## 1 Introduction
According to the American Society of Plastic Surgeons (ASPS) ([[https://www.plasticsurgery.org/documents/News/Statistics/2020/plastic-surgery-statistics-full-report-2020.pdf](https://www.plasticsurgery.org/documents/News/Statistics/2020/plastic-surgery-statistics-full-report-2020.pdf)]([https://www.plasticsurgery.org/documents/News/Statistics/2020/plastic-surgery-statistics-full-report-2020.pdf](https://www.plasticsurgery.org/documents/News/Statistics/2020/plastic-surgery-statistics-full-report-2020.pdf)), accessed on 10 May 2022), 15.6 million cosmetic procedures were performed in the United States in 2020, with three of the top five cosmetic procedures involving the face, namely 352,555 rhinoplasties, 352,112 eyelid surgeries and 234,374 facelift procedures. The total cost was approximately $16.7 billion in the U.S. alone. Information about an individual's facial morphology can have several important clinical and forensic applications: Information on patient-specific models, enhancement and reduction of the need for extensive surgery for craniofacial abnormalities/trauma, prediction/reconstruction of facial shape from skeletal remains and the identification of suspects from DNA [12]. The fast-growing beauty market urgently needs a more precise definition of the beauty standard for faces. In animation and computer game design, research into the beauty of faces can also be a reference for designers creating virtual characters [13]. Compared to other tasks in facial image analysis, such as face recognition, facial expression recognition, gender classification, face age estimation and ethnicity classification, evaluating the beauty of faces is more challenging because it is difficult to apply a well-defined concept to describe the beauty information of facial images, which is a key problem in this field. Moreover, the classification of facial shape, which is of great importance for many beauty and fashion purposes, appears to be relatively complex and requires many features to distinguish [14]. Attempts to quantify facial beauty have been made by investigators from different areas, such as psychology, the arts, plastic surgeons and, more recently, image analysis [15; 16]. In general, the task of automatically evaluating the beauty of a face can be accomplished by three categories of procedures. The first category concerns classification, in which beauty is defined by levels or classes. The second category deals with the ordering of face images, where the task is to rank the images according to their attractiveness. The third category deals with the automatic scoring of the beauty of faces. Schemes belonging to this category are the most general ones, since the solution for the first two categories is solved implicitly. The existing methods rely on machine learning and computer vision techniques and have proven to achieve promising results. Likely the first attempt for an accurate predictor of facial attractiveness was the one proposed in [17], where numerous facial features (90 geometric features and eight related to face symmetry, hair and skin colour and skin smoothness) were used along with an average human attractiveness score. The facial attractiveness ratings provided by the final predictor correlated strongly with the human ratings. However, one of the major challenges of research in this area is how to create accurate face representations, which can be either feature-based, holistic or hybrid. The first category includes geometric, colour, texture or other local representations. Geometric features are based on the use of landmarks in the face and take into account their positions, distances between them or the relationship of these distances to each other [18]. On the other hand, holistic approaches focus on global information of the face instead of local features, e.g., using eigenfaces [19]. Other approaches were based on a family of convolutional neural networks whose input is the raw image, and the output is the beauty score [20; 21].