# Modeling Pedestrian Motion in Crowded Scenes Based on the Shortest Path Principle
## 5 Experiment Results Analysis
### Pedestrian Motion Simulation  
The objective of this experiment was to simulate the pedestrian motions by the partially observed trajectories. Here, we take the movement path to represent the pedestrian motion. Other simulation details, such as speed, will be discussed in the crowd motion simulation experiment below. We found 680 complete trajectories in the original trajectories obtained by the KLT tracker, which reached the entrance and exit regions in the scene, as shown in Figure 7a, and they were taken as the true movement paths of pedestrians. We simplified and segmented the complete trajectories with the Douglas Peucker algorithm, and obtained 2428 trajectory segments. These segments were taken as the partially observed trajectories, and each trajectory corresponds to an independent pedestrian. Given a partially observed trajectory, we first found the origin and destination of it. Then, we generated the feasible shortest path of the trajectory from the origin to destination as the simulated movement path of the pedestrian. The MDA model uses an affine transformation matrix to expand the past and future movement paths of the trajectory to generate the simulated movement path. We use both the pattern accuracy of the simulated paths and the distance between the simulated and the true path to evaluate the simulation. First, we analyzed the pattern accuracy of the simulated paths. We judged the pattern of a simulated path to be correct if the entrance and exit of the simulated path were the same as those of the corresponding true path. We show the pattern accuracies of the simulated paths obtained by our model and the MDA model in Figure 7b,c, respectively. The accuracy of our model was 74.92%; that of the MDA model was 53.42%. The green trajectory indicates the correct simulated path, and the red trajectory indicates an erroneous one. It is worth noting that if the entrances and the exits of the trajectories are adjacent, the error rates of both models will increase markedly, which is demonstrated well by the dense red trajectories among the entrance/exit regions 8, 9 and 10. The dense regions exist because the regions near the entrance/exit are usually crowded; pedestrians are often forced to change their routes frequently when passing between an adjacent entrance and exit, causing difficulties for motion models. However, we can see that even in these extreme cases, the accuracy of our model was significantly higher than that of the MDA model. Next, we calculated the distance between the simulated path and the true path. For a fair comparison, we only used the paths simulated correctly by both two motion models. We respectively sampled the simulated paths and the true paths at equal distances. The sampling frequency of the true paths was set to five times that of the simulated paths. For each sampling point on the simulated path, we took the minimum distance between it and all sampling points on the true path as the distance from the sampling point to the true path. The distance  
Figure 6: A brief introduction of the experimental data. (**a**) We show the trajectories with different colored lines, and the human labeled entry/exit regions by yellow bounding boxes. (**b**) A histogram of the trajectory lengths; the unit of length is the number of image grids. Most of the trajectories are very short. between the simulated path and the true path was defined as the average distance from all sampling points on the simulated path to the true path. We calculated the mean values and standard deviations of the distances between the simulated paths and the corresponding true paths obtained by our model and the MDA model. In our results, the mean distance was 7.07; the standard deviation was 3.82. For the MDA model, the mean distance was 6.94; the standard deviation was 4.74. The unit of distance is the pixel. The mean distances obtained by the two models are approximately the same, though our model slightly outperformed the MDA model in terms of standard deviation.