal correlation

9. 9 =0.05 Computer Simulation Synthetic Random Image =0.05 =0.60 =0.30 =0.05 =0.30 =0.60 IIIIIIIV

10. 10 Computer Simulation for Gradient-based Method  Γ= 4 pixels × 4 pixels × 2 frames =0.05 =0.60 =0.30 =0.05 =0.30 =0.60 III IIIIV

11. 11 Computer Simulation for Cross-correlation Method  Block size: 8×8, search range:16×16 =0.05 =0.30 =0.05 =0.60 =0.30 =0.60 I II III IV

12. 12 Computer Simulation Discussion  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.

13. 13 Debris Flow Velocity Estimation  Debris flow occurred on 14 July 1993 at the Mt. Yakedake Volcano, Japan. (640×480 pixels)

14. 14 Debris Flow Velocity Estimation Cross-correlation method, Mean:11.59 pixels/frame Mode:12.00 pixels/frame Gradient-based method, Mean:11.30 pixels/frame Mode:13.50 pixels/frame

15. 15 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.