Proportions of the aesthetic African-Caribbean face: idealized ratios, comparison with the golden proportion and perceptions of attractiveness

Subjects and sample selection

After the photographs were acquired, they were uploaded into an online survey on SurveyMonkey® and resized to be seen clearly by the participants. As only proportional facial ratios were calculated, and not exact linear distances, photographs did not have to be of a standardized distance from the camera during sample selection. The online survey that participants received included the aims of the study and was voluntary; anonymous and only demographic data (age, gender, ethnicity and profession) were gathered. The survey was then forwarded to university students and orthodontists. Participants were asked to act as an evaluation jury, through appointing an aesthetic evaluation of the face ranging from 0 to 10 (0 = not attractive, 10 = very attractive). A total of 287 responses were gathered, and the photographs of the models who received the highest frequency of high grades (8, 9 or 10) were considered “best graded models” and the ones with the lowest frequency “not well-graded models”.

Anthropometric facial measurements

For each sample of the photographs, the Ricketts [4] method was used to measure the golden proportions in the vertical and horizontal facial planes (Fig. 1). Table 1 indicates the seven facial reference landmarks that were used.

Anthropometric landmark	Definition
Lateral canthus	The most lateral point where the superior and inferior eyelids meet
Soft tissue dacryon	The most medial point where the superior and inferior eyelids meet (i.e. medial canthus)
Soft tissue borders of temporal bone	Most lateral borders of the face in the temporal region
Lateral alae	The most lateral points on the rims of the wings of the nose
Cheilion	The point located at each lateral oral commissure, i.e. the angle of the mouth
Soft tissue menton	The most inferior midline point of the soft tissue chin
Trichion	The midline point at the junction of the hairline and forehead

Using the above measurements, different ratios were calculated in the horizontal and vertical planes, which were then compared with the golden proportion. The following ratios were calculated in the horizontal and vertical planes:

Horizontal ratios

Statistical analysis

SPSS Statistics for Windows, Version 21.0 (Armonk, NY:IBM Corp. Released 2012), Minitab v16 (Minitab Inc., USA) and Microsoft Excel (Microsoft Corporation, USA) were used to perform statistical tests and create graphs. It is estimated that for the study to have 95% power to detect between-group differences with a 6% margin of error, a sample of 260 responses would be needed. A total of 287 responses were gathered. The data were tested for normality and then parametric or non-parametric tests applied as appropriate.

The statistical significance in inter-gender, inter-age and inter-professional differences was calculated using the chi-squared test. Furthermore, significant statistical differences of ratios between the best graded (higher frequency of high scores) and least well-graded photographs were examined using the Mann-Whitney test. All ratios of the model photographs were then compared with the golden proportion using Wilcoxon signed rank test, and then for these ratios, an estimated confidence interval was calculated to produce a numerical range of the ideal ratio for each facial feature (using the median values of the models’ facial ratios). All graphs produced from these results were created with Microsoft Excel.

Inter-sex, inter-age and inter-professional grading disparities

Best graded photographs and least well-graded photograph disparities

In the black female group, three out of the 12 ratios demonstrated significant difference between facial ratios when comparing the best graded and least well-graded photographs, namely the forehead height/intereye-interalae, forehead height/stomion-soft menton and intereye-interalae/interalae-stomion (p <  0.001). In the black male group, seven out of the 12 facial ratios demonstrated statistical significant differences, namely the forehead height/intereye-interalae, forehead height/stomion-soft menton and intereye-interalae/interalae-stomion, which were also significantly different in the female group, but also interalae/interdacryon, interalae/nose width, intercheilion/interdacryon, and intercheilion/interalae (p <  0.001).

Compliance of facial ratios with the golden proportion

Table 6 illustrates the comparison of all facial ratios of each group in comparison to the golden proportion using a Wilcoxon test. Considering that the samples selected were all professional models promoted in social media, a median value was found for each facial ratio for the two groups. Out of the 12 ratios, only one of them was similar to the golden proportion (intereye-soft menton/intereye-stomion, p > 0.05), whilst the rest all demonstrated statistically significant differences (Fig. 2).

Ratio	Black female model median	Female p value	Black male model median	Male model p value
Intertemporal/intercanthal	1.314	< 0.001	1.313	< 0.001*
Intercanthal/intercheilion	1.903	< 0.001	1.773	< 0.001*
Interalae/interdacryon	1.063	< 0.001	1.17	< 0.001*
Interalae/nose width	2.159	< 0.001	1.968	< 0.001*
Intercheilion/interdacryon	1.443	= 0.002	1.606	p = 0.695
Intercheilion/interalea	1.386	= 0.001	1.377	< 0.001*
Forehead height/intereye-interalae	1.552	= 0.173	1.303	< 0.001*
Forehead height/stomion-soft menton	1.519	= 0.05	1.176	< 0.001*
Ala-soft menton/stomion-soft menton	1.708	= 0.002	1.691	< 0.001*
Intereye-interalae/interalae-stomion	1.408	= 0.006	1.352	< 0.001*
Intereye-soft menton/interalae-soft menton	1.566	= 0.022	1.531	< 0.001*
Intereye-soft menton/intereye-stomion	1.591	= 0.151	1.639	0.323

*Significant differences of ratio between the facial ratios and the golden proportion

Proposal of “ideal” facial ratios

Using the median values, in which the majority appears not to correlate with the golden proportion, it was possible to calculate the confidence interval regarding where the value of each facial ratio lies (Table 7). To do this, the median value of each ratio from the whole sample was used. This is because the median value of male and female models was closely similar (Table 6), and thus calculating different confidence interval for each gender would not necessarily provide a different result or be clinically relevant or significant. The results illustrate that there may be an “ideal” range for each facial ratio (Fig. 3).

Ratio	Median	Min	Max
Intertemporal/intercanthal	1.314	1.191	1.556
Intercanthal/intercheilion	1.833	1.583	2.089
Interalae/interdacryon	1.116	0.550	1.459
Interalae/ nose width	1.992	1.357	3.174
Intercheilion/interdacryon	1.50	1.050	2.033
Intercheilion/interalea	1.389	1.188	1.909
Forehead height/intereye-interalae	1.432	0.832	2.222
Forehead height/ stomion-soft menton	1.344	0.774	2.051
Ala-soft menton/stomion-soft menton	1.701	1.535	1.909
Intereye-interalae/interalae-stomion	1.350	1.031	2.045
Intereye-soft menton/ interalae-soft menton	1.544	1.423	1.744
Intereye-soft menton/intereye-stomion	1.600	1.458	1.864

Inter-sex, inter-age and inter-professional grading disparities

The concept of golden proportions being related to facial beauty is not new, and it is still proposed by some artists and sculptors as being a requirement of beauty [2]. Recently, a meta-analysis by Langlois et al. [12] published in the American Psychological Association found that facial attractiveness is a “variable” that is highly consistent between people’s judgements within and across cultures and thus established that irrespective of people’s ethnicity and cultural background, there is agreement about who is and is not attractive. This was also supported by Coetzee et al., who provided further evidence for strong cross-cultural agreement in facial aesthetics [13].

Previous investigations on facial aesthetics and the perception of beauty are extremely important; however, the subject requires modern evaluation due to the potential for changing perceptions over time. For example, female nudes from Renaissance art and sculpture would be considered potentially overweight by modern societal standards, but were appealing during their time, perhaps because a higher body mass was linked with wealth and high socioeconomic status.

Comparison of facial ratios with the golden proportion

Despite the common perception that beauty is a subjective experience [4], it is relevant for one to have clear guidelines that gauge aesthetic facial surgery to provide a consistent and accurate result for each patient. Evidence-based guidelines are not currently used in practice. Previous investigations have studied the correlation between Ricketts’ facial ratios and the golden proportion, resulting in conflicting evidence regarding the topic [8–10]. To the best of the authors’ knowledge, this is the first study to examine this correlation of facial attractiveness and the golden proportion in a black population, as all studies that have been carried out were focused on Caucasian populations.

These results of discordance of facial rations with the golden proportion agree with some relevant literature. In one study, Brazilian women were initially evaluated according to their facial attractiveness and then compared with the golden proportion, and no correlation was found between perception of beauty and the golden proportion [30]. A more recent study investigating the same topic conducted by Rossetti et al. [31] also concluded that the attractive female and male facial ratios did not correlate with the golden proportion. These results also agree with research conducted on European male and female facial proportions by Bashour [32]. Therefore, there appears to be modern research suggesting that the golden proportion cannot be applied in aesthetic facial surgery to provide consistency of results both in Caucasian and black populations.

Our results contradict findings from previous literature that illustrated that attractive faces tend to conform with the golden ratio compared to non-attractive ones. The relationship between attractive female faces and the golden proportion has also been studied by Marquardt, who created an “ideal” mask, deriving from fashion models, using the golden ratio [33]. However, this has been found to be an inaccurate and biased method to predict attractiveness [34]. As illustrated by Holland, as there are so many facial ratios one is bound to find correlations amongst some ratios with the golden ratio, making it an inherently biased method of predicting attractiveness [34]. Medici et al. [6] used facial photographs, which were modified according to the golden ratio and then ranked by judges regarding their attractiveness. It was found that the photographs with ratios that were closer to the golden proportion tended to be perceived as more attractive; however, the participant size was relatively small (12 judges involved) so the results have low statistical power. Pancherz et al. [5] also evaluated facial photographs of professional models and compared them with non-professional facial photographs, concluding that facial ratios of professional models tend to be closer to the golden proportions than non-professionals. However, as well as low statistical power, these studies demonstrate that some authors identify ratios “close to” the golden proportion as positive evidence of a link between this ratio and facial beauty.

Proposal of ideal facial ratios

The results of this investigation demonstrate that the facial proportions of professional black models do not accurately fit the golden proportion. It is therefore relevant to identify whether any proportions are correlated with facial attractiveness, which may subsequently guide facial aesthetic surgery according to a specific guideline. Several other studies have tried to identify the ideal facial ratios to produce guidelines for future aesthetic surgery [25, 35], but these published studies only have a focus on the ideal facial shape in terms of height and width rather than identifying every individual ratio and its ideal range.

This study uniquely identifies that each facial ratio appears to be individualistic and needs to be treated separately from the others rather than attempting to find one proportion that will fit all. More specifically, the most attractive horizontal ratios found were as follows (p < 0.05): intertemporal/intercanthal 1.314 (1.115 to 1556), intercanthal/intercheilion 1.852 (1.583 to 2.089), interalae/interdacryon 1.099 (0.550 to 1.459), interalae/nose width 2.026 (1.33 to 3.174), intercheilion/interdacryon 1.479 (1.050 to 2.033) and intercheilion/interalaa 1.390 (1.188 to 1.909). The most attractive vertical ratios found were as follows (p < 0.05): forehead height/intereye-interalae 1.410 (0.811 to 2.222), forehead height/stomion-soft menton 1.346 (0.676 to 2.051), ala-soft menton/stomion-soft menton 1.699 (1.467 to 1.909), intereye-interalae/interalae-stomion 1.357 (0.912 to 2.139), intereye-soft menton/interalae-soft menton 1.540 (1.342 to 1.806) and intereye-soft menton/intereye-stomion 1.613 (1.458 to 1.864).

These findings may eventually help towards generating guidelines for aesthetic and reconstructive surgeons for patients of different ethnic backgrounds. It should be noted that most of the facial ratios evaluated in attractive male and female black subjects do not appear to conform to the golden proportion. It should also be emphasized that the results of one study are not enough to claim findings of new proportional canons—further investigation and dispassionate analysis will be required.

Limitations

The use of a mean to generalize an ideal ratio also may be considered a limitation, as the harmony of proportions may be more important than strict, hard-ruled ratios, and should be tailored to each individual patient. Further research to consolidate the validity of the proposed ratios found in this study should be undertaken. This can be done through performing a similar methodology to a wider set of pictures or through modifying pictures according to these ratios and inviting participants to grade them before and after the modification. The data in this study was based on 2D images. Furthermore, we have assumed that no digital manipulation of the images had been undertaken by the models or their agency. 3D imaging and/or adopting standardized medical photographic techniques could influence the results.