Automated Neoclassical Vertical Canon Validation in Human Faces with

Machine Learning

Ashwinee Mehta

1 a

, Maged Abdelaal

2 b

, Moamen Sheba

2 c

and Nic Herndon

1 d

Department of Computer Science, East Carolina University, Greenville, U.S.A.

School of Dental Medicine, East Carolina University, Greenville, U.S.A.

Keywords:

Vertical Canon, One Thirds, Facial, Dental Reconstruction, Anthropometric Landmarks, Machine Learning.

Abstract:

The proportions deﬁned by the neoclassical canons for face evaluation were developed by artists and

anatomists in the 17

and 18

centuries. These proportions are used as a reference for planning facial or

dental reconstruction treatments. However, the assumption that the face is divided vertically into three equal

thirds, which was adopted a long time ago, has not been veriﬁed yet. We used photos freely available on-

line, annotated them with anthropometric landmarks using machine learning, and veriﬁed this hypothesis.

Our results indicate that the vertical dimensions of the face are not always divided equally into thirds. Thus,

this vertical canon should be used with caution in cosmetic, plastic, or dental surgeries, and reconstruction

procedures.

1 INTRODUCTION

The face is one of the most important factors affect-

ing the physical appearance of a person. Different

facial proportions can be used for measuring the fa-

cial attractiveness, for recommending hairstyles, fash-

ion jewelry, eyeglasses, etc. The measurement of fa-

cial attractiveness is also applicable in cosmetics, or-

thodontics and plastic surgery. Dental practitioners

take into consideration the different facial proportions

in order to create a denture of suitable shape, size, and

position.

The neoclassical canons used for proportional

evaluation of the face were developed in the 17

and

centuries. These canons were based on the as-

sumption that certain ﬁxed ratios existed between dif-

ferent parts of a human face. They are still used to

deﬁne the proportions between various areas of the

head and face. One of these eight deﬁned neoclassi-

cal canons is the vertical canon, which states that the

face is divided into three equal sections. The ﬁrst sec-

tion is from the top of the forehead (Trichion), to the

bridge of the nose (Glabella), as shown in Figure 1,

the second section is from the bridge of the nose to

https://orcid.org/0000-0002-7167-2563

https://orcid.org/0000-0002-7414-423X

https://orcid.org/0000-0003-1188-2080

https://orcid.org/0000-0001-9712-148X

the base of the nose (Subnasale), and the third sec-

tion is from base of the nose to the chin (Menton).

Trichion, Glabella, Subnasale and Menton are the an-

thropometric landmarks that are identiﬁed before tak-

ing the measurements of the facial thirds. The vertical

canon is widely used in facial surgeries and dental re-

construction procedures.

Farkas et al. (1985) ﬁrst investigated the appli-

cability of the neoclassical facial canons in young

North American Caucasian adults. Following this, the

canons were also validated on several other popula-

tion groups including Nigerians, African-Americans,

Turkish, Vietnamese, Thai, and Chinese individuals.

These studies were performed by adopting the stan-

dard anthropometric methods and the measurements

were obtained using anthropometric tools like milli-

metric compass, sliding calipers, etc. Some studies

have used images pre-annotated with the anthropo-

metric landmarks.

Missing teeth with age causes a person’s face to

collapse. While ﬁxing the patient’s teeth, it is also im-

portant to consider restoring the patient’s facial shape.

With a collapsed face, only the bottom one third of

the face, i.e., from Subnasale to Menton is affected

and needs to be restored. This facial restoration also

needs some reference for comparing the facial shape

proportions to convert the collapsed face into normal

facial shape. Inclusion and evaluation of facial aes-

thetics is important while planning for facial or den-

Mehta, A., Abdelaal, M., Sheba, M. and Herndon, N.

Automated Neoclassical Vertical Canon Validation in Human Faces with Machine Learning.

DOI: 10.5220/0011300200003269

In Proceedings of the 11th International Conference on Data Science, Technology and Applications (DATA 2022), pages 461-467

ISBN: 978-989-758-583-8; ISSN: 2184-285X

461

(a) The neoclassical vertical canon states that the face is di-

vided into three equal thirds.

(b) To test this hypothesis we used the Dlib-81 library to auto-

matically place facial landmarks on an image.

used the ten circled landmarks to place the four lines.

Trichion to Glabella

Glabella to Subnasale

Subnasale to Menton

0.25

0.30

0.35

0.40

0.45

0 10 20 30

Frequency

Normalized Distances

(d) The density distributions of the three distances using anno-

tated images from LFW, MUCT, and CUHK datasets seem to

invalidate this hypothesis.

Figure 1: Facial landmarks are used to automatically place the lines for Trichion, Glabella, Subnasale, and Menton. These

lines were used in one of the neoclassical canons, the vertical canon, to surmise that each face is divided into three equal

sections. However, evidence shows that these distances are not equal.

tal reconstruction treatment. Many clinical textbooks

and journal articles recommend to use these neoclas-

sical canons for evaluating the aesthetics. However,

before blindly applying these recommended neoclas-

sical formulae, it is important to validate them. With

the advancements in technology, it is no longer re-

quired to use the traditional anthropometric tools to

take measurements from the human face. We can

use machine learning to train a model to automati-

cally identify the different anthropometric landmarks

of the human face and thus avoid the need for direct

contact with patients. The objective of this study is to

DATA 2022 - 11th International Conference on Data Science, Technology and Applications

462

verify the vertical canon by using machine learning to

eliminate the need to take the measurements manually

using different anthropometric tools.

All the canon validation methods that have been

proposed have used different physical instruments (Le

et al., 2002; Bozkir et al., 2004; Al-Sebaei, 2015;

Eboh, 2019) and software applications for taking

measurements of the face (Burusapat and Lekdaeng,

2019). Some of the proposed techniques have used a

ready-made database that had images with the anthro-

pometric landmarks annotated (Schmid et al., 2008;

Pavlic et al., 2017). However, none of the techniques

have used automated tools for getting the measure-

ments and validating this canon. These techniques are

discussed in Section 4.

Our proposed method used large volume of pho-

tos available online, annotated them with automated

tools, and veriﬁed this hypothesis. We have per-

formed the automatic validation of the vertical canon

by annotating the images from three freely available

image databases using machine learning. By using

the proposed method, one can validate the vertical

canon automatically without the need to use tradi-

tional anthropometric tools or instruments directly on

the patient.

2 MATERIALS AND METHODS

We tested the applicability of the vertical neoclassi-

cal canon on the facial images collected from three

freely available datasets: Labeled Faces in the Wild

(LFW) face database (Huang et al., 2007), the Milbor-

row / University of Cape Town (MUCT) face database

(Milborrow et al., 2010), and the Chinese Univer-

sity of Hong Kong student database (Wang and Tang,

2009). The LFW is a database of face photographs

designed for studying the problem of unconstrained

face recognition. The data set contains 13,233 facial

images of 5749 individuals collected from the web.

All the images in the LFW database have a resolution

of 250 × 250 pixels. The MUCT face database con-

sists of 3,755 facial images of 276 individuals. The

individual were sampled from students, parents at-

tending graduation ceremonies, high school teachers

attending a conference, and employees of the univer-

sity at the University Of Cape Town campus in De-

cember 2008. This diverse population includes a wide

range of subjects, with approximately equal numbers

of males and females, and a cross section of ages and

races. All the images in the MUCT database have a

resolution of 480 × 640 pixels. The CUHK database is

for research on face sketch synthesis and face sketch

recognition, and consists of 188 facial images of 188

individuals. All the images in the CUHK database

have a resolution of 1024 × 768 pixels. All the fa-

cial images were not labeled with any anthropometric

landmarks.

Our proposed workﬂow had the following steps:

1. Annotation: The ﬁrst step was to annotate

these images with facial anthropometric landmarks.

We initially evaluated the Dlib’s 68-point facial land-

mark detector (King, 2009), the most popular facial

landmark detector. It can ﬁnd 68 different facial land-

mark points including chin and jaw line, eyebrows,

nose, eyes and lips. In our preliminary work we de-

termined that this library does not provide facial land-

marks for the forehead. Therefore, we used an ex-

tended version of this library, 81 Facial Landmarks

Shape Predictor, which provides 13 additional land-

marks that delineate the forehead. Not all the land-

marks generated are needed to get the measurements

of the thirds of the face. Out of all the 81 landmarks,

we used only the following landmarks, as shown in

Figure 1c:

• 69 and 72, for the left- and right-forehead, respec-

tively. These landmarks were used for the place-

ment of the Trichion line.

• 77, 17, 26, and 78, for the left-temple, left-

exterior eyebrow, right-exterior eyebrow, and

right-temple, respectively. These landmarks were

used for the placement of the Glabella line. This

is the only line for which we used four landmarks,

since none of the 81 landmarks are placed at the

position for the bridge of the nose. Therefore, we

used the mid-vertical distance between landmarks

77 and 17, along with the mid-vertical distance

between landmarks 26 and 78, as the anchors for

the Glabella line.

• 31 and 35, for the left- and right-base of the nose,

respectively. These landmarks were used for the

Subnasale line.

• 7 and 9, for the left- and right-side of the chin,

respectively. These landmarks were used for the

Menton line.

2. Assess the Annotation: The second step was

to visually inspect the placement of the four lines

mentioned above, on all the images from the three

datasets. During this manual inspection we noticed

that the predictor placed the landmarks in the cor-

rect positions in images that had eyeglasses, beard,

bald heads, hats, as well as for people of different age

groups and races, and to different background colors

and patterns. However, some of the lines were not

correctly placed for images that did not have a front

proﬁle view. For some of these images, the 81 Facial

Landmarks Shape Predictor misplaced some of the

Automated Neoclassical Vertical Canon Validation in Human Faces with Machine Learning

463

landmarks, which led to the incorrect placement of

the Trichion, Glabella, Subnasale and Menton lines,

as shown in Figure 2.

3. Select Images: Therefore, to get a correct and

unbiased measurement of the thirds of the face, in the

third step we planned to select about 500 images, that

had correctly positioned landmarks. We identiﬁed

464 images from the LFW dataset, 86 images from

the MUCT dataset, and 29 images from the CUHK

dataset (for a total of 579 images), that had the cor-

rect automatic placement of the four lines.

4. Calculate Distances: We used these images, in

the fourth step to calculate the three facial distances:

between Trichion and Glabella, between Glabella and

Subnasale, and between Subnasale and Menton. The

initial distance measurements were taken in number

of vertical pixels between each two lines. Since we

used images from all the three image databases, we

had to take into consideration the fact that the images

were provided with different resolutions. Therefore,

we performed normalization of all the three distance

values using Equation 1.

∑

j=1

(1)

where d

is the normalized distance of d

, and d

one of the three distances.

5. Plot Density Distributions of These Dis-

tances: In the ﬁnal step we used these normalized dis-

tances to generate density plots for the three distances.

These are shown in Figure 1d for the 579 combined

images, and in Figures 3b, 3d, and 3f, for the 464 im-

ages from the LFW database, the 86 images from the

MUCT database, and the 29 images from the CUHK

database, respectively.

3 RESULTS AND DISCUSSION

Figure 1d shows the distribution of the three distances

across the selected images from the three databases.

These density plots show that the forehead, the dis-

tance between Trichion and Glabella, varies between

about a fourth and a third of the face, with the mean

around 30%. The nose, between Glabella and Sub-

nasale, has a wider distribution, with length values be-

tween about 25% and 38% of the vertical length of the

face, and a mean closer to one third. The mouth, be-

tween Subnasale and Menton, seems to be the longest

of the three distances, with lengths between about

32% and 45% of the vertical length of the face, and

a mean of about 38%.

One of the confounding factors of these varia-

tions is the resolution of the images in our analysis.

For images with lower resolution the misplacement

of the landmarks has a bigger inﬂuence of the dis-

tances, since 1 or 2 extra pixels could increase or

decrease a distance by about 4%. For images with

higher resolution such a misplacement would have a

lesser impact on the normalized distances. To eval-

uate this impact we plotted the density distributions

for each dataset separately, as shown in Figure 3.

While there doesn’t seem to be signiﬁcant differences

in the lengths of forehead and nose, across the three

datasets, the length of the mouth, the distance be-

tween Subnasale and Menton, seems to have more

variance for images with lower resolution, than for

images with higher resolution.

One thing that is common across these density

plots is the fact that these distances are not equal,

with about 1/3 for forehead, 1/3 for nose, and 1/3 for

mouth, as stated in the neoclassical canon, but rather

that they have a range of values, with longer length for

mouth than for nose and forehead. Thus, they suggest

that this canon is not valid, and therefore it should be

used with caution in cosmetic, plastic, or dental surg-

eries, and reconstruction procedures.

This analysis would require further evaluation,

as many groups were not well represented in these

datasets. For example, there are very few children,

very few people over the age of 80, and a relatively

small proportion of women. In addition, many eth-

nicities have very minor representation or none at all.

In addition to creating a new dataset that has a wider

representation, we also recommend collecting meta-

data about the images, which should include the de-

tails about each individual, such as age, race, etc., as

well as whether they have all teeth or if they have den-

tures (which is difﬁcult to determine from these im-

ages). Furthermore, the images should include a side

proﬁle view for each person, in addition to the frontal

view.

Another alternative to a new image database, that

is worth exploring, is to collect and annotate three-

dimensional scans. These have the potential to en-

able better localization of the four lines, as with two-

dimensional front views it is difﬁcult to determine the

position of the Trichion and Glabella.

4 RELATED WORK

Bozkir et al. (2004) have performed the validation of

vertical and horizontal neoclassical facial canons in

Turkish young adults. They used a millimetric com-

pass to take the measurements manually. The mea-

DATA 2022 - 11th International Conference on Data Science, Technology and Applications

464

Figure 2: Incorrect placement of landmarks on some images from the MUCT database due to shift in face positions. The left

and middle images have the Glabella line misplaced, and the right image has the Glabella and Menton lines misplaced.

surements were taken manually twice by the same in-

vestigators by ﬁlling out a form for recording the val-

ues. Based on their measurements, it was observed

that only one male face had an equally divided facial

proﬁle. It was observed that the neoclassical canons

were not valid in the majority of the population and

the canons vary among races and also countries.

Al-Sebaei (2015) have performed the validation of

the vertical canon, the orbital canon and the orbito-

nasal canon in young adults originating from the

Arabian Peninsula. They measured the neoclassical

canon using a caliper and analyzed the measurements

using Student’s t-test, general linear modeling, and

pairwise comparison of means. The results indicated

that all the three canons had variations in measure-

ments. It was found out that the lower and upper

thirds were longer than the middle thirds, the intercan-

thal distance was wider than eye ﬁssure length and the

nasal width was wider than the intercanthal distance.

Eboh (2019) has performed a study of young

adults in South-South Nigerian Ethnic Groups, Izon

and Urhobo, to determine if there is a variation in

length among the upper, middle and lower thirds of

the face. The measurements of the thirds were taken

in millimeters by using a sliding caliper. They per-

formed data analysis with SPSS 23 by using descrip-

tive and inferential statistics. In conclusion, it was

found out that the three thirds of the face varied in

lengths. The mean lengths of the upper and lower

thirds were signiﬁcantly longer in the Izon than the

Urhobo, while the mean height of the middle third

was signiﬁcantly longer in the Urhobo than the Izon.

The mean height of the male lower third was sig-

niﬁcantly longer in the Izon than the Urhobo, while

Urhobo females had signiﬁcant longer middle third

than the Izon.

Schmid et al. (2008) have developed a model to

predict the attractiveness of the face based on neo-

classical canons, symmetry and golden ratios. They

used the feature point database that consists of the lo-

cations of the feature points for the faces from the

FERET database and the faces of famous people.

Neoclassical canons were one of the many predictors

of attractiveness. One of these neoclassical canons

used was the vertical canon where forehead height =

nose length = lower face height. From the experiment

results, it was found out that the vertical canon had

a signiﬁcant relationship with attractiveness. It was

also found out that the attractiveness scores decreased

signiﬁcantly as the proportions of the face deviated

from the proportions deﬁned by the canons.

Pavlic et al. (2017) have explored the presence

of neoclassical canons of facial beauty among young

people in Croatia and checked for any possible

psychosocial repercussions occurring in those who

demonstrate deviations in relation to the canons. Nine

neoclassical canons of facial beauty were analyzed on

a sample of 249 people with face and proﬁle pho-

tographs taken in Natural Head Position. Calculations

were performed in the statistical software MedCalc

14.8.1 and based on previously published data. One

of the 9 canons analyzed is the three portion facial

proﬁle canon where trichion – nasion (tr – n) = nasion

– subnasale (n – sn) = subnasale – gnathion (sn – gn).

All analyses were performed in the software Audax-

Ceph. Signiﬁcant deviations from neoclassical facial

beauty canons were found in 55–65% of adolescents

and young adults and gender and age showed no rela-

tion to deviations. Most of the deviations from canons

that affected the quality of life were the ones related

to proportions of facial thirds.

Le et al. (2002) have performed the validation of

Automated Neoclassical Vertical Canon Validation in Human Faces with Machine Learning

465

(a) Sample image from the LFW dataset. The images in this

dataset have a size of 250 × 250 pixels.

Trichion to Glabella

Glabella to Subnasale

Subnasale to Menton

0.25

0.30

0.35

0.40

0.45

0 10 20 30 40

Frequency

Normalized Distances

(b) The density distributions of the three distances for the

464 images used from the LFW dataset.

this dataset have a size of 480 × 640 pixels.

Trichion to Glabella

Glabella to Subnasale

Subnasale to Menton

0.25

0.30

0.35

0.40

0.45

0 10 20 30

Frequency

Normalized Distances

(d) The density distributions of the three distances for the

86 images used from the MUCT dataset.

(e) Sample image from the CUHK dataset. The images in

this dataset have a size of 1024 × 768 pixels.

Trichion to Glabella

Glabella to Subnasale

Subnasale to Menton

0.25

0.30

0.35

0.40

0.45

0 10 20 30 40

Frequency

Normalized Distances

(f) The density distributions of the three distances for the 29

images used from the CUHK dataset.

Figure 3: Examples of images used in this analysis, shown to scale, from the following datasets: LFW, MUCT, and CUHK,

along with their corresponding distance distributions. The distributions for each dataset indicate that the neoclassical vertical

cannon is not valid.

DATA 2022 - 11th International Conference on Data Science, Technology and Applications

466

six neoclassical canons among healthy young adult

Chinese, Vietnamese and Thais by taking nine pro-

jective linear measurements. The nine projective lin-

ear measurements were taken by the authors by us-

ing standard anthropometric methods. These nine

measurements corresponded to six neoclassical facial

canons. It was found out that in neither Asian nor

Caucasian subjects were the three sections of the fa-

cial proﬁle equal.

Burusapat and Lekdaeng (2019) have performed a

comparative study among sixteen Miss Universe, six-

teen Miss Universe Thailand, neoclassical canons and

facial golden ratios to ﬁnd out the most beautiful fa-

cial proportion in the 21st century by using twenty-

six facial proportion points. Acrobat Reader was used

to measure the distances and angles and the data was

recorded in Microsoft Excel to compare the facial pro-

portions. From the results, it was found out that the

three-section proportion was longer in Miss Universe

Thailand than in Miss Universe group.

Amirkhanov et al. (2020) have proposed a solu-

tion for integrating aesthetics analytics into the func-

tional workﬂow of dental technicians. They have pre-

sented a teeth pose estimation technique that can gen-

erate denture previews and visualizations that helps

the dental technicians for designing the denture by

considering the aesthetics and choosing the most aes-

thetically ﬁtting preset from a library of dentures, in

identifying the suitable denture size, and in adjusting

the denture position. In one of the use cases that are

demonstrated in this paper, it is stated that the den-

tal technician uses the facial and dental proportions to

identify the correspondence between the denture and

the face which means that it is important to have the

facial proportions correct for the denture to ﬁt well on

a patient.

5 CONCLUSIONS

The neoclassical canons were used to deﬁne the dif-

ferent proportions between various areas of the head

and the face. These facial canons have been rec-

ommended in various textbooks about orthodontics,

prosthodontics, plastic and dental reconstructive surg-

eries for planning the treatment procedure. We tested

the hypothesis of the face being vertically divided

equally into thirds using machine learning. Our re-

sults indicate that the vertical dimensions of the face

are not always divided equally into thirds. Thus, this

vertical canon should be used with caution in cos-

metic, plastic or dental surgeries or any reconstruction

procedures.

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