# Quantifying Perceived Facial Asymmetry to Enhance Physician-Patient Communications
###### Abstract
[PERSON] et al. proposed quantitative metrics to assess pre- and post-operative differences [25]. [PERSON] et al. compared the performance of bi-maximillary and maxillary osteotomy [26]. Pre- and post-orthognathic surgeries of 44 patients (20 Class III cases of bi-maximillary osteotomy; 12 Class III cases of maxillary osteotomy; 12 Class II cases of bi-maximillary osteotomy) were assessed. [PERSON] et al., [PERSON] et al., and [PERSON] et al. mirrored faces and aligned feature points [1; 27; 28]. [PERSON] et al. proposed an asymmetry index (AI) for each individual facial landmark of interest [7]. [PERSON] et al. computed facial contour asymmetry instead of landmark asymmetry [29]. [PERSON] et al. constructed a transfer learning model to score the asymmetry of facial contour maps and to assess the efficacy of an orthognathic surgery [30]. The above-mentioned studies employed the Frankfurt horizontal plane or the natural head position to derive 3D head coordinate systems. Questionnaires were used to elicit and quantify people's perception of facial asymmetry. [PERSON] et al. claimed that non-experts' assessments for facial asymmetry should be first considered because the ultimate demand and perception rested upon the patients [31]. [PERSON] et al. maintained similar comments [32]. [PERSON] et al. conducted visual questionnaires among professional orthodontists, general dentists, and laypersons. [8]. Their study showed that abilities to assess facial symmetry were different over varied professional backgrounds, and the orthodontists had the most profound capabilities of differentiating symmetrical from asymmetrical faces. [PERSON] et al. employed playback of photographs to trigger conscious perception of the observers [21]. In the study of [PERSON] et al., three groups of respondents, i.e., orthognathic patients, clinicians, and laypeople, were invited to assess how mandible and chin landmarks related to perceived asymmetry [22]. The result demonstrated that the perception of clinicians and patients were more critical than laypeople. [PERSON] et al. classified the participants into five groups: laypeople, dental students, dental care professionals, dental practitioners, and orthodontists [33]. To grade the degree of asymmetry, [PERSON] et al. invited oral surgeons and orthodontists to subjectively evaluate facial asymmetry and defined grade#0 as good symmetrical frontal view, grade#1 as little asymmetry, grade#2 as localized asymmetry, and grade#3 as marked asymmetry [34]. [PERSON] et al. adopted a six-point scale to rank facial symmetry (1: very symmetrical; 6: very asymmetrical) [1]. [PERSON] et al. categorized the frontal facial image into two groups [24]. Patients in Group A exhibited symmetrical or little asymmetrical frontal views, without having to undergo a surgical treatment. Patients in Group B exhibited marked asymmetry and a surgical treatment was required. [PERSON] et al. requested the observers to classify the facial images displayed on the screen into normal, slightly abnormal but socially acceptable, or abnormal [33]. The building blocks to achieve the aim of this work are threefold. (1) Define a 3D facial coordinate system regardless of the head direction and compute asymmetry index vector (\(\overset{\rightharpoonup}{\text{AI}}\)) for individual facial features and overall asymmetry index (oAI). (2) Build an artificial neural network classifier to model perceived asymmetry acquired from the questionnaires and classify a face as perceived normal (PN), perceived asymmetrically normal (PAN), or perceived abnormal (PA), with associated confidence vectors (\(\overset{\rightharpoonup}{\text{C}}\)). (3) Propose the quadruple \(\langle\)oAI, \(\overset{\rightharpoonup}{\text{AI}}\), PN\(|\)PAN\(|\)PA, \(\overset{\rightharpoonup}{\text{C}}\rangle\) as a tool to promote transparent communications between the surgeon and the patient. The degree of overall facial asymmetry (oAI) together with laypeople-deemed classification (PN\(|\)PAN\(|\)PA) articulate the severity of asymmetry.