## 4 Case Study
### Results and Discussion  
#### 4.2.1 Location of Facial Emotion Description Points and Emotional Feature Extraction  
A total of 49 facial emotion description points in the 900 video clips and newly collected videos were all located accurately by the built AAM.  
Using the proposed feature extraction method based on \"geodesic distance + sample entropy\", a total of 900 feature vectors for the four classes of cognitive emotions were obtained. We showcased some of the typical feature vectors for each type of cognitive emotion in terms of emotional description point (dimension), and visualized the typical feature vectors (Figure 7) to highlight the characteristics of the extracted features.  
Figure 6: Examples of selected facial expression videos.  
The above figures clearly reflect the rough morphology of the feature vectors for the different cognitive emotions.  
1. Characteristics and analysis of the feature vector for \"frustration\" The feature vector for \"frustration\" first showed two significant increases with the increase in the serial number of the feature description points, with a peak around 0.95 and a low valley (below 0.2) in the middle, with a tendency towards flattening out, followed by a zigzag increase between 0.2 and 0.6. This means that when frustrated, the emotional description points (local expressions) near the eyebrows and eyes in the center of the face change in a complex manner. There were no complex changes in the nose, and the changes in the mouth were more complex than those in the nose.
2. Characteristics and analysis of the feature vector for \"boredom\" The feature vector for \"boredom\" first slowly rose to a peak (around 0.92), and then began to decline to a trough (around 0.1), and finally slowly rebounded. This shows that when bored, the changes in the eyebrows and eyes are extremely complex, and there are fewer changes in the nose.
3. Characteristics and analysis of the feature vector for \"doubt\" The feature vector for \"doubt\" fluctuated upwards starting from the beginning, reaching its peak between the 43 rd to 46 th emotional description points, and finally rapidly decreasing. This indicates that there was no significant change in the eyes and eyebrows when making an expression of doubt, while there was a strong change in the nose and mouth.
4. Characteristics and analysis of the feature vector for \"pleasure\" The feature vector for \"pleasure\" rapidly rose from around 0.3 to reach its peak, and then it rapidly decreased, reaching its lowest value near the 20 th emotional description point, and then rose in twists and turns. It reached its peak again between the 31 st to 37 th emotional description points, and then rapidly dropped to its lowest value before rebounding to around 0.7. This can be explained as intense changes in a person's eyebrows, eyes, nose, and mouth when expressing pleasure.  
Figure 7: The average feature curves of the 4 cognitive emotions based on “geodesic distance + sample entropy”: (a) frustration, (b) boredom, (c) doubt, (d) pleasure.  
Overall, it is not difficult to see that some relatively noticeable differences were revealed in the feature vectors for the four classes of cognitive emotions. Some local similarities, such as the nose tip and upper lip in the expression of \"frustration\", \"boredom\", and \"pleasure\", as well as the eyes in the expression of \"boredom\" and \"pleasure\", may cause recognition errors. Therefore, it was worth testing the performance of our proposed method.