## 4 Application in Channel Experiment
### Results  
The images were processed, and the result of 180 frames is shown in Figure 13. Comparison is made among the results from the classic method without Kalman filter (Figure 1), the present method without the third step (Figure 13a), and the current three-step method (Figure 13b). Note that the trajectories are identified and plotted in different colors with number label. The difference between Figures 1 and 13a is clear, i.e., more complete trajectories were identified in Figure 13a. However, some broken chains are still easily spotted in Figure 13a, e.g., 21# and 30#, 76# and 90#, to cite a few. After these broken chains being connected and repaired by spline interpolation, and removing the false  
Figure 12: Sketch of the experimental setup. chain the final result is shown in Figure 13b. A video was made to illustrate the process of particle tracking (attached to the paper). After manual checking of the method based on 180 frames, a total number of 60,000 frames were processed for quantitative comparison of bed-load transport parameters between the classic and the present method. The average values are listed in Table 2. The most important parameters in bed-load transport are included, such as the number of moving particles in each frame, \(N\), velocity along the flow direction, \(U\), length of trajectories, \(L\), and duration of trajectories, \(T\). It is seen from Table 2 that a significant difference occurs in \(N\), \(U\), \(L\) and \(T\). The differences in \(U\), \(L\) and \(T\) between two methods are similar with results in Section 3.2. The difference of \(N\) in the true image between two methods is much larger than that in the simulated image. The differences may be due to smaller pixels and more complex conditions like bubbles and particle deformation in the true image. It is worth to mention that the length of trajectories \(L\) is about 8 particle diameters which seems too small to present particle jump length. When a moving particle rest at bed throughout trajectories (0.16 s in Table 2), it was recognized as an independent trajectory. In this paper, it aims to obtain the number of active particles, velocity, the entrained particle and deposited particle in the sampling area. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & \(N\) & \(U\)**(cm/s)** & \(L\)**(cm)** & \(T\)**(s)** \\ \hline Classic & 2.66 & 10.81 & 0.21 & 0.02 \\ Present & 5.53 & 12.59 & 1.97 & 0.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of different algorithms. Figure 13: Particle tracking results by (**a**) new method without the third step; (**b**) new method; The different colors represent different trajectories. The true particle jump length and duration should be measured with different criteria of reconnecting the \"artificial depositions\" and larger sampling area. Based on the present method, it is possible to classify an active particle (showing displacement) into being entrained (from static to motion), deposited (from motion to static), or gliding (in motion) during consecutive images. The number of active particles equal to the sum of number of three kinds of motion state. We statistic the number of entrained, deposited and gliding particles in space based on the time-series image and normalized them by the maximum number of moving particles. The normalized spatial distributions of three kinds of motion state are shown in Figure 14. The area of lower number (blue part in Figure 14) and higher number (red part) represent that less and more particles had moved in this area in separate. As shown at the bottom row in Figure 14, the distributions of entrained, deposited and gliding particles coincide a lot with each other. This is due to \"artificial depositions\" of trajectories by the classic two-step method. The three-step method solved a lot of \"artificial depositions\". Then the top row in Figure 14 shows the difference of the distributions of entrainment, deposition and motion state.