Machine learning-powered decoding of facial complexity: a diamond-and-triangle geometry for frontal facial analysis

Facial configuration is far more complicated and variable than the representations offered by a couple of conventionally used mathematic laws, necessitating development of a comprehensive and interracially comparable system for frontal facial analysis. In this study, based on morphological analysis of 33 Caucasian and 33 Asian female faces with high perceived facial attractiveness (i.e. facial esthetic appeal in frontal views), validated by independent layperson ratings, in contrast with 'ordinary' faces of 67 Caucasian and 67 Asian females, a machine learning-powered model, building on a diamond-and-triangle geometric framework, was constructed to decode the esthetic-determining facial traits and quantify the probability of a face conforming to the generally accepted attractiveness. The SVM models demonstrated excellent efficacy in this task, based on the input of 21 facial proportion indices derived from the diamond-and-triangle geometry. By interpreting the contribution of input features to each model's diagnosis, the Asian and Caucasian faces shared prioritization of proportional coordination of facial height with mid-facial width and outer canthal distance in determining facial harmony, and exhibited ethnicity-specific variations in hierarchical importance of other proportion indices. The highly coordinated diamond-and-triangle geometric framework distinguished the attractive faces from the ordinary, with cross-ethnic similarities between Caucasian and Asian females. The machine learning-powered model, integrated with the diamond-and-triangle geometry, provides references for cross-ethnic facial analysis and customized treatment planning.