Meeting patient desires for enhanced facial esthetics requires that providers have standardized and objective methods to measure esthetics. We evaluated the effects of objective 3-dimensional (3D) facial shape and asymmetry measurements derived from 3D facial images on perceptions of facial attractiveness.

3D facial images of 313 adults in Iowa were digitized with 32 landmarks and objective 3D facial measures capturing symmetric and asymmetric components of shape variation, centroid size and fluctuating asymmetry were obtained from the 3D coordinate data using geo-morphometric analyses. Frontal and profile images of study participants were rated for facial attractiveness by ten volunteers (5 females and 5 males) on a 5-point Likert-scale and a visual analogue scale (VAS). Multivariate regression was used to identify the effects of the objective 3D facial measurements on the attractiveness ratings.

Several of the objective 3D facial measures had significant effects on attractiveness ratings. Shorter facial heights with protrusive chins, mid-face retrusion, faces with protrusive noses and thin lips, flat mandibular planes with deep labio-mental folds, any cants of the lip commissures and floor of the nose, larger faces overall and increased fluctuating asymmetry were rated as significantly (

Perceptions of facial attractiveness can be explained by specific 3D measures of facial shapes and fluctuating asymmetry, which has important implications for clinical practice and research.

Physical attractiveness continues to be an important factor in today’s society, and facial appearance remains one of the most defining components of attractiveness. Individuals who are perceived as more attractive are commonly shown to achieve better social and labor market outcomes such as dating/marriage or greater earnings [

Given the increased demand for esthetic services, much research has been conducted to examine the aspects/components of the face that predict facial attractiveness. Previous studies have utilized a variety of 2-dimnesional (2D) imaging techniques [

In this study, we present comprehensive evidence on the relationships between multiple objective 3D measures of facial shape and symmetry derived from 3D images with perceptions of facial attractiveness. Specifically, we examine the effects of objective 3D facial shape and asymmetry measurements generated from 3D facial images from a large sample of individuals on attractiveness ratings provided by a group of raters who evaluated these images. The extant research is focused on how objective 2D measures of the face correlate with attractiveness ratings. Our key contribution is deriving objective 3D facial measures directly from 3D data by using advanced geo-morphometric methods, thus capturing more complex aspects of facial shape variation than what is captured by 2D measures. Furthermore, previous evidence remains largely based on small samples, and we employ one of the largest samples to date for examining this question.

The Institutional Review Board at the associated university approved the protocol for this study. Three-dimensional images were collected by the study investigators between 2009 and 2013 from 325 adult males (n=102) and females (n=223) of varying ages (mean=35.6 years, range=18 to 70 years). Individuals were required to be adults living in Iowa. These individuals were recruited for studies of oral clefts or facial variation. About 37% of these individuals were parents of children with oral clefts, but none of the participants had oral clefts. Nearly 90% of the sample self-reported their race as White. Three-dimensional images of each participant were captured using a 3dMD system and software (3dMD, Atlanta, GA, USA). The 3dMD system combines both stereophotogrammetry and structured light mechanisms to capture facial surface images very quickly (~1.5 milliseconds) and accurately (RMS of 0.2 mm) [

The 3D coordinates of the 32 landmarks were exported and submitted to geo-morphometric shape procedures implemented in the software Morpho J for data with object symmetry [

In PCA by construction, the first principal component (PC) accounts for the largest amount of variance followed by the second component, third, and fourth successively. In this study we utilized the first 4 PCs of each symmetric and asymmetric variations as our first and second categories of objective measures of facial shape. We also measured overall facial size via centroid size, calculated as the square root of the sum squared distances between the centroid and all other points in the landmark configurations. Finally, we evaluated fluctuating asymmetry (FA) which represents the overall magnitude to which an individual is asymmetric based on a zero mean value (laterality and directionality are not considered) using Mahalanobis distances (scaled relative to the variation of asymmetry in the sample) which complement the PCA of the asymmetric component of shape variation. While Asymmetric PCs provide detailed resolution on the particular aspects of asymmetry that explain the most variation in all the faces, individual FA scores capture overall levels of left–right differences in each individual. In summary, a total of 4 categories of objective facial shape measurements were obtained including: 4 PCs of symmetric and asymmetric variation, centroid size, and Mahalanobis FA scores.

Ten university students and staff (5 females and 5 males) were identified from a convenience sampling approach to rate facial attractiveness. Frontal and lateral (left and right) facial image views of each study subject were presented to the study raters. The frontal and lateral views presented to the raters sufficiently captured facial shape and symmetry features for the purpose of evaluating how one would view attractiveness in real life. We did not provide the images to the raters in a 3D viewing software that allows them to see the image in whatever position they wanted because it would unlikely add measurement precision and may instead introduce measurement error and noise. Humans typically view faces and assess facial attractiveness in frontal and profile dimensions in real life and not in flipped, rotated, reversed, or horizontal positions. Thus, allowing raters to manipulate images for rating attractiveness could bias attractiveness perceptions. For instance, seeing a vertically or obliquely flipped face is not meaningful for capturing how one may rate facial attractiveness in real life and may bias the rating downward. Furthermore, such manipulations could reduce rater sensitivity to meaningful and real differences in attractiveness between faces. Therefore, it is important to standardize how images are presented to the raters in order to reduce as much as possible random noise and systematic biases in how images are viewed and rated.

The raters were asked to rate overall facial attractiveness based on the frontal and lateral views on a 5-point Likert-scale (1=very unattractive, 2=unattractive, 3= average attractiveness, 4=attractive, 5=very attractive) and a 100-point visual analogue scale (VAS) (from 0 very unattractive to 100 very attractive); the VAS had no pre-markings other than the anchoring points. Thirty-three images were randomly duplicated to assess test-retest reliability.

We employed linear regression analysis to examine the effects of the objective facial shape and symmetry measures on attractiveness ratings. Our regression model was based on the following specification:

The dependent variable ^{th} percentile as the reference category (i.e., 4 indicators for each measure) in order to capture non-linear effects of deviations from intermediate values. For example, four binary (0/1) indicators were used to represent the first symmetric PC, another four indicators represented the second symmetric PC, and so on. Finally, we estimated a regression that simultaneously included all these four categories of objective measures of facial shape in order to jointly assess their effects on attractiveness ratings.

The regression controlled for subject’s gender (

In order to further account for potential dependence of the error terms within raters (e.g., some raters may tend to rate in the high, low, or medium range), we estimated the variance-covariance matrix using the Huber-type estimator with standard errors clustered at the rater level; this estimator is robust to both heteroscedasticity and non-independence of the errors within clusters [

We also estimated an alternative model to the random effects that included rater fixed effects (equivalent to including 0/1 binary indicators for the raters; raters’ gender was omitted as it is accounted for by the fixed effects), also clustering the errors at the rater level. This model relaxes the assumption of no unobservable rater-level confounders. That model yielded similar regression coefficients but with less precision (higher standard errors) than the random effects model as expected [

^{st} and 5^{th} quintiles for each of the components. ^{rd} quintile, 40–60^{th} percentile) as the reference category. We also report the results for the regressions when each of the four facial measure categories was included in the regression on its own without the other categories in Supplementary Tables S1–S4 online. The results were overall comparable when including all these measures jointly so we focus on discussing the results from the full model (

All categories of objective 3D facial variation were significantly related to the attractiveness ratings when included simultaneously in the regression, indicating that each is capturing unique variation in perception of attractiveness. Beginning with the first four principal components of symmetry, all of these had significant effects on one or both of the rating scales (Likert-scale or VAS). Individuals who were farther from the intermediate scores (40–60^{th} percentile) in either direction had lower attractiveness ratings, but reductions were more prominent for those in the first two quintiles. The first PC of symmetry (Symm PC1) accounted for 21.2% of the total variation in symmetric shape. It captured variation in total face height, chin projection, facial width and profile convexity or concavity as shown in ^{th} percentile) were perceived as less attractive. The second PC (Symm PC2) accounted for 13.2% of the total variation in symmetric shape and captured variation ranging from mid-face protrusion and profile convexity to mid face retrusion and profile concavity (^{th} percentile) were perceived as more attractive, while those with mid face retrusion and profile concavity (60–100^{th} percentile) were perceived as less attractive. Symm PC3 accounted for 10.3% of the total variation in symmetric facial shape and captured variation in lip height (i.e., lip thickness) and nose prominence as shown in ^{th} percentile) were perceived as less attractive. Symm PC4 accounted for 8.9% of variation in symmetric facial shape and reflected variation in lower facial height, mandibular plane inclination and depth of the labio-mental fold as (^{th} percentile) were perceived as less attractive.

The components of asymmetric facial variation also had significant effects on attractiveness ratings yet to a lesser extent than the symmetric components above. Some asymmetry components showed slightly inconsistent results for their effects on attractiveness ratings. The first PC of asymmetry (Asymm PC1) accounted for 17.3% of the variation in asymmetric facial shape and captured variation in the tip of the nose and chin, relative to the midsagittal plane as shown in ^{th} percentile) were perceived as more attractive, whereas individuals with less deviation in the same direction were less attractive (20–40^{th} percentile). Asymm PC2 accounted for 14.9% of the variation in asymmetric facial shape and depicted orbital cants and asymmetry in the length of the mandibular border as shown in ^{th} percentile), who were perceived as slightly more attractive. Asymm PC3 accounted for 7.5% of the variation in asymmetric facial shape and reflected cants of the commissures of the lips and of the floor of the nose as seen in ^{th} percentile) regardless of direction were perceived as significantly less attractive. Finally, Asymm PC4 accounted for 6.7% of the variation in asymmetric shape and represented deviations in the root and bridge of the nose relative to the midsagittal plane (^{th} percentile) were perceived as less attractive.

Centroid size capturing facial size also had significant effects on attractiveness. Large faces (60–100^{th} percentile) were perceived as less attractive whereas smaller faces (0–20^{th} percentile) were considered more attractive. Finally, fluctuating asymmetry, as determined by Mahalanobis distances, also had significant effects on perceived facial attractiveness. Individuals with greater facial asymmetry (60–100^{th} percentile) were perceived as less attractive overall. However, the effect was only significant for those in the 60–80^{th} percentile.

Male study participants were rated overall as more attractive than female participants. However, there were overall no major differences in ratings between male and female raters; male raters had lower VAS scores on average but the difference was only marginally significant.

In summary, 3D facial shape components related to facial height, midfacial projection, chin and nose prominence, lip thickness, mandibular plane inclination as well as specific and overall 3D aspects of facial asymmetry were significantly related to attractiveness ratings on the Likert-scale and VAS (^{th} percentile), steeper mandibular plane angle, shallow labio-mental folds (60–80^{th} percentile) and smaller faces (0–20^{th} percentile). Conversely, the following facial shapes were related to lower ratings of facial attractiveness: Shorter facial heights with protrusive chins (0–40th percentile); mid face retrusion (80–100^{th} percentiles); faces with protrusive noses and thin lips (20–40%); flat mandibular planes with deep labio-mental folds (0–20%^{th} percentile); any cants of the lip commissures and floor of the nose (0–40th and 60–100th percentiles); larger faces (60 −100th percentile); and increased FA (60–100th percentile).

We examined the relationships between objective 3D measures of facial shape and symmetry directly derived from 3D images and subjective ratings of facial attractiveness in a large sample of images. We found several of these 3D measures to be significantly related to perceptions of attractiveness including those related to facial height, midfacial projection, chin and nose prominence, lip thickness, lower facial height, mandibular plane inclination and labio-mental fold depth as well as specific and overall aspects of facial asymmetry (FA). Furthermore, our analysis examined how deviations from the “average” values of these measures in either direction and in magnitude matter for attractiveness ratings. When considering the principal components (PCs) of symmetry, the first and the second PCs had the largest impact on perceived attractiveness. Symm PC1 and Symm PC2 depicting variation mainly on total facial height and midfacial protrusion/retrusion were associated with large changes in facial attractiveness ratings, with both extremes of total facial height or midfacial retrusion being perceived as less attractive. With regards to facial asymmetry, Asymm PC3 was associated with the greatest impact on perceived facial attractiveness indicating that cants of the lip commissures or of the floor of the nose in any direction have negative impacts on perceived facial attractiveness. Facial size, as measured by centroid size, also had effects of large magnitude on facial attractiveness that were observed at the extremes. Very small faces were perceived as more attractive, while very large faces were perceived as less attractive. While some facial shape indicators such as overall facial size and FA have unidirectional effects on perceived attractiveness, measures captured by the symmetric and asymmetric components have bidirectional effects for deviations from intermediate values that are more prominent at the extremes. This observation of decreased facial attractiveness as facial shape components approach the extremes is consistent with the averageness theory of facial attractiveness, which postulates that within a given population of faces, those closer to the mathematical average face are perceived as more attractive than faces that deviate from the average [

Upper face retrusion with lower face protrusion was found to be associated with reduced attractiveness ratings, consistent with other studies [

The impact of facial asymmetry on perceived attractiveness has been generally inconsistent in the literature, with some studies finding it to be a significant predictor of facial attractiveness [^{th} percentile. Thus, our study supports an impact of facial asymmetry on perceived attractiveness however not as significant as other aspects of facial variation.

Our study has important implications for clinical practice as well as research. For practice, the study identifies several objective 3D measures of facial shape that clinicians can consider in planning treatments aimed at improving facial esthetics such as orthodontic treatments and orthognathic surgeries and, in consultation with patients, add these into the set of objective indicators of treatment success, especially the ones with large effects. Our findings indicate that perceptions of facial attractiveness are complex in being related to several aspects of 3D facial variation in unique ways. Follow-up studies to examine the interplays between these objective 3D indicators including how they influence each other’s effects can be useful to further understand how individuals perceive attractiveness. For social scientists interested in examining how attractiveness modifies social and economic outcomes such as labor market participation, earnings, and marriage opportunities, our study provides strong evidence that taking 3D images of study participants when possible can provide objective 3D assessment of attractiveness in lieu of subjective ratings.

A limitation of our study is generalizability of results. Our study sample included mainly White individuals from the Midwest and all raters reported their race/ethnicity as non-Hispanic Whites. Therefore, findings may not be fully applicable across racial/ethnic groups and geographic areas due to cultural differences in perceptions of attractiveness. We are unable to evaluate in our study if and how race and ethnicity modify the relationships between objective facial measures and attractiveness ratings. Examining this question in racially/ethnically diverse populations is needed to evaluate generalizability of our results.

Objective 3D measures of facial shape variation derived from 3D images have significant effects on perceived attractiveness. Aspects of symmetric shape variation have the most impact and include facial height, midfacial projection, chin and nose prominence, lip thickness, lower facial height, mandibular plane inclination and labio-mental fold depth. Components of asymmetric variation such as cants of the lip commissures and the base of the nose have the most impact along with higher levels of fluctuating asymmetry and overall facial size.

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Special thanks to the individuals and raters that participated in his study. We also thank Steven F. Miller for his support on the geometrics morphometric analyses and Chika Richter and Patricia Hancock for their help in acquiring patient images, maintaining our study databases and reviewing the landmarking quality of the images.

Funding:

The study was supported by an internal research grant (Iowa Dental Research Grant) received from the University of Iowa College of Dentistry. The 3dMD photo collection was supported by grant R01 DD000295 from the Centers for Disease Control and Prevention (CDC). The contents of this work are the sole responsibility of the authors and do not necessarily represent the official views of the CDC, and also by the National Center for Advancing Translational Sciences, the National Institutes of Health (grants 2 UL1 TR000442-06 and T32-DEO14678-09) and by the American Association of Orthodontics Foundation (grants OFDFA_2008–2011 and BRA 2012).

A graphical representation of the location of all 32 coordinate landmarks. For a complete list of landmarks names see

Anthropometric Landmarks used for Facial Shape Analysis

Number | Landmark | Number | Landmark |
---|---|---|---|

1 | Glabella | 17 | Left Exocanthion |

2 | Nasion | 18 | Left Palpebrale Inferius |

3 | Pronasion | 19 | Right Alare |

4 | Subnasale | 20 | Right Alar Curvature Point |

5 | Labiale Superius | 21 | Right Subalare |

6 | Stomion | 22 | Right Columnella |

7 | Labiale Inferius | 23 | Left Alare |

8 | Sublabiale | 24 | Left Alar Curvature Point |

9 | Pogonion | 25 | Left Subalare |

10 | Gnathion | 26 | Left Columnella |

11 | Right Endocanthion | 27 | Right Chelion |

12 | Right Palpebrale Superior | 28 | Right Crista Philtri |

13 | Right Exocanthion | 29 | Left Chelion |

14 | Right Palpebrale Inferius | 30 | Left Crista Philtri |

15 | Left Endocanthion | 31 | Right Otobasion Inferius |

16 | Left Palpebrale Superius | 32 | Left Otobasion Inferious |

Descriptive Statistics of Study Variables

Mean | Standard | Min | Max | |
---|---|---|---|---|

Attractiveness Ratings | ||||

Likert-Scale | 2.68 | 0.75 | 1 | 5 |

VAS | 39.84 | 17.46 | 0 | 93 |

Facial Symmetry Components | ||||

PC1 | 0.00 | 0.03 | −0.08 | 0.09 |

PC2 | 0.00 | 0.03 | −0.08 | 0.07 |

PC3 | 0.00 | 0.02 | −0.06 | 0.10 |

PC4 | 0.00 | 0.02 | −0.06 | 0.06 |

Facial Asymmetry Components | ||||

PC1 | 0.00 | 0.01 | −0.03 | 0.03 |

PC2 | 0.00 | 0.01 | −0.02 | 0.02 |

PC3 | 0.00 | 0.01 | −0.02 | 0.02 |

PC4 | 0.00 | 0.01 | −0.01 | 0.01 |

Centroid Size | 269.50 | 13.18 | 238.70 | 302.72 |

Fluctuating Asymmetry | ||||

Procrustes distance | 0.02 | 0.00 | 0.01 | 0.03 |

Mahalanobis distance | 6.25 | 0.91 | 4.00 | 8.98 |

Male participant | 0.31 | 0.46 | 0 | 1 |

Male rater | 0.50 | 0.50 | 0 | 1 |

Notes: The descriptive statistics are shown for the continuous objective measures. In the regression analyses, these measures are represented by dummy variables for their quintiles.

Effects of All Facial Objective 3D Measures when Included Jointly in One Regression on Facial Attractiveness Ratings

Objective 3D Measures | Main aspect of facial shape variation captured | Likert-Scale | VAS | ||
---|---|---|---|---|---|

| |||||

β | SE | β | SE | ||

Total face height (TFH) & chin projection | |||||

| |||||

1^{st} quintile | Short TFH, protrusive chin | −0.242 | (0.044) | −4.076 | (0.888) |

2^{nd} quintile | Long TFH, retrusive chin | −0.129 | (0.042) | −1.888 | (0.672) |

4^{th} quintile | ↓ | −0.014 | (0.020) | 0.356 | (0.547) |

5^{th} quintile | −0.039 | (0.032) | −0.571 | (0.960) | |

| |||||

Mid face projection | |||||

| |||||

1^{st} quintile | Mid face protrusion | 0.084 | (0.025) | 1.327 | (0.529) |

2^{nd} quintile | ↓ | 0.065 | (0.028) | 0.683 | (0.523) |

4^{th} quintile | −0.045 | (0.028) | −3.333 | (0.707) | |

5^{th} quintile | Mid face retrusion | −0.252 | (0.039) | −7.939 | (1.140) |

| |||||

Nose projection and lip thickness | |||||

| |||||

1^{st} quintile | Protrusive nose & thin lips | −0.027 | (0.028) | −0.870 | (0.742) |

2^{nd} quintile | ↓ | −0.061 | (0.027) | −1.692 | (0.554) |

4^{th} quintile | −0.021 | (0.029) | −0.756 | (0.507) | |

5^{th} quintile | Retrusive nose & thick lips | 0.046 | (0.041) | 1.266 | (1.047) |

| |||||

Lower face height (LFH), mand. plane inclination & labio-mental fold depth | |||||

| |||||

1^{st} quintile | Flat mand. plane, deep labio-mental fold | −0.063 | (0.023) | −1.688 | (0.559) |

2^{nd} quintile | ↓ | −0.019 | (0.026) | 0.506 | (0.582) |

4 quintile | 0.070 | (0.030) | 1.408 | (0.968) | |

5^{th} quintile | Steep mand. plane, shallow labio-mental fold | 0.030 | (0.036) | 1.108 | (0.830) |

| |||||

L-R deviation of nose tip and chin | |||||

| |||||

1^{st} quintile | Nose tip deviates right, chin left | 0.061 | (0.022) | 1.985 | (0.688) |

2^{nd} quintile | ↓ | −0.093 | (0.033) | −1.058 | (0.627) |

4^{th} quintile | −0.017 | (0.039) | −0.127 | (0.758) | |

5^{th} quintile | Nose tip deviates left, chin right | 0.027 | (0.035) | 0.457 | (0.525) |

| |||||

Orbital cants, chin deviation and lateral size discrepancy of mand. border | |||||

| |||||

1^{st} quintile | Left to right inferior orbital cant, chin deviates right & smaller mand. right border | −0.042 | (0.025) | 0.843 | (0.441) |

2^{nd} quintile | −0.021 | (0.021) | −0.423 | (0.504) | |

4^{th} quintile | ↓ | −0.037 | (0.029) | −1.236 | (0.632) |

5^{th} quintile | Right to left inferior orbital cant, chin deviates left & smaller mand. left border | −0.004 | (0.032) | −0.462 | (0.515) |

| |||||

Commissure and floor of the nose cants | |||||

| |||||

1^{st} quintile | Right to left inferior floor of the nose & commissure cant | −0.170 | (0.038) | −4.201 | (0.561) |

2^{nd} quintile | ↓ | −0.171 | (0.033) | −5.039 | (0.793) |

4^{th} quintile | −0.158 | (0.024) | −4.557 | (0.949) | |

5^{th} quintile | Left to right inferior floor of the nose & commissure cant | −0.171 | (0.027) | −4.801 | (0.559) |

| |||||

Root & bridge of the nose deviation | |||||

| |||||

1^{st} quintile | Root & bridge deviates right | 0.018 | (0.057) | −1.022 | (0.937) |

2^{nd} quintile | ↓ | 0.014 | (0.047) | −1.146 | (1.001) |

4^{th} quintile | 0.020 | (0.045) | −1.082 | (0.712) | |

5^{th} quintile | Root & bridge deviates left | −0.065 | (0.040) | −3.446 | (0.756) |

| |||||

Overall facial size | |||||

| |||||

1^{st} quintile | Smallest size | 0.288 | (0.033) | 6.533 | (0.989) |

2^{nd} quintile | ↓ | 0.021 | (0.021) | 0.179 | (0.432) |

4^{th} quintile | −0.235 | (0.037) | −5.929 | (1.065) | |

5^{th} quintile | Largest size | −0.342 | (0.033) | −9.312 | (1.071) |

| |||||

Overall Asymmetry | |||||

| |||||

1^{st} quintile | Smallest Asymmetry | −0.034 | (0.022) | −0.428 | (0.718) |

2^{nd} quintile | ↓ | 0.001 | (0.040) | 0.462 | (0.866) |

4^{th} quintile | −0.154 | (0.023) | −3.843 | (0.618) | |

5^{th} quintile | Largest Asymmetry | −0.029 | (0.029) | −1.013 | (0.701) |

Notes: The Table reports the effects (β) and their standard errors (SE) of the objective 3D measures of facial shape and variation on the Likert scale and VAS ratings of attractiveness when these objective measures are included simultaneously in the regression for the attractiveness ratings. Each objective 3D measure is represented by 4 dummy variables for its 1^{st}, 2^{nd}, 4^{th}, and 5^{th} quintiles with the 3^{rd} quintile (representing the average shape captured by each measure) as the reference category. The βs represent the effects of these quintiles on attractiveness relative to the 3^{rd} quintile. For example, the first β under VAS of −4.076 indicates that individuals who ranked in the first quintile of the first symmetry principal component were rated as less attractive by about 4 units on average compared to those ranking in the third quintile of that principal component. The column labeled “Main aspect of facial shape variation captured” describes the facial shape captured by each objective 3D measure, and the solid downward arrow represents the overall change in facial shape when transitioning from the 1^{st} quintile to the 5^{th} quintile of that measure. The effects of the objective 3D measures were estimated using generalized least squares linear regression including random effects for the raters and controlling for raters’ and study participants’ gender (not shown for brevity). Separate regressions were estimated for the Likert scale and the VAS ratings of attractiveness. Standard errors are clustered at the rater level using a Huber-type estimator. PC=principal component.

The regressions are estimated for 3130 ratings (10 raters each rating 313 study participants).