M. VERDENIK et al.: A NEW METHOD OF DETERMINING FACIAL SIZE FOR THREE-DIMENSIONAL ...
25–31
A NEW METHOD OF DETERMINING FACIAL SIZE FOR
THREE-DIMENSIONAL PHOTOGRAMMETRY QUANTIFICATION
NOVA METODA DOLO^ANJA VELIKOSTI OBRAZA V
TRIDIMENZIONALNI FOTOGRAMETRIJI
Miha Verdenik
1*
, Nata{a Ihan Hren
1
, @iga Kadivnik
2
, Igor Drstven{ek
3
1
Department of Oral and Maxillofacial Surgery, University Medical Center Ljubljana, Zalo{ka 2, 1000 Ljubljana, Slovenia
2
Ortotip LLC, Obrtna ulica 40, 9000 Murska Sobota, Slovenia
3
Faculty of Mechanical Engineering, University of Maribor, Smetanova ulica 17, 2000 Maribor, Slovenia
Prejem rokopisa – received: 2020-06-09; sprejem za objavo – accepted for publication: 2020-07-24
doi:10.17222/mit.2020.113
Contemporary craniofacial surgery includes the pre- and post-operative optical 3D scanning of faces as a method for diagnosing
and verifying the achieved results. The influence of head size in 3D scans must be excluded in order to accurately and uniformly
compare different three-dimensional facial shapes in craniofacial surgery. Regarding this purpose, different head-size parame-
ters must be measured to obtain the scaling factor. A special device, a so-called head ring, has been produced as a structure that
can be fixed to a person’s head. Among defined points, different linear distances (head width, length and height) and volumetric
parameters (lower and upper head volumes) were calculated and compared to body-size measurements. Measurements were per-
formed on 3D scans of the heads of 26 healthy adults with normocclusion (12 men and 14 women) taken using the head ring set.
Body mass index (BMI) statistically significantly correlates with the lower and whole-head volume in men, while in women
more precisely with the upper-head volume. BMI in men does not correlate with any linear distance, while in women it is
closely connected to the facial width. In men the head width and lower head volume are the main contributors to head size,
while in women the crown-to-chin length and upper volume determine the size of the head. A conclusion can be made that the
correlation between the head volume, the BMI and the linear head parameters exists and is gender dependent.
Keywords: 3D, facial, size, photogrammetry
Na podro~ju karniofacialne kirurgije so vedno bolj uveljavljene 3D-metode, med njimi tudi neinvazivni povr{inski posnetki
glave in obraza. Za natan~no primerjavo 3D-posnetkov razli~nih obrazov med seboj, je potrebno izkllju~iti vpliv velikosti glave
in obraza. Za namen bolj objektivne registracije, je bil izdelan poseben pripomo~ek, ki smo ga poimenovali naglavni obro~. Z
njegovo uporabo smo pridobili dodatne podatke, kot so: razdalja med u{esi, razdalja med najvi{jo to~ko glave in brado, razdalja
med navideznim sredi{~em in bazo nosu ter s pomo~jo markerjev izmerjeni volumen spodnje in zgornje piramide ter volumen
elipsoida, ki ga markerji opi{ejo. Dodatno je mo`no, kot parameter dolo~anja velikosti obraza, uporabiti tudi indeks glave (kot
analog obraznemu indeksu) izra~unan kot razmerje med obrazno dol`ino in {irino. Meritve so bile izvedene na 26 zdravih
preiskovancih brez skeletnih in zobnih nepravilnosti (12 mo{kih in 14 `enskah). ITM (indeks telesne mase) je zna~ilno koreliral
z volumnom spodnje obrazne piramide in celotnim volumnom pri mo{kih preiskovancih, pri `enskah pa z volumnom zgornje
piramide. ITM pri mo{kih ni imel zna~ilne povezave z opazovanimi linearnimi razdaljami, pri `enskah pa smo na{li povezavo z
razdaljo med u{esi. Pri mo{kih smo ugotovili, da k velikosti glave najbolj prispevata razdalja med u{esi in volumen spodnje
piramide, pri `enskah pa razdalja med najvi{jo to~ko glave in brado ter volumen zgornje piramide. Ugotovljene so bile zna~ilne
povezave med ITM, spolom in nekaterimi obraznimi parametri, ki smo jih dolo~ili s pomo~jo naglavnega obro~a.
Klju~ne besede: 3D, obraz, velikost, fotogrametrija
1 INTRODUCTION AND BACKGROUND
The tree-dimensional (3D) analysis of facial soft tis-
sues is an important diagnostic and research tool in
craniofacial surgery,
1
but it could also be useful for de-
tecting changes during growth and treatment. There are
two major problems in a comparison of two faces. First,
we have to distinguish between size and shape.
2
If we
want to compare just the facial shapes, we must scale the
faces to the same size, which is hard to define. The cen-
troid size from general procrusted analysis is mostly
used,
2–4
with some disadvantages, as it used for a limited
number of points for size determination, whilst 3D sur-
face scanning provides us with an enormous data set.
The second problem is how to orient two facial scans
within a working space to achieve their optimal registra-
tion. The cranial base is often used for super-imposition-
ing when comparing lateral cephalograms
5
as well as dif-
ferent CT scans
6
because it shows minimal changes after
childhood and it is a good reference point for comparing
two different faces. But facial scans represent only
soft-tissue contours, so we are unable to compare them
based on skeletal structures as a cranial base. There are
other methods available, i.e., general procrusted analysis,
iterative closest point (best-fit)
5
regional best-fit
6,7
mid-endocanthion registration,
3
but none of them is per-
fect. We have used iterative closest-point registration in
our 3D description of class-III faces.
8
We have also de-
termined the average Slovenian facial shell
9
because of
its ethically bonded facial characteristics.
10
The pre-
sented research was triggered by the discrepancies when
Materiali in tehnologije / Materials and technology 55 (2021) 1, 25–31 25
UDK 616-089.8:617.52:53.08 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 55(1)25(2021)
*Corresponding author's e-mail:
miha.verdenik@gmail.com (Miha Verdenik)

calculating the differences between face shapes before
and after orthognathic surgery. The results gathered in
the described way were unsatisfactory because they did
not reflect the actual displacements of the facial struc-
tures for several reasons, among which changes in the
body mass index and differences in body sizes between
the averaged and the actual face seemed to be the main
reasons.
In order to avoid these generalisations induced by the
best-fit method, two obvious possibilities are available.
One is to scan the whole head’s volume, which is a tech-
nically impossible process because the hairy surfaces
cannot be scanned without special preparation. The sec-
ond is to find a way of uniformly defining the orientation
of a facial scan by introducing special markers that do
not change for subsequent scans and that do not depend
on personal particularities.
This study was aimed at finding a correlation for dif-
ferent facial, head, and body-size parameters. An innova-
tive head ring was used to obtain additional data that are
usually excluded during 3D surface facial scanning. The
aim of our study was to find the best parameter that will
be used as a descriptor of the head volume. This parame-
ter can then be used as a coefficient to scale the faces of
different sizes for shape analysis.
2 METHODS
A special device called a head-ring has been pro-
duced that consists of a structure that can be fixed to a
person’s head with spherical markers attached to the
holding structure in such a way that enables their move-
ments to touch the characteristic points on the head,
while still preserving a position relative to the origin of
the whole structure, e.g., the person’s head volume (Fig-
ure 1). Five spherical markers point to five characteristic
points of a human head: both acoustic ducts, the crown
of the head (the highest point of the head during a natu-
ral head position), the nasal base, and the chin. Since
these points are hard to detect while scanning, the mark-
ers have been designed in such a way that enables their
exact scanning in the head-space, while simultaneously
marking these five points exactly on the head’s surface.
This has been achieved by designing a marker that con-
sists of a scanning sphere, a "skin-piece" that touches the
head’s surface and a pole that connects the spherical
marker to the skin piece. In this way the marker not only
represents a point on the face’s surface, but also a vector
that points to the origin of the head’s volume.
To prove the measurement principles and usability of
the head-ring, its prototype was produced from
polyamide (PA12) using the selective laser sintering pro-
cess. The first trials pointed out some awkward solutions
in the design (fixation of markers, positioning the ring
onto the crown of the head, etc.), but they did not influ-
ence the facial scanning. A pilot study was performed
that included 27 young adults (14 female and 13 male,
average age 25±2 and 26±3 years). They were all healthy
M. VERDENIK et al.: A NEW METHOD OF DETERMINING FACIAL SIZE FOR THREE-DIMENSIONAL ...
26 Materiali in tehnologije / Materials and technology 55 (2021) 1, 25–31
Figure 1: Innovated head-ring with a schematic view of the coordi-
nate system
Figure 2: Photos and 3D facial scan with the innovated head ring set on

with normocclusion, without any dentofacial deformities.
We obtained a signed, informed consent.
Each participant’s weight and height were measured
and 3D facial scans were (Figure 2) obtained using an
Artec 3D MH scanner that uses the flying-triangulation
method.
11
The scans were taken in a relaxed environ-
ment, with the subjects sitting on an ergonomic chair in a
straightened posture, with the gaze fixed on a determined
point in the distance, so as to exclude the subject’s
self-awareness of the facial muscles and reconstruct a re-
alistic physiological rest position. The volunteers were
asked to refrain from any movements – if possible, as
well from blinking – for the period of the scanning pro-
cedure (about 15–20 s). During the scanning they wore
the head-ring on the head and 3D facial scans were later
processed in the Artec Studio software. Furthermore, the
distances were measured between the ears, between the
crown of the head and the chin, and between the head
volume’s origin and nasal base. The head-width as the
distance between the ears, length as distance between the
crown of the head and the chin and the facial depth as
distance between the centre and the nose. The volumes
of the upper and lower pyramids, as well as the whole
head’s and ellipsoid volumes (Figure 3), were calculated
using these data. Additionally, the head index, was calcu-
lated from the distance between the crown of the head to
the chin and, both ears distance relationships.
Each of the 11 obtained parameters (Table 1)d e -
scribes the facial size in its own way. In the first part the
similarity and correlation had to be checked among
them. The observed subjects were arranged from the
smallest to tallest according to their body heights fol-
lowed by graphical visualisations of how other parame-
ters follow (Figure 4). Further on the Pearson correlation
M. VERDENIK et al.: A NEW METHOD OF DETERMINING FACIAL SIZE FOR THREE-DIMENSIONAL ...
Materiali in tehnologije / Materials and technology 55 (2021) 1, 25–31 27
Figure 3: Measured parameters (lower, upper head volume, width, length, facial depth, ellipsoid) shown on the 3D facial scan
Table 1: Obtained parameter descriptions
Parameter Definition – equation Unit Description
Height Body height cm
Weight Body weight kg
BMI Weight/Height
2
kg/m
2
Distance between ears (b)
Distance from left to right point, where head ring touches the
external acoustic ducts.
mm Head width
Distance from crown of
the head to the chin (a)
Distance from the uppermost point on the head in the natural
head position, to the chin.
mm Head length
Distance from centre to
the nasion (c)
Distance from the centre point, origin of the head volume cre-
ated where vectors from other spherical markers meet, to the
tip of the nose.
mm Face depth
Head-index (a/b)
Is an analogue of facial one (the ratio of the facial height to
the zygomatic width) calculated from the distances between
the crown of the head to the chin and both ears.
Head form
Upper-volume
Volume of upper pyramid between the crown of the head, both
ears and the nasion.
cm
3
Lower-volume
Volume of lower pyramid between both ears, nasion, and the
chin.
cm
3
Whole-volume Sum of both volumes cm
3
Head volume
Ellipsoid
Calculated volume of ellipsoid defined as #, where a, b, and 2c
represent the three axes of the ellipsoid.
cm
3

was used to statistically assess the correlation among
these data (p < 0.5). It was supposed that the head vol-
ume would describe the facial size best; therefore, a lin-
ear regression model was made with the head-volume as
the dependent value. This model was used to check the
impacts of head width, length, facial depth, body weight,
and height.
3 RESULTS AND DISCUSSION
In the presented study, the young adults with
normocclusion were similar regarding BMI. The average
BMI was 22.8 (SD 3.1), which meant that abnormal in-
dexes were excluded. The number of observed partici-
pants was small, but enough for statistically relevant re-
sults. Both genders were separately observed because of
M. VERDENIK et al.: A NEW METHOD OF DETERMINING FACIAL SIZE FOR THREE-DIMENSIONAL ...
28 Materiali in tehnologije / Materials and technology 55 (2021) 1, 25–31
Table 2: Values of all obtained parameters for all the subjects
ID Height Weight BMI
Dist.
between
ears
Dist.
crown of
the head –
chin
Dist.
centre –
nasion
Head-
index
Upper-
volume
Lower-
volume
Whole-
volume
Ellipsoid
MALE
1 173 93 31.1 139.5 259.1 110.8 1.86 319.1 300.8 619.9 335.6
2 175 68 22.2 127.7 254.5 102.5 1.99 313.4 217.5 530.8 279.2
3 175 68 22.2 127.0 252.9 109.9 1.99 339.1 238.3 577.4 295.7
4 177 70 22.3 139.6 252.7 105.0 1.81 304.0 274.5 578.5 310.2
5 180 100 30.9 134.6 245.0 97.8 1.82 262.5 241.6 504.0 270.2
6 180 80 24.7 139.3 259.1 102.5 1.86 352.4 238.1 590.6 309.8
7 183 83 24.8 136.0 264.0 111.7 1.94 336.0 261.0 597.0 336.0
8 186 88 25.4 139.0 262.2 114.2 1.89 349.2 301.1 650.3 348.6
9 187 84 24.0 130.2 257.6 104.8 1.98 304.7 254.9 559.5 294.4
10 189 76 21.3 131.6 259.8 99.6 1.97 255.7 234.7 490.4 285.1
11 190 79 21.9 136.9 259.0 103.4 1.89 327.7 249.8 577.5 307.1
12 190 83 23.0 138.5 250.8 110.7 1.81 303.1 272.7 575.8 322.3
13 194 90 23.9 130.2 256.5 111.6 1.97 285.5 240.8 526.3 312.4
183 82 24.4 134.6 256.4 106.5 1.91 311.7 255.8 567.5 308.2
±SD 7 10 3.0 4.7 5.1 5.2 0.07 30.5 25.4 45.2 23.4
FEMALE
1 156 52 21.4 127.1 233.8 102.0 1.84 267.6 216.1 483.7 2342.9
2 158 57 22.8 135.2 250.3 95.9 1.85 290.4 231.1 521.5 2931.2
3 161 53 20.4 131.8 246.5 99.9 1.87 301.2 202.9 504.0 2579.3
4 162 50 19.1 128.0 228.2 99.1 1.78 271.1 199.0 470.1 2124.5
5 163 73 27.5 135.1 253.2 103.2 1.87 325.0 224.2 549.1 3350.7
6 165 60 22.0 136.6 248.5 103.6 1.82 314.3 238.8 553.1 3477.2
7 166 66 24.0 130.1 241.8 98.9 1.86 309.7 195.4 505.1 2560.9
8 170 58 20.1 132.3 236.9 93.1 1.79 220.5 218.6 439.1 1773.5
9 171 68 23.3 137.0 235.8 94.5 1.72 289.0 198.8 487.8 2348.2
10 174 62 20.5 124.9 237.9 106.3 1.91 292.9 217.1 510.0 2717.1
11 177 64 20.4 130.2 256.7 104.3 1.97 295.3 248.6 543.9 3344.6
12 178 66 20.8 124.4 243.5 101.5 1.96 281.9 208.3 490.3 2412.2
13 178 58 18.3 122.5 234.8 107.7 1.92 281.0 209.5 490.5 2418.7
14 180 75 23.1 132.3 253.7 101.4 1.92 333.3 220.5 553.8 3409.2
169 62 21.7 130.5 243.0 100.8 1.86 290.9 216.3 507.3 2699.3
±SD 8 8 2.3 4.7 8.7 4.3 0.07 27.8 15.7 34.1 528.9
Figure 4: Graphically visualised male parameters’ distribution
Figure 5: Graphically visualised female parameters’ distribution

the sexual dimorphism.
12,13
However with respect to ever
more reports about ethnically conditioned differences
14,10
we had to appreciate the fact that the observed subjects
were Slovenians.
The measured values are shown in Table 2 and visu-
alised in the graph (Figures 4 and 5). Subjects are ar-
ranged from lowest to tallest according to their body
heights and separated according to gender. The results of
the Pearson correlation and linear multivariate analyses
are presented in Tables 3 and 4.
The fact that the facial size could not be defined in
one definite way, led us to find the best approximation.
Different parameters were used to describe it: the arith-
metic mean of selected landmarks (centroid),
2–4
those
different linear face distances that describe facial height
and width, and the relationships between them.
15,16
There
were studies for describing the volume of the head, but
mostly measured by CT scans.
17,18
The CT scans as all
other x-ray imaging modalities also give us information
about deeper structures, such as bone and so where more
obtained data brings advantages over surface scanning
modalities. However, x-rays with known radiation risk
are of question for study of facial growth and develop-
ment. The idea of measuring the head volume using
anthropometrically assessed landmarks
19
led us to de-
signing the head-ring. When using it additional data was
acquired for determining the head size and for checking
the accuracies of standard methods. We obtained head
distances that can be presented as head lengths, width
and face depth.
The expectation that body height would be in correla-
tion with the head volume was unconfirmed. It most
M. VERDENIK et al.: A NEW METHOD OF DETERMINING FACIAL SIZE FOR THREE-DIMENSIONAL ...
Materiali in tehnologije / Materials and technology 55 (2021) 1, 25–31 29
Table 3: Pearson correlation showing the relationships between the observed parameters
MALE Weight BMI
Between
ears dist
Crown of
the head
chin dist
Centre
nasion dist
Head
index
Upper
volume
Lower
volume
Whole
volume
Ellipsoid
Height
.40
.20
–.34
.29
–.01
.97
.16
.62
.05
.87
.070
.83
–.41
.19
–.07
.82
–.31
.33
.06
.86
Weight
.73
**
.01
.41
.18
.481
.11
.55
.06
–.221
.49
.03
.92
.60
*
.04
.38
.22
.69
*
.01
BMI
.444
.15
.375
.23
.50
.10
–.291
.36
.31
.33
.67
*
.02
.61
*
.04
.65
*
.02
Between
ears dist
.234
.47
.21
.52
–.916
**
.00
.32
.31
.72
**
.01
.65
*
.02
.72
**
.01
Crown –
chin dist
.10
.75
.18
.58
.25
.44
.21
.51
.39
.36
.43
.16
Centre
nasion dist.
–.18
.61
.36
.25
.63
*
.03
.62
*
.03
.79
**
.00
Head index
–.22
.49
–.64
*
.02
–.54
.07
–.55
.06
Upper vol-
ume
.25
.43
.81
**
.00
.47
.13
Lower vol-
ume
.78
**
.00
.85
**
.00
Whole vol-
ume
.82
**
.00
FEMALE
Height
.55
*
.04
–.24
.40
–.36
.21
.16
.58
.33
.25
.51
.06
.10
.74
.08
.78
.12
.69
.12
.68
Weight
.67
**
.01
.28
.34
.56
*
.04
.09
.77
.28
.34
.59
*
.03
.14
.64
.55
*
.04
.53
.05
BMI
.63
*
.02
.51
.06
–.16
.58
–.11
.70
.59
*
.03
.10
.73
.53
.05
.51
.07
Between
ears dist
.45
.11
–.55
*
.04
–.53
.05
.29
.31
.28
.34
.36
.20
.39
.17
Crown –
chin dist
.17
.57
.53
.05
.64
*
.01
.67
**
.01
.83
**
.00
.85
**
.00
Center –
nasion dist.
.68
**
.42
.14
.29
.32
.47
.09
.46
.10
Head index
.33
.25
.38
.19
.44
.11
.44
.12
Upper vol-
ume
.17
.57
.89
**
.00
.84
**
.00
Lower vol-
ume
.59
*
.03
.67
**
.01
Whole vol-
ume
.99
**
.00

probably only correlate (p = 0.06) with the female head
index, which meant that taller women usually have nar-
rower faces. The weight alone was less important and
was included in the more descriptive BMI. The initial
observations showed that BMI had some statistically sig-
nificant correlation with the head volume in general.
Specifically, it correlated with the lower head volumes
and ellipsoid sizes in men, while in women there was a
highly significant correlation with the upper head vol-
ume that effected the whole volume. Whilst BMI in men
did not correlate with any linear distance, in women it
was significantly connected to facial width and to facial
length (p = 0.06). Any connection to BMI was a surprise
because the measured head volume was based on land-
marks set on structures with less subcutaneous fat, whilst
the greatest impact of higher BMI was in other areas.
In men facial width and depth correlated to lower
volumes, which were significantly connected to the head
and ellipsoid volumes. The same correlation among the
lower volumes, the ellipsoids, and the whole head vol-
umes could be seen in women, but the upper volume had
a higher impact on the ellipsoid. Facial length showed
correlations to lower, upper, ellipsoid, and whole vol-
umes, while the distances between the ears and those
from the centre to the nasion did not show any signifi-
cant correlation with the volumes. It seems that the head
length was the more important parameter during the head
size determination for the women, while the head width
determined the head sizes in men. All the parameters de-
scribing the head volume more frequently correlated
with the lower volume for men, but to the whole head’s
volumes for women. The ellipsoid was in correlation
with almost all the volumes in both genders, except for
the upper ones in men. These results were expected to
some extent as a head’s shape can be approximated by an
ellipsoid, the volume of which depends on the lengths of
all three axes. In the case of the head, the distance be-
tween the chin and the crown of the head represents the
major axis, and the distance between the ears being one
of the minor axes and the doubled distance between the
nasion and the centre being the second minor axis.
The linear-regression model used to observe any in-
terrelationships’ influences between the head length,
width, face depth, body weight and height, and the
head-volume confirmed some previously stated connec-
tions. In both genders the distances from the centre to the
nasion (facial-depth) had the highest impacts on the head
volumes. The head-width had a slightly lower influence
on the heads’ volumes, but both of them were statisti-
cally significant. In women, the head length had signifi-
cantly positive influence on the head volumes, in con-
trast to men where this relationship was insignificant.
Similar studies could not be found in the literature.
No differences in the influences of sizes on facial-shape
between genders were reported;
12
but the study was made
on the skulls of known sexes.
There is no data available about volumetric propor-
tions among upper and lower facial parts as in our study,
which makes it difficult to compare the results with any
other research. The different correlations between upper
or lower volumes in women and men were very interest-
ing. In Indians, through linear measurements the ratio of
the anterior facial height to the total anterior facial height
was found to be non-gender specific
20
and a similar phe-
nomenon was reported for Sweden.
21
If there are differ-
ences between them and our population they are ethni-
cally conditioned, as it was confirmed that the average
Slovenian male and female faces with normocclusion
have more developed chin region when compared to the
Welsh population.
9
Gender-specific differences found in
the chin region have been described,
22,23
but they were
observed independently of the upper part of the head and
face. The described gender-specific differences in the
lower volume compared to the upper could also be ex-
plained by more masculine faces with pronounced lower
parts of the face, which have been evolutionarily more
M. VERDENIK et al.: A NEW METHOD OF DETERMINING FACIAL SIZE FOR THREE-DIMENSIONAL ...
30 Materiali in tehnologije / Materials and technology 55 (2021) 1, 25–31
Table 4: Linear multivariate analysis; the whole volume obtained with the head ring is the dependent value, and the parameters that describe the
head in different linear perspectives, body height and width, are the independent variable
MALE
Non-standardised coefficients
Standardised coeffi-
cients t Sig.
B Std. Error Beta
(Constant) –813.16 694.01 –1.17 0.29
Height –1.91 1.23 –0.32 –1.55 0.17
Weight –0.681 1.50 –0.13 –0.45 0.67
Between ears dist. 4.64 1.74 0.53 2.67 0.04
Crown – chin dist 2.38 2.22 0.22 1.07 0.32
Centre – nasion
dist.
5.16 2.02 0.57 2.56 0.04
FEMALE
(Constant) –815.66 255.91 –3.19 0.01
Height –0.51 0.65 –0.12 –0.78 0.46
Weight 0.84 0.72 0.19 1.17 0.28
Between ears dist. 3.10 1.33 0.42 2.33 0.05
Crown – chin dist 1.75 0.57 0.45 3.09 0.02

often selected for reproduction, as explained in anthro-
pologic studies.
24
4 CONCLUSIONS
The head size parameters are gender-specific in
Slovenians. In men the head-width and the lower head
volume are the main contributors to the head size, while
in women the head length and upper volume determine
the women’s head sizes. BMI significantly correlates to
the whole head and lower head volumes in men, while in
women highly significantly influences the upper head
volume. The BMI in men does not correlate with any lin-
ear distance; however, in women it is closely connected
to the facial width.
Ethical approval and consent to participate
This study was reviewed and approved by the
Slovenian National Medical Ethics Committee, Approval
No. 166/02/13. Signed, informed consent was obtained
from The subjects before entering the study.
Consent for publication
We acquired subject’s written permission for the
identifiable images.
Competing interests
The authors declare that they have no competing in-
terests.
Funding
No source of funding must be declared.
Acknowledgement
Thanks to George Yeoman for his proofreading and
Ivan Verdenik for support regarding statistics.
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M. VERDENIK et al.: A NEW METHOD OF DETERMINING FACIAL SIZE FOR THREE-DIMENSIONAL ...
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