# Modeling Pedestrian Motion in Crowded Scenes Based on the Shortest Path Principle
## 5 Experiment Results Analysis
### Motion Pattern Classification and Traffic Flow Statistics  
We classified the motion pattern based on the entrances and exits of the scene. First, we categorized the trajectories whose origins and destinations belonged to the same entry  
Figure 8: Some examples of the simulated paths obtained by our model and the MDA model. The green line represents the partially observed trajectory; the green dashed line represents the true path. The blue and red dashed lines represent the simulated paths obtained by our model and the MDA model, respectively. The EN and ET indicate the entrance and exit.  
Figure 7: (**a**) The complete trajectories which reach the entrance and exit regions. The pattern accuracies of simulated paths obtained by our model (**b**) and the MDA model (**c**). The green trajectory represents a correct pattern of the whose simulated path, and the red trajectory represents an error.  
and exit regions into the same motion patterns. Then, we calculated the flow value of the trajectory according to the motion pattern to which it belonged. Taking the trajectory \(ab\) in Figure 5a as an example, it belongs to the motion pattern characterized by entrance 5 to exit 13. We define the flow value of trajectory \(ab\) as:  
\[Fv_{ab}=\frac{S_{tr}(g_{a},g_{b})}{S(g_{o},g_{a})+S_{tr}(g_{a},g_{b})+S(g_{b},g_{ d})}.\]  
Finally, we summed up the flow values of all trajectories which belonged to a motion pattern to count the traffic flow of the motion pattern.  
We show the top 12 motion patterns with the largest flow values obtained by our model and the MDA model in Figure 9a,b, and mark their flow values. We can see that there are 11 intersections between the 12 motion patterns obtained by these two models, which demonstrates that both models could identify the main motion patterns well in the scene. However, there are some differences in the spatial distributions of trajectories for the same motion patterns obtained by the two motion models, which is particularly obvious in the motion pattern of entrance 11 to exit 1. In the results of the MDA model, almost all trajectories in this motion pattern enter the scene from the right half of entrance 11 and pass along the left side of the central ticket machines. In our model's results, the trajectories enter the scene from every part of entrance 11, and a small portion of the trajectories pass along the right side of central ticket machines. This difference exists because the MDA model uses a linear dynamic system to constrain the shapes of motion patterns. All trajectories in a motion pattern approximately satisfy the same affine transformation, which limits the path selection of trajectory. Our motion model does not preset the shapes of the motion patterns but directly looks for the origin and destination of a trajectory based on the shortest path principle, which makes the trajectory free to select the path. To sum up, compared with the results of the MDA model, our results better retain the diversity of path decision-making caused by pedestrians' behavior habits and senses, surrounding environments and other uncertain factors in the real situation. Note that feature point extraction has limitations. For example, some pedestrians have several feature points, whereas others have no feature points. The trajectory flow value calculated in this paper can only be a rough measurement but not an accurate pedestrian counter.