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Fig. 5. The effect of varying crowd size on prediction runtime To test the performance of our proposed algorithm, we vary the size of crowd while measuring the average time taken to predict the emotion of each crowd image on a Core 2 Duo, with a clock-speed of 2.0GHz and 3GB of RAM. The individuals placed in the crowd are selected at random and the results are given in Fig. 5. The results show a linear relationship between crowd size and prediction runtime. We note that for small crowds of 1 to 20 people, prediction takes less than 1 s. On the other hand, for larger crowds of 200 to 220 people, it takes in the region of 12 to 13 s for each prediction. Overall the algorithm shows potential for real-time application. 3 Comparison to Results in Literature

Figure 5 The effect of varying crowd size on prediction runtime To test the performance of our proposed algorithm, we vary the size of crowd while measuring the average time taken to predict the emotion of each crowd image on a Core 2 Duo, with a clock-speed of 2.0GHz and 3GB of RAM. The individuals placed in the crowd are selected at random and the results are given in Fig. 5. The results show a linear relationship between crowd size and prediction runtime. We note that for small crowds of 1 to 20 people, prediction takes less than 1 s. On the other hand, for larger crowds of 200 to 220 people, it takes in the region of 12 to 13 s for each prediction. Overall the algorithm shows potential for real-time application. 3 Comparison to Results in Literature

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Fig. 1. Fully-connected undirected graph for a crowd of 20 people ».4 Computing the Closest Neighbours of Each Face
Fig. 1. Fully-connected undirected graph for a crowd of 20 people ».4 Computing the Closest Neighbours of Each Face
Fig. 2. Minimum spanning tree for a crowd of 20 people spanning tree is represented by the sum of the weights of all edges in the tree. A MST is a spanning tree where the cost is a minimum. Numerous approaches have been suggested for finding a MST. The two most popular approaches are Kruskal’s algorithm and Prim’s algorithm [27]. In this work, Prim’s algorithm was used to find the MST. Starting with an empty MST, for each step of Prim’s algorithm, we consider a group of edges that connects the set of nodes already included in the MST with the set of nodes not yet included. The edge with minimum weight is selected and the node is added to the MST. The procedure is repeated until all nodes have been included in the MST. The MST for the fully-connected undirected graph of the crowd given in Fig. 1 is shown in Fig. 2. In a MST there is a total of N — 1 edges. In a MST there is a total of N — 1 edges.
Fig. 2. Minimum spanning tree for a crowd of 20 people spanning tree is represented by the sum of the weights of all edges in the tree. A MST is a spanning tree where the cost is a minimum. Numerous approaches have been suggested for finding a MST. The two most popular approaches are Kruskal’s algorithm and Prim’s algorithm [27]. In this work, Prim’s algorithm was used to find the MST. Starting with an empty MST, for each step of Prim’s algorithm, we consider a group of edges that connects the set of nodes already included in the MST with the set of nodes not yet included. The edge with minimum weight is selected and the node is added to the MST. The procedure is repeated until all nodes have been included in the MST. The MST for the fully-connected undirected graph of the crowd given in Fig. 1 is shown in Fig. 2. In a MST there is a total of N — 1 edges. In a MST there is a total of N — 1 edges.
Fig. 3. Finding chains of emotion in the crowd early detection of potentially problematic crowds. Consider the crowd given in Fig.2. The emotion chains for the crowd are illustrated in Fig. 3, where the values above each node represent the node number and predicted FER emotion label of the node. There are a total of 2 unique emotion chains in the crowd; one with emotion label 0 (anger) and another with emotion label 4 (neutral). In this work, the required threshold is set to thresh = 30% (this value is considered optimal since negative groups of emotion in the crowd can be detected early while false detections are kept to a minimum). The size of both chains are greater than the required threshold. The anger chain has a greater weighting than the neutral chain and because there are no other emotion chains with an equivalent or greater weighting, the overall emotion of the crowd is predicted to be anger.
Fig. 3. Finding chains of emotion in the crowd early detection of potentially problematic crowds. Consider the crowd given in Fig.2. The emotion chains for the crowd are illustrated in Fig. 3, where the values above each node represent the node number and predicted FER emotion label of the node. There are a total of 2 unique emotion chains in the crowd; one with emotion label 0 (anger) and another with emotion label 4 (neutral). In this work, the required threshold is set to thresh = 30% (this value is considered optimal since negative groups of emotion in the crowd can be detected early while false detections are kept to a minimum). The size of both chains are greater than the required threshold. The anger chain has a greater weighting than the neutral chain and because there are no other emotion chains with an equivalent or greater weighting, the overall emotion of the crowd is predicted to be anger.
Fig. 4. Generated crowd image with ground-truth emotion anger We thus propose the creation of a novel Crowd Emotion dataset with known ground-truth emotion labels. Images from the Extended Cohan-Kanade (CK+) [19] facial expression dataset are pre-processed and placed together in an empty environment to simulate crowd images. The images represent a crowd under optimal conditions with no facial obscurities present. Each crowd image consists of 2 groups of 10 subjects. To produce a ground-truth emotion, subjects in one group are placed so that they are expressing random emotions, none of which exceed the threshold value, while the subjects in the remaining group are placed so that they are expressing the ground-truth emotion. A generated crowd image with ground-truth emotion anger is shown in Fig. 4. 3.2 Testing Procedure
Fig. 4. Generated crowd image with ground-truth emotion anger We thus propose the creation of a novel Crowd Emotion dataset with known ground-truth emotion labels. Images from the Extended Cohan-Kanade (CK+) [19] facial expression dataset are pre-processed and placed together in an empty environment to simulate crowd images. The images represent a crowd under optimal conditions with no facial obscurities present. Each crowd image consists of 2 groups of 10 subjects. To produce a ground-truth emotion, subjects in one group are placed so that they are expressing random emotions, none of which exceed the threshold value, while the subjects in the remaining group are placed so that they are expressing the ground-truth emotion. A generated crowd image with ground-truth emotion anger is shown in Fig. 4. 3.2 Testing Procedure
Table 1. Recognition accuracy (%) for 8, 7 and 2 classes of crowd emotion Table 2. Crowd confusion matrix (%) for 8 classes of crowd emotion
Table 1. Recognition accuracy (%) for 8, 7 and 2 classes of crowd emotion Table 2. Crowd confusion matrix (%) for 8 classes of crowd emotion
An average recognition accuracy of 81.3% was achieved for 7 classes of crowd emotion. This shows a 16.7% improvement compared to when neutral emotion was included. Examining the crowd emotion confusion matrix in Table 4, we note that while all emotion classes displayed an improvement in recognition accuracy compared to 8 class testing, in particular, anger and sadness emotions experi- enced the largest improvement; having increased more than threefold. This is
An average recognition accuracy of 81.3% was achieved for 7 classes of crowd emotion. This shows a 16.7% improvement compared to when neutral emotion was included. Examining the crowd emotion confusion matrix in Table 4, we note that while all emotion classes displayed an improvement in recognition accuracy compared to 8 class testing, in particular, anger and sadness emotions experi- enced the largest improvement; having increased more than threefold. This is
Table 3. FER confusion matrix (%) for 8 classes of crowd emotion supported by the FER confusion matrix given in Table5, where anger and sad- ness emotions experienced the most significant increase in recognition accuracy out of the 6 facial emotions on test. With neutral emotion excluded, the average FER recognition accuracy improved by 7.6% from 85.4% to 93%. Further exam- ination of both 7 class and 8 class FER confusion matrices shows that pleasing emotions such as joy and surprise tend to exhibit higher recognition accuracies compared to other displeasing emotions such as anger, fear and disgust, which often get confused between one another. This is evident in Table5, where anger and fear is confused with disgust and sadness.
Table 3. FER confusion matrix (%) for 8 classes of crowd emotion supported by the FER confusion matrix given in Table5, where anger and sad- ness emotions experienced the most significant increase in recognition accuracy out of the 6 facial emotions on test. With neutral emotion excluded, the average FER recognition accuracy improved by 7.6% from 85.4% to 93%. Further exam- ination of both 7 class and 8 class FER confusion matrices shows that pleasing emotions such as joy and surprise tend to exhibit higher recognition accuracies compared to other displeasing emotions such as anger, fear and disgust, which often get confused between one another. This is evident in Table5, where anger and fear is confused with disgust and sadness.
Table 4. Crowd confusion matrix (%) for 7 classes of crowd emotion We reduce the 8 and 7 classes of crowd emotion into just 2 classes - positive and negative. Emotions that can be considered pleasing are grouped into the positive class while emotions that can be considered displeasing are groupec into the negative class. For what was previously 7 classes of crowd emotion we group joy and surprise into the positive class while anger, fear, disgust anc sadness are grouped into the negative class. For what was previously 8 classes o’ crowd emotion, we consider neutral emotion to be non-negative and place it ir
Table 4. Crowd confusion matrix (%) for 7 classes of crowd emotion We reduce the 8 and 7 classes of crowd emotion into just 2 classes - positive and negative. Emotions that can be considered pleasing are grouped into the positive class while emotions that can be considered displeasing are groupec into the negative class. For what was previously 7 classes of crowd emotion we group joy and surprise into the positive class while anger, fear, disgust anc sadness are grouped into the negative class. For what was previously 8 classes o’ crowd emotion, we consider neutral emotion to be non-negative and place it ir
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Computer ScienceArtificial IntelligenceCrowd Psychology
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