## 3 Results and Discussion
### Limitations of the Proposed Technique  
It is worth citing certain limitations for the use of the proposed technique. The authors see the following main limitations of the proposed technique.  
1. To be able to apply the method of the geometric interpretation of facial areas, the following landmarks must be present when using third-party tools to automatically detect feature points (markers) on a face image:  
* Two points above the upper lip;
* A point in the middle of the lower lip;
* Points of the tip of the nose and corners of the lips;
* Points of the corners of the eyes and the middle of the lower and upper eyelids;
* Points on the inner tips of the eyebrows and the middle of the bridge of the nose;
* Points of the middle of the eyebrows and the tip of the nose;
* Points of the outer tips of the eyebrows and the middle of the lower eyelid;
* Points of the middle of the eyebrows and lower eyelids.  
The requirement for the mandatory presence of the above points is not critical since the study found that such applications generally provide such a possibility.  
In addition, for the geometric interpretation method to function, it is necessary to set the minimum and maximum values of the landmarks used, taking into account the values of the landmarks. Obtaining the minimum and maximum values of the landmarks for the datasets to be used is also not a critical limitation--calculating the required values is a simple technical task.  
2. The limitation of the hyperplane classification method is the need to use datasets with faces of people that are typical for the location where the proposed technique will be used, namely:  
* Relevant categories of faces by age and by gender;
* Racial and cultural characteristics;
* Consideration of clothing and climatic features (time of year, etc.).  
This restriction is more significant than the previous one, yet not critical. One can use existing datasets that satisfy the above limitations or create a unique dataset and test it using the visual analytics technique presented in this study for further application.  
3. Emotional states are dynamic and often evolve, which is an aspect our current model does not fully account for. In our technique, we analyze each frame of the video individually, assigning an emotional state based on the facial expression in that frame. This process can overlook the temporal continuity of emotional states in the video sequences, potentially leading to inaccuracies when rapid emotional shifts occur.  
However, there are additional approaches that emphasize the importance of temporal context in emotion recognition. For example, an active learning paradigm [52] can consider the temporal sequences in video streams, thereby improving emotion recognition accuracy. As such, a potential direction for future work could be integrating an active learning paradigm into our technique. This could involve designing a model that accounts for the temporal context of emotional states through techniques like RNNs or other sequence modeling approaches. Such a modification could enhance the model's ability to understand the fluid nature of emotions, improving its overall accuracy in emotion recognition from video streams.  
As discussed, the above limitations of the proposed technique are not critical and have straightforward steps to eliminate them. In this regard, the research findings confirm that the proposed technique allows for localizing groups of people with a sharp change in emotional state based on the external photo and video recording materials with high accuracy.