# Detection of Salient Crowd Motion Based on Repulsive Force Network and Direction Entropy

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## Abstract

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## 1. Introduction

## 2. Calculation of Crowd Velocity Vector Field

## 3. Construction of Repulsive Force Network

#### 3.1. Establishment of a Network Node

^{w}node set $Q=\{{q}_{1},{q}_{2},\cdots ,{q}_{n}\}$ can be generated, where n is the total number of nodes. The number of network nodes is equal to the number of particles in the crowd velocity field.

#### 3.2. Establishing the Network Edges Using Repulsive Force Model

#### 3.3. Calculation of Node Strength

## 4. Optimizing Node Strength Field Using Direction Entropy

#### 4.1. Establishment of Vector Direction Entropy Matrix

_{i}in all direction ranks. According to the definition of Shannon entropy [21] and [23], we can assign the velocity direction entropy between the central particle ${q}_{xo}{}_{yo}$ and other particles ${q}_{xy}$$(x\ne {x}_{0},y\ne {y}_{0})$ neighboring the central particle. The calculation is determined by the following formula:

_{11}, H

_{12}……H

_{MN}is the entropy at the corresponding position of the crowd particle field. In order to facilitate the node strength field optimization operation in later stage, the direction entropy matrix is normalized as follows:

#### 4.2. Optimizing the Node Strength Field

## 5. Experimental Results and Analysis

#### 5.1. Crowd Retrograde Behavior Detection

#### 5.2. Crowd Motion Instability Region Detection

#### 5.3. Detection Results Using Different Neighborhood Size

#### 5.4. Performance Evaluation and Comparison

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Framework of salient crowd motion detection based on repulsive force network and direction entropy.

**Figure 4.**Expressing the effect of optical flow reversal: (

**a**) original sample frame; (

**b**) detection result using original optical flow; (

**c**) detection result using reversed optical flow; (

**d**) detection result after the integration of optical flow.

**Figure 5.**Retrograde motion detection in train station scene: (

**a**) input frame; (

**b**) node strength field of repulsive force network; (

**c**) detection result using direction entropy; (

**d**) salient region detection after optimized; (

**e**) overlap the salient region with input frame.

**Figure 6.**Retrograde motion detection in single retrograde scene: (

**a**) input frame; (

**b**) node strength field of repulsive force network; (

**c**) detection result using direction entropy; (

**d**) salient region detection after optimized; (

**e**) overlap the salient region with input frame.

**Figure 7.**Salient crowd instability motion detection in marathon scene: (

**a**) original video frame and ground true (red box); (

**b**) node strength field of repulsive force network; (

**c**) detection result using direction entropy; (

**d**) salient region detection after optimized; (

**e**) overlap the salient region with original video frame.

**Figure 8.**Salient crowd instability motion detection in pilgrimage scene: (

**a**) original video frame and ground true (red box); (

**b**) node strength field of repulsive force network; (

**c**) detection result using direction entropy; (

**d**) salient region detection after optimized; (

**e**) overlap the salient region with original video frame.

**Figure 9.**Retrograde motion detection in train station scene using different neighborhood size: (

**a**) original video frame; (

**b**) detection result using 5 × 5 neighborhood; (

**c**) detection result using 13 × 13 neighborhood; (

**d**) detection result using 23 × 23 neighborhood.

**Figure 10.**Retrograde motion detection in single retrograde scene using different neighborhood size: (

**a**) original video frame; (

**b**) detection result using 5 × 5 neighborhood; (

**c**) detection result using 15 × 15 neighborhood; (

**d**) detection result using 23 × 23 neighborhood.

**Figure 11.**Instability motion detection in marathon scene using different neighborhood size: (

**a**) original video frame and ground truth region; (

**b**) detection result using 5 × 5 neighborhood; (

**c**) detection result using 11 × 11 neighborhood; (

**d**) detection result using 23 × 23 neighborhood.

**Figure 12.**Instability motion detection in pilgrimage scene using different neighborhood size: (

**a**) original video frame and ground truth region; (

**b**) detection result using 5 × 5 neighborhood; (

**c**) detection result using 15 × 15 neighborhood; (

**d**) detection result using 25 × 25 neighborhood.

Crowded Scenes | Symbol of Parameter | The Value |
---|---|---|

Train station scene in Figure 5 | ε M × N | 13 480 × 360 |

Single retrograde scene in Figure 6 | ε M × N | 15 480 × 360 |

Marathon scene in Figure 7 | ε M × N | 11 640 × 480 |

Pilgrimage scene in Figure 8 | ε M × N | 15 640 × 480 |

Crowded Scenes | Statistics | Size of Neighborhood | Results |
---|---|---|---|

marathon | Pr | 5 × 5 | 0.862 |

11 × 11 | 0.910 | ||

23 × 23 | 0.531 | ||

R | 5 × 5 | 0.841 | |

11 × 11 | 0.909 | ||

23 × 23 | 0.877 | ||

pilgrimage | Pr | 5 × 5 | 1 |

15 × 15 | 1 | ||

25 × 25 | 0.684 | ||

R | 5 × 5 | 0.244 | |

15 × 15 | 0.867 | ||

25 × 25 | 0.656 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Lin, D.; Zheng, J.; Tang, X.; Fang, Y.; Yu, H.
Detection of Salient Crowd Motion Based on Repulsive Force Network and Direction Entropy. *Entropy* **2019**, *21*, 608.
https://doi.org/10.3390/e21060608

**AMA Style**

Zhang X, Lin D, Zheng J, Tang X, Fang Y, Yu H.
Detection of Salient Crowd Motion Based on Repulsive Force Network and Direction Entropy. *Entropy*. 2019; 21(6):608.
https://doi.org/10.3390/e21060608

**Chicago/Turabian Style**

Zhang, Xuguang, Dujun Lin, Juan Zheng, Xianghong Tang, Yinfeng Fang, and Hui Yu.
2019. "Detection of Salient Crowd Motion Based on Repulsive Force Network and Direction Entropy" *Entropy* 21, no. 6: 608.
https://doi.org/10.3390/e21060608