# Quantifying Perceived Facial Asymmetry to Enhance Physician-Patient Communications
## 4 Discussion  
We transformed a normal face rather than using a series of realistic asymmetric faces to maintain perception stability of the questionnaire respondents, similar to the approach proposed by [PERSON] et al. [1]. The degree of deformation can therefore be computed to correspond to the respondents' ratings over different faces. The facial texture is removed before deformation in our study to mitigate perception distractions by skin color, rashes, moles, etc. Table 8 illustrates the classification results of the facial asymmetry for the 64 stimulus faces. The 8 \(\times\) 8 matrix is arranged so that the left side shows varied degrees of nose rolls, whereas different degrees of chin rolls are shown on the top. As shown in Table 2, each increment of \(i\) denotes 0.5\({}^{\circ}\) of nasal roll, whereas each increment of \(j\) denotes 0.56\({}^{\circ}\) of chin roll. Presumably, the stimulus faces towards the upper left are likely to be categorized as PN, where those towards the lower right are likely to be classified as PAN or PA. The perceived asymmetry is, in general, aligned with this assumption, with the exceptions of the four red-shaded entries (\(n_{09}c_{01}\), \(n_{11}c_{01}\), \(n_{13}c_{01}\), and \(n_{11}c_{07}\)), where there exhibit inconsistencies in the asymmetry classifications. When exploring the confidence vector (C) of the four seemingly erroneous classifications, as depicted in Table 9, we find \"ambiguous zones\" lying around the PN-PAN and \begin{table}
\begin{tabular}{c c c c} \hline \hline \(n_{i}c_{j}\) & (**oAI, PN\(|\)PAN\(|\)PA, \(\hat{C}\)**) & \(n_{i}c_{j}\) & (**oAI, PN\(|\)PAN\(|\)PA, \(\hat{C}\)**) \\ \hline \(n_{03}c_{01}\) & (1.1772, PN, 0.80) & \(n_{11}c_{01}\) & (2.6179, PA, 0.35) \\ \(n_{03}c_{03}\) & (1.9404, PN, 0.79) & \(n_{11}c_{03}\) & (3.3811, PAN, 0.42) \\ \(n_{03}c_{05}\) & (2.7051, PAN, 0.51) & \(n_{11}c_{05}\) & (4.1459, PAN, 0.37) \\ \(n_{03}c_{07}\) & (3.4697, PAN, 0.53) & \(n_{11}c_{07}\) & (4.9105, PAN, 0.43) \\ \(n_{03}c_{09}\) & (4.2338, PA, 0.60) & \(n_{11}c_{09}\) & (5.6746, PA, 0.74) \\ \(n_{03}c_{11}\) & (4.9972, PA, 0.73) & \(n_{11}c_{11}\) & (6.4379, PA, 0.80) \\ \(n_{03}c_{13}\) & (5.7595, PA, 0.91) & \(n_{11}c_{13}\) & (7.2003, PA, 0.87) \\ \(n_{03}c_{15}\) & (6.5208, PA, 0.92) & \(n_{11}c_{15}\) & (7.9615, PA, 0.88) \\ \(n_{05}c_{01}\) & (1.5375, PN, 0.66) & \(n_{13}c_{01}\) & (2.9771, PN, 0.42) \\ \(n_{05}c_{03}\) & (2.3007, PN, 0.46) & \(n_{13}c_{03}\) & (3.7403, PAN, 041) \\ \(n_{05}c_{05}\) & (3.0654, PAN, 0.50) & \(n_{13}c_{05}\) & (4.5050, PA, 0.48) \\ \(n_{05}c_{07}\) & (3.8300, PAN, 0.53) & \(n_{13}c_{07}\) & (5.2697, PA, 0.67) \\ \(n_{05}c_{09}\) & (4.5941, PA, 0.53) & \(n_{13}c_{09}\) & (6.0338, PA, 0.61) \\ \(n_{05}c_{11}\) & (5.3575, PA, 0.87) & \(n_{13}c_{11}\) & (6.7971, PA, 0.69) \\ \(n_{05}c_{13}\) & (6.1199, PA, 0.91) & \(n_{13}c_{13}\) & (7.5595, PA, 0.90) \\ \(n_{05}c_{15}\) & (6.8811, PA, 0.91) & \(n_{13}c_{15}\) & (8.3207, PA, 0.90) \\ \(n_{07}c_{01}\) & (1.8979, PN, 0.54) & \(n_{15}c_{01}\) & (3.3356, PA, 0.61) \\ \(n_{07}c_{03}\) & (2.6612, PN, 0.56) & \(n_{15}c_{03}\) & (4.0988, PA, 0.58) \\ \(n_{07}c_{05}\) & (3.4259, PAN, 0.43) & \(n_{15}c_{05}\) & (4.8635, PA, 0.58) \\ \(n_{07}c_{07}\) & (4.1905, PAN, 0.51) & \(n_{15}c_{07}\) & (5.6281, PA, 0.58) \\ \(n_{07}c_{09}\) & (4.9546, PA, 0.52) & \(n_{15}c_{09}\) & (6.3922, PA, 0.81) \\ \(n_{07}c_{11}\) & (5.7179, PA, 0.82) & \(n_{15}c_{11}\) & (7.1556, PA, 0.78) \\ \(n_{07}c_{13}\) & (6.4803, PA, 0.86) & \(n_{15}c_{13}\) & (7.9180, PA, 0.86) \\ \(n_{07}c_{15}\) & (7.2415, PA, 0.89) & \(n_{15}c_{15}\) & (8.6792, PA, 0.91) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Classifications of respondents’ perceived asymmetry (pre-revision). PAN-PA borders where there are competing values in corresponding confidence vectors. In Table 9, the highest confidence value in a confidence vector is starred (*); and the second highest confidence value is underlined.