# Quantifying Perceived Facial Asymmetry to Enhance Physician-Patient Communications
## 2 Materials and Methods
### Visual Questionnaire Surveys  
To generate transformed faces with varied degrees of asymmetry, we perform combined counter-clockwise rolls (rotations of the \(Y\)-axis) of the nose and the chin [7]. In total, 8 nose rolls together with 8 chin rolls yield 64 stimulus faces with off-the-mid-sagittal distances covering from normal to serious asymmetry [33], as shown in Table 2. In our study, the off-the-mid-sagittal distance ranges are 0.35-5.31 mm for the nose and 1.14-17.04 mm for the chin. For example, a stimulus denoted as \(n_{09}c_{03}\) indicates that the transformation involves 4.5\({}^{\circ}\) of nose roll and 1.68\({}^{\circ}\) of chin roll, and the corresponding Pronasale (\(Prn\)) and Menton (\(Me\)) displacements off the mid-sagittal plane are 3.19 mm (or \(\delta_{x}(Prn)\)) and 3.42 mm (or \(\delta_{x}(Me)\)), respectively. Figure 2a,b illustrate the facial coordinates and the counter-clockwise roll, and Figure 2c illustrates a series of deformed faces.  
The 64 stimulus faces are randomly shuffled and compiled into a visual questionnaire. When conducting the questionnaires, each face is displayed for five seconds, sufficiently enough for a respondent to reach a decision [35; 36]. A blank screen, lasting for two seconds, is shown between consecutive faces to remove residual stimuli. The study recruits 128 laypeople to serve as the questionnaire respondents. Respondents' informed consents are obtained before taking the survey. A questionnaire survey would take less than  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Nose (\(n\))**} & \multicolumn{2}{c}{**Chin (\(c\))**} \\ \hline \(n_{i}\) **or \(c_{j}\)** & \(\theta\) (\({}^{\circ}\)) & \(\delta_{x}(Prn)\) **(mm)** & \(\theta\) (\({}^{\circ}\)) & \(\delta_{x}(Me)\) **(mm)** \\ \hline
01 & 0.5 & 0.35 & 0.56 & 1.14 \\
03 & 1.5 & 1.06 & 1.68 & 3.42 \\
05 & 2.5 & 1.77 & 2.81 & 5.70 \\
07 & 3.5 & 2.48 & 3.93 & 7.97 \\
09 & 4.5 & 3.19 & 5.05 & 10.25 \\
11 & 5.5 & 3.90 & 6.17 & 12.52 \\
13 & 6.5 & 4.60 & 7.29 & 14.78 \\
15 & 7.5 & 5.31 & 8.42 & 17.04 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Roll rotations of the nose and the chin.  
Figure 2: Procedure of composing the facial asymmetry quadruple. (**a**) Facial coordinates; (**b**) Counter-clockwise roll around the \(Z\)-axis with Nasion (N) as the origin; (**c**) Deformed faces.  
10 minutes, including time spent for opening, closing, and other miscellaneous preparations. Two simple questions for a face are asked: (Q1) Do you think this face is symmetrical? (Q2) Is it abnormally asymmetrical and you would consider a surgery? A face is rated as perceived normal (or PN) if the answer to Q1 is YES. A face is rated as perceived asymmetrically normal (or PAN) if the answer to Q1 is NO and the answer to Q2 is NO. A face is rated as perceived abnormal (or PA) if the answer to Q1 is NO and the answer to Q2 is YES. All respondents' answers are gathered, and each face is categorized as PN, PAN, or PA, if it receives the most votes for that class. Furthermore, the percentage of votes each face receives over PN, PAN, and PA, respectively, constitute the corresponding confidence vector (\(\overset{\cdot}{\text{C}}\)). For example, a face receives 20% votes for PN, 30% votes for PAN, and 50% votes for PA. This face is therefore categorized as PA with a confidence vector \(\overset{\cdot}{\text{C}}=[0.2,\,0.3,0.5]^{T}\).