It has been proposed that the proportions of the human face are crucial for facial aesthetics. If this is the case, we should describe the relationship among proportions of face components quantitatively. This study aims to develop a mathematical model of facial proportions to provide a quantitative description of facial attractiveness. Furthermore, we expect that plastic surgeons can use models in clinical work to enhance communication efficiency between doctors and patients. Face alignment technique was used to analyse 5500 frontal faces with diverse properties (male/female, Asian/Caucasian, ages) to obtain the ratios among the nose length ($ {N}_{L} $), the nasal base width ($ N $), and the inner canthus width ($ {E}_{I} $). A mathematical model ($ {N}_{L}^{2} = a{E}_{I}\mathrm{*}{N}_{L}+b{E}_{I}\mathrm{*}N+cN\mathrm{*}{N}_{L} $) was developed to describe the relationship among these proportions. To validate the effectiveness of this approach, we simulated the post-operative photos using Adobe Photoshop. Our findings show that the ratio of nose length to nose width, the ratio of inner canthus width to nose length and the ratio of inner canthus to nose width play a significant role in determining facial attractiveness. These results provide a possible strategy to quantitatively describe the relationship among human face proportions.
Keywords: doctor-patient communication; face; facial analysis; facial attractiveness; proportion.