1 Surface Velocity Computation of Debris Flows by Vector Field Measurements Physics and Chemistry of the Earth H. Inaba, Y. Itakura and M.Kasahara

2 Outline Introduction Spatio Temporal Derivative Space Method Multi Resolution STDSM Results for Debris Flow Videos Conclusions

3 Introduction The surface velocity of natural debris flow is one of the main physical parameters for developing effective disaster prevention techniques. Surface velocity –Many remote sensing measurement methods, EX: spatial filtering, laser-Doppler, etc. Velocity vector field –Spatio Temporal Derivative Space Method (STDSM) We propose a multi resolution STDSM here…

4 Spatio Temporal Derivative Space Method f(x, y, t) –Luminance of a pixel –(x, y) : spatial coordinates –t : time –(u, v) : its velocity – Constant intensity assumption

5 Spatio Temporal Derivative Space Method –Γ: the neighborhood of an observation point –(i, j : x, y, t) It can be proved that –det(S) = 0 In the real measurement, the determinant of S is not exactly zero for the turbulence of noice

6 Spatio Temporal Derivative Space Method We assume that each of the derivatives of J for u and v are equal to zero –

7 Multi Resolution STDSM A. Error Index of STDSM When small, accuracy of velocity vector is low Error index (in Ando 1986) – : minimized value of J – ∣ Γ ∣ : the number of pixels included in Γ The error index is a little modified as follows:

8 Multi Resolution STDSM B. Relationship between Resolution and Error The choice of Γ is very important. –When Γ larger, the error of measured velocity is smaller –When Γ larger, the spatial resolution at velocity measurement is worse. –The measurement error and the spatial resolution make a trade-off relation.

9 Multi Resolution STDSM C. Algorithm of Multi Resolution STDSM Step 1: Calculate for stored image planes. Step 2: Set level L be 1 where i, j is one of x, y, or t Step 3: Calculate from and also calculate Step 4: Calculate, and

10 Multi Resolution STDSM C. Algorithm of Multi Resolution STDSM Step 5: if L+1’s error index satisfies the following condition: then, permutate the level L’s vector by the level L+1’s vector Step 6: let the level be L=L+1, and repeat step 4 and 5 till a pre-defined level.

11 Multi Resolution STDSM C. Algorithm of Multi Resolution STDSM The computation time is not so increased in comparison with the conventional STDSM.

12 Results for Debris Flow Videos Two video sequence –The video type of two natural debris flow which occurred on May 1, 1995 (Fig 2) and June 3, 1995 at the Nojiri river of Mt. Sakurajima Volcano, Kagoshima Prefecture. –The video type of a debris flow which occurred on July 8, 1996 at the Moscardo torrent in Italy (Fig 5).

13 Results for Debris Flow Videos

14 Results for Debris Flow Videos

15 Results for Debris Flow Videos

16 Conclusions Knowledge of the velocity vector field instead of simple velocity magnitude gives more effective information countermeasure against natural turbulent flow hazards. A new method for measuring the velocity vector field of random flow, based on STDSM was proposed in this paper.

17 Thank you