# Viewpoint Robustness of Automated Facial Action Unit Detection Systems
## 1 Introduction  
With the rise in affectivism [1], automatic facial action detection system is gaining widespread attention [2, 3, 4, 5]. Given the importance of facial expressions for emotional communication [6, 7], machines that can automatically detect facial movements are expected to be useful for studies of facial expressions and emotional communication. The most common index of facial movement is the action unit (AU), which is derived from the Facial Action Coding System (FACS) [8]. FACS describes facial movements in anatomical terms, while AU represents a single facial movement. For example, pulling of the lip corner and lowering of the eyebrows correspond to AUs 12 and 4, respectively. Automated facial action detection systems mainly provide outputs in terms of AUs. As for automated facial action detection systems, the processing pipeline includes face detection, face registration, feature extraction, and classification [9]. A wide variety of algorithms have been proposed at each stage [2, 3, 4, 5]. For example, [PERSON] et al. [10] proposed a novel end-to-end deep learning framework for joint AU detection and face alignment, resulting in robust AU detection. Many facets of automated facial action detection systems (e.g., 3D [11] and multimodal information [12]) have been discussed in several review papers [2, 3, 4, 5, 13, 14]. However, too few automated facial expression analysis systems are available for novice users who are motivated to study human facial expressions but are not experts in engineering techniques. For such demands, the available options include commercial software [15] and limited open software (e.g., OpenFace [16], AFARtoolbox [17], and Py-Feat [18]), which usually have several pre-trained facial databases. Commercial tools are expensive, and open-source software often lacks user-friendly graphical user interfaces. To evaluate the software available to non-programmers with the best graphical user interface and performance for facial action detection, [PERSON] et al. [19] compared the performances of three automatic facial action detection systems (AFAR toolbox, OpenFace, and FaceReader) using several dynamicfacial databases, including one derived from YouTube. OpenFace [16] was able to detect facial expressions more accurately than the other automatic facial action detection systems, including commercial software. Thus, among the many automated facial action detection systems available, OpenFace is easy for naive researchers to use and performs well. The identification of facial expressions in an unconstrained setting is limited by the commonly observed variability among facial poses. A major issue is the perception of facial movements from varying angles, including the facial profile. Human facial angles influence the psychological reactions of observers. A recent study reported that emotion recognition was more accurate for the frontal view of the face compared to the profile [20]. However, other studies reported that emotion recognition had similar accuracy between the profile and frontal views of the face [21,22]. Additionally, perception intensity [21], face recognition [23], impression evaluation [24], and threat perception [25] depend on the facial angle. Assuming that perceptions of facial expressions change with facial angle, automated facial action detection systems must show robustness to facial angles with respect to the detection of facial expressions to be useful for psychological experiments. Thus, it is important to systematically evaluate the robustness of these systems to different facial angles. To the best of our knowledge, no previous study has compared the facial expression detection accuracy of pre-trained facial action detection systems as the facial angle changes from the frontal to profile view. The current study aimed to investigate the viewpoint robustness of four automated facial action detection systems: OpenFace, AFAR toolbox, Py-feat, and FaceReader.