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C. Runte and D. Dirksen
Feature has no influence on
attractivity and
reproductive success
Natural selection:
Feature has little or no
influence on survival
Couple moves to a
distant island
“Founders” of a new population
with low genetic variation
Fig. 14.8 “Founder effect” caused by isolation of a small
group. Following generations lead to a population with a
higher percentage of special properties and a reduced
genetic variation. This mechanism has been suggested to
be the reason for the high prevalence of oculocutaneous
albinism in Hopi, Navajo, Zuni, Kuna, and other Native
American people [40]
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Fig. 14.9 Banana plant with repetitive elements exhibit-
ing combinations of translational and high-order rotational symmetry on leafs and fruit
tial orientation, e.g., in a forest with trees of
approximately the same diameter. Architecture
has frequently used all four kinds of symmetry:
Facades, cupolas, colonnades, and the repetition
of similar arches in different seizes (e.g., the Pont
du Gard) exemplify the high esthetic importance
of all mentioned kinds of symmetry.
Perception of symmetry is easier with structures of high brightness contrast and independent
from the recognition of the subject. In Salvador
Dali’s painting “Metamorphosis of Narcissus”
from 1937, the painter showed two different
objects with remarkably high translational
invariance.
Dali also depicted scaled “faces within faces,”
e.g., in his paintings “Slave Market with the
Disappearing Bust of Voltaire” from 1940 and
“The Face of War” from 1941, the latter also
exemplifying self-similarity.
Deviation from symmetry is often assumed to
be correlated to reduced attractiveness. However,
the correlation is not strong [47]. Unsurprisingly,
even small deviations are easily detected in the
structures rich in contrast located at the edges of
the Yarbus triangle, eyes and mouth [48].
It can be concluded that different types of
symmetry attract our attention and inuence our
esthetic judgment. However, the whole natural
human face only shows bilateral symmetry. The
eyes are also roughly mirror symmetrical for
themselves and the iris and pupils show rotational
225
symmetry. If the teeth are exposed in a smiling
face, the teeth and interdental spaces show some
kind of transformation and scaling symmetry.
However, at a closer look the differences between
the shapes of the lateral incisors and canines
become visible.
14.4 Beauty andFacial
Proportions
As it has been stated before, structures rich in
contrast are extracted from all visual information and therefore probably have more impact
on the process of perception. In ancient Egypt,
artisans used strings imbibed with red paint to
draw a rectangular grid before starting with the
sketch and the nal painting. As the grids were
made up of square elements, at least major proportions were usually ratios of integral
numbers.
One early attempt to determine beauty by
facial proportions was the Canon of Polykleitos.
Although the text was lost during the centuries, it
had great inuence beyond its time. The roman
architect Vitruvius argued that a building could
only be suitable if it was well proportioned following the example of the well-proportioned
human body as it had been observed and
described by ancient sculptors (Vitruvius Pollio,
rst century BC [49]). In this context he mentioned the vertical division of the face in three
equal parts: “One third of the length of the face is
from the chin to the nasal orices: From the nasal
orices to the place, where the nose ends between
the eyebrows, an equal distance; and from here to
the beginning of the hair, where the forehead
ends, one third as well” (authors translation from
German edition; Fig. 14.10). The height of the
face was said to be one tenth of the whole body
height, the whole head one eighth. This would
mean the part above the trichion would be one
quarter of the facial height.
In medieval times, artists like Villard de
Honnecourt also depicted the Vitruvian vertical
trisection of the human face. However, as the
given proportions are put into fractions of small
integer numbers, the accuracy will be limited.
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Fig. 14.10 Vitruvian vertical trisection of the face
Still in the early eighteenth century, Dionysius
of Fourna instructed painters in his manual of
iconography:
Start by making the rst measurement, which you
divide into three sections: the forehead for the rst,
the nose for the second, and the chin for the third.
Draw the hair out of your rst measurement at the
length of one nose. Divide the space between chin
and nose into another three parts; two for the chin
and one for the mouth […]. As big as one eye is,
the other one is also and just as much is one away
from the other (Authors’ translation from German
edition, Schaefer [50]).
During the Renaissance (ca. fteenth and sixteenth century), in Europe ancient knowledge of
geometry and facial proportions was rediscovered
by artists and mathematicians like Piero della
Francesca (1415–1492), Luca Pacioli (ca. 1447–
1517), Leonardo da Vinci (1452–1519), and
Albrecht Dürer (1471–1528). Both Dürer and
Leonardo were not satised with the traditional
information but published their own measurement
C. Runte and D. Dirksen
results. Furthermore, they developed and built
mechanical and optical instruments to improve
measuring techniques and perspective. Dürer [
51]
still took over the Vitruvian division of the face by
three. His sketch of a head was also based on a
division of the whole body height by eight. In vertical direction, the proportion of the face to the
whole head was 23/30 (i.e., ≈76.67%). Only if the
head was considered as too big in comparison to
the face, he reduced the upmost part but kept all
other proportions. However, in contrast to
Vitruvius and Dürer, other authors measured this
proportion as one sixth of the facial height, thus
dividing the height of the whole head by seven
with the lower six seventh (i.e., ≈85.71%) making
up the face from the chin to the trichion (e.g.,
Schadow 1834 [
52]; Fig.14.11). As the top of the
head is often hidden by hair, a crown, or a hat or
showing low contrast to the background, this
structure is obviously not of much importance for
the esthetic perception. Only if there are unfamiliar visual elements in this position, e.g., an
extraordinary haircut, the top of the head arouses
more interest (Yarbus described one situation,
where an observer “spent considerable time
examining the amusing tuft of hair on the child’s
head” ([14], p.192). We would therefore suspect
that the vertical proportion is not as important for
the esthetic judgment as the area of the facial surface to the area of the whole head.
In horizontal direction, Dürer divided the face
into ten equal parts. The outmost 1/10 was subdivided by 2. In the outmost 1/20, he drew the ears
and short cut hair (Fig.
14.12). All in all, his divi-
sion by ten reects the older division by ve,
with each eye and the nose measuring one fth.
From his construction of the head, Dürer went
on by studying the esthetic effects if he scaled
and bended the grid.
14.4.1 The Golden Proportion
If a line combined from two lines a and b has the
total length a+b and the ratio a/b equals (a+b)/a,
then their proportion a/b is called the golden
ratio, golden proportion, or golden section. There
are only two possible solutions for a/b to the
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Fig. 14.11 Division of the face by seven squares in verti-
cal and ve in horizontal direction. In this example, the
trichion and the top of the head (dashed black lines) had to
be added because of Nefertiti’s crown. In our picture, the
right eye is slightly lower than its predicted position, and
the inter-endocanthal distance and nasal width (green dotted lines) are slightly longer than the width of the eyes.
The red dotted line depicts the position of the top of the
head according to Dürer’s proposal. He also used equal
distances between the sides of the nose and the corners of
the mouth (green dotted lines). The superimposed sketch
from a detail of Dürer’s proportional study (depicting a
male gure) of the head was scaled to the pupil position of
Nefertiti’s bust in vertical direction and to the bipupillar
distance in horizontal direction (which means that Dürer’s
sketch had to be stretched slightly in vertical direction).
The comparison shows the narrow mouth, long nose, and
short upper lip using Dürer’s proposals. However, in his
own portraits including his famous self- portrait from the
year 1500, he obviously violated some of his rules
equation: 1.61803… and 0.61803…, both are
irrational numbers and have interesting mathematical properties. The golden proportion can
easily be constructed by using a right triangle
with one leg half the length of the second one.
Making a circle from the shorter leg to the hypotenuse and another from the point of intersection
to the longer leg will cut the long leg in the golden
section. The perimeter of a circle can be divided
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Fig. 14.12 Horizontal division of the face at the level of
the eyes by ve squares. The lateral borders usually are
difcult to outline precisely as the perspective and hairstyle inuence the appearance (artwork by Nina Runte).
Dürer used a division by ten and subdivided the outmost
section into 2/20. The outline of the face extended to the
inner border of the last 1/20, hair and ears were placed
within this last 1/20. Figures drawn by this rule have very
tight tting ears
into two parts in the golden proportion by the
golden angle (222.49224…°; Fig.14.13).
The golden proportion can be found in several
two- and three-dimensional regular geometrical
objects, e.g., the pentacle and Dürer’s truncated
triangular trapezohedron (Fig. 14.14). Approximations of the golden proportion are, e.g.,
5/8=0.625, 8/13=0.61538…, 13/21=0.61905…,
21/34=0.61765…, and 34/55 =0.61818. Each
of these approximations is composed of two consecutive numbers from the Fibonacci sequence.
Fibonacci numbers and the golden proportion
often appear in nature, especially in the plant
world (Fig.14.15).
The golden proportion was supposed to be of
special esthetic value. In 1876, Gustav T. Fechner
[53] published an experiment, where test persons
had to select the most pleasing rectangle from ten
samples with different edge length ratios. His
results indicated there was a preference for rectangles near the golden proportion (Fig.
14.16).
However, Fechner’s results could be reproduced
in some studies, in others this attempt failed.
Therefore, Friedenberg [54] called the conrmation of the golden proportion an “ephemeral”
nding. In his studies, he found no preference for
the golden proportion in triangles.
Nonetheless, some authors proposed the
golden proportion as the clue to facial beauty
(Danilas and Panagopoulos [55]: “Optimum aesthetic results may be accomplished with the
application of the Golden Ratio in facial and
body-contouring procedures”).
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Fig. 14.13 The golden ratio derived geometrically (left) and the circle divided by the golden angle. a and b are the two
legs of a right-angled triangle with a=2*b. Φ is the golden ratio, r the radius of a given circle divided by the golden angle
C. Runte and D. Dirksen
b=Φ ∗a
b=Φ ∗a
a’
Fig. 14.14 The golden proportion within the pentagram and in Dürer’s truncated triangular trapezohedron from the
famous chalcography “Melencolia I”
a
b’=Φ ∗a’
Vertical and horizontal divisions of the head
and face are depicted in Figs. 14.17 and 14.18,
using the suggestions of Danilas and Panagopoulos
[55] and Kois [56]. However, there are open ques-
tions about the use of the golden section for facial
proportions: Do certain facial proportions really
follow the golden ratio precisely? Is it reasonable
to think of a proportion with favorable mathematical properties in facial structures? Does our
understanding of the process of visual perception
support the idea of a facial proportion that will
please automatically? If this would be the case–
why do other facial structures of esthetic impor-
a
tance (like the ratio of the Yarbus triangle, width/
height of the eyes and lips) so obviously fail to
match the golden ratio?
Alam etal. [57] could not verify the golden ratio
in the height/width ratio and vertical division of the
face in a Malaysian population with three ethnic
groups. Only 17.1% of the subjects (n= 286 randomly selected persons) had a facial height/width
ratio (facial index) between 1.6 and 1.699; the
majority of the subjects had a shorter face (facial
index <1.6). In addition, there was no correlation
between the facial index and the facial evaluation
score. Similar results were found for the Afro-
a
10
15
20
25
30
35
1:16:5 5:44:3 29:20 3:234:21 23:13 2:15:2
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229
Caribbean population examined by Mantelakis
etal. [58]. The only proportion matching the golden
ratio in their study was the distance intereye line—
soft menton/intereye line—stomion. Yet it must be
noticed that using the soft tissue nasion instead of
the intereye line and the subnasal point instead of
the interalar line would have increased the vertical
ratio in favor of the nasal length: In Mantelakis’
study, the median was 1.523 for the best graded and
1.265 for the least well-graded photographs (male
subjects). This should not be taken as a proof for
the value of the golden proportion, as the propor-
Fig. 14.15 Romanesco cabbage shows phyllotaxis using
the golden angle. The inset on the left side shows the
golden angles between the ve most external branches.
Fibonacci spirals and self-similarity at different scales are
also properties with possible esthetic implications
tion of the best graded faces is closer to 2/3 than it
is to the golden proportion.
The central incisor width was also suspected to
be part of the sequence of golden proportions in
horizontal direction. Abdullah’s measurements
[59] among 120 male and 109 female subjects
showed a mean proportion between the inner canthal distance and twice the width of a single central maxillary incisor was 0.6181 for male subjects
and 0.6222 for females, respectively. His results
were conrmed by Arun Kumar etal. [60].
Kois [56] proposed the golden ratio not only
between facial landmarks, but also between the
perceived widths of the upper incisors, canines
and bicuspid teeth for an esthetic outcome of
dental treatment (Fig.14.19). However, his proposals were only conrmed for long teeth by
Rosenstiel [61]. Other authors did not verify the
golden ratio in tooth proportions [62, 63].
We described several common landmarks
used for proportional studies. If we only take the
top of the head, trichion, nasion, tip of the nose,
subnasale, stomion, pogonion and gnathion, and
the points of intersection in the median sagittal
plane with the intereye line and the interalar line,
respectively, this makes in total ten points. The
number of possible proportions between three
points out of these ten can be calculated using
the formula for combinations without repetition.
5
0
Fig. 14.16 Preference of the golden proportion (approxi-
mated as 34/21) from ten given rectangles (data from
Fechner’s experiment). Rectangle proportions are given
on the x-axis; the y-axis shows the percentage of subjects
choosing the respective ratio. Fechner used white rectangular pieces of paperboard with the same area (64 square
centimeters) on a black background. His test persons had
to choose the most pleasing rectangle. In cases where they
were indecisive between two or three rectangles, all were
chosen and rated in their proportion (1/2 or 1/3,
respectively)
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C. Runte and D. Dirksen
Fig. 14.17 Vertical division of the face by the golden
ratio (Φ): several proportions of the face (but not all of
them) approximate the golden ratio of 0.618034…. Most
proportions are taken from Danilas and Panagopulos
(2004, [
55]): The frontal view of the head is said to show
the golden proportion in height to width, which in this
example leads to a slightly more slender proportion than
Nefertiti’s head. The classical proportion of 7/5 is slightly
wider than the golden proportion and Nefertiti’s head. The
eyes should be at the center of the height of the head. In
this example (from left to right), the soft tissue nasion
divides the height of the face roughly in the golden proportion (a), and the tip of the nose is a landmark dividing
the height of the face in the golden ratio as well (b) but in
opposite direction. Both divisions are contradicting the
In this case, 120 vertical combinations of three
points are available (with the restriction to 2
lines with 1 common point). In addition, facial
width measured between the two most external
points, exocanthal and endocanthal points,
pupils, alae, and corners of the mouth can be
used as landmarks for horizontal or inclined
measurements, adding another 12 points or 6
points on each half of the face. Counting out
symmetrically identical points, a number of 16
points is available for proportional measurements; this makes 560 proportions in vertical,
horizontal, and inclined directions. Obviously,
there are enough possibilities to nd any given
Vitruvian division by three, as the height of the nose is
much less than one third of the facial height. The vertical
distance from the soft tissue gnathion to the bipupillar line
is divided approximately in the golden ratio by the base of
the nose (c) and by the inter-lips line (or the corners of the
mouth) in the opposite direction (d). The mouth (stomion)
divides the lower part of the face from the nasal base to the
soft tissue gnathion near the golden proportion (e). This is
an obvious difference to Dürer’s proportions, as he used a
ratio of 1/3 for the upper lip. And nally, the bipupillar
line divides the distance soft tissue subnasal point to trichion roughly in the golden ratio (f). Other proportions, e.g.,
the height/width ratio of a triangle between the pupils and
the mid-point of the lips, are approximately 12/11
proportion between 1/1 and 1/10 with a sufcient tolerance and measurement error. It is not
our intention to abnegate any meaning of given
proportions, but it seems sensible to judge them
with less enthusiasm and more caution than it is
frequently seen. Especially it should be questioned whether there is a true connection between
a mere number (even if it is a number with special mathematical properties, easy to calculate,
or called the “golden” one) and its appearance in
the distances between three landmarks of the
beautiful face or if this appearance is only coincidental or even a result of wishful thinking and
choosing the appropriate landmarks.
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Fig. 14.18 Repeated horizontal division of the face by
the golden ratio: In comparison to the division by ve in
equal parts (scale given below), using the golden ratio the
way it was proposed by Kois [56] leads to slightly wider
distance (+3%) of the exocanthal points (3/5= 0.6 and
Φ≈0.618034). The same is true for the nasal width and
the endocanthal distance (1/5=0.2 and Φ
i.e., +18%). Nefertiti’s pupil does not t to the position
calculated by the nasal width in the golden proportion.
The right central incisor was added according to
Abdullah’s measurement [
59]
3
≈0.236068,
14.5 Beauty andSkin Color
andTexture
Skin discoloration and unusual texture are frequent symptoms of diseases, some of them contagious and some even fatal. The healthy appearance
of facial skin has been shown to be correlated to
attractiveness [64, 65]. Several theories explain
the evolution of skin pigmentation in humans
based on the fact that pigmentation decreases
with distance to the equator [66]. However, this
does not necessarily affect attractiveness, as
Langlois et al. [13] found a high cross-ethnic
agreement in attractiveness judgments.
231
Fig. 14.19 Repeated horizontal division of the anterior
teeth by the golden ratio in comparison to a natural smile:
In this case and in the given perspective, only the incisors
are well within the predicted ratio, but the visible surfaces
of the canine and the following teeth are differently proportioned, e.g., the canine close to 90% of the lateral incisor. Dotted outlines indicate the predicted gingival shape
within the golden ratio
14.6 Variation, Divergence,
andDisgurement
As we have discussed, beauty is difcult to
dene. The same is true for disgurement.
Disgurements may originate from mechanical
injuries, burns, congenital facial disorders, skin
disorders including paraneoplastic and neoplastic
ones, conditions after tumor surgery or radiation,
and systemic diseases. They range from discrete
to severely disguring. A variation from average
parameters that is not relevant in the whole visual
perception or presented in a special context may
not be perceived as unpleasant but beautiful in its
own way. Discolored faces are unremarkably in
the context of the Holi festival. If a threat by a
contagious disease is conclusively ruled out to
the beholder’s belief, an obvious skin discoloration like vitiligo [67] may not be disguring.
Today, vitiligo is no longer an impediment for
even becoming a famous model (e.g., Winnie
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Fig. 14.20 Computerized analysis of a facial scan after
orbital exenteration. Colors represent distances between
the original and the mirrored surface. The orbital region
from the healthy side has been mirrored to the affected
one in order to construct a facial prosthesis. Therefore,
symmetry is nearly ideal in this region (color scale in
upper left corner)
Harlow). The concept categories and prototypes
might be used as an explanation: If a new category with its own prototype is learned from the
social environment or a given explanation, a formerly disgusting stimulus might become indifferent or pleasing (and vice versa).
Intra- and cross ethnic variations of facial proportions and skin color do not affect attractiveness
substantially, as it has been shown by Langlois
[13]. There are obvious variances in facial dimen-
sions between trisomy 21 and euploid subjects;
however, there is a large overlap [68].
In 1987, Higgins published his “selfdiscrepancy theory” [69]. According to this theory, the self-concept implies perceptions of
actual, ideal, and ought self. Higgins explains
how disgurement leads to a discrepancy between
the actual and the ideal self. As discrepancies are
C. Runte and D. Dirksen
related to specic emotional reactions, depression might be a consequence of disgurement
[69, 70]. Psycho-social support may be necessary
to help affected persons [71]. The serious consequences of a “lost face” and the feelings of
affected persons have been described to the general public by Cole [72]. The reduction or elimination of prejudices against visual stimuli should
be a social and political obligation. However, if a
person’s health, self-esteem, and social position
are threatened by visible features, medical treatment has also to be taken into consideration, as
disgured faces cause disgust in the eye of the
beholder [
42]. Of course, the treatment decisions
are among the most challenging ethic tasks in
medicine. The threat of a pathologic background
to the patient, the risks of therapy, and the relevance of the disgurement have to be weighed
up. The risk of body dysmorphic disorder also
has to be ruled out [73].
The greatest need of treatment is found in the
facial regions of attention, i.e., the edges of the
Yarbus triangle. Not surprisingly, Stone and
Potton [43] found the most negative emotional
reactions to faces with disgurements within the
Yarbus triangle. Skin texture and structure variations with high contrast are distinctive and therefore should be corrected if possible, as they will
also attract attention. Particularly, children are in
need of care, as their development might be
severely disturbed by disgurements [74].
Hypertelorism is a severe consequence of craniosynostosis in Apert and Crouzon syndrome. It
also gives the affected children characteristic
facial appearance. Treatment includes craniofacial surgery to correct the facial appearance [
75].
Another severe disgurement is the orbital exenteration [76]. Treatment options include surgical
reconstruction as well as facial prostheses. The
latter can be constructed symmetrically using
facial scans and CAD-CAM technology
(Fig.14.20). By reestablishing facial symmetry
on the affected side, it is possible to approximate
the patients’ actual face to his “ought self” to a
certain extent. However, the function of the eye
cannot be regained today and facial prostheses
14 Aspects ofFacial Esthetics andDisgurement
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233
Fig. 14.21 Effects of symmetrization: Addition of
Nefertiti’s left eye reduces disgurement (comparable to
leukoma treatment [83, 84]), whereas a symmetrization of
a nevus, which is disguring for itself, even increases disgurement [
eye would even increase disgurement as well as removing the single nevus on the right side would increase
85]. In contrast, adding leukoma to the right
usually cannot mimic eye and lid movements,
although prototypes of moving facial prostheses
have been described [77].
The approximation of the ideal type of face,
the average face, or the face of the patients’ self-
beauty. This exemplies that categorizing a pattern as disguring might be more important than its symmetrical or
asymmetrical appearance. Both patterns, the white,
opaque eye and the dark spot on the facial surface, might
indicate a contagious disease or genetic untness and
therefore be explained by processes of evolutionary biology mentioned above
concept, respectively, is the goal for treatment.
Proportions and symmetry are just helpful instruments to get there. For example, regaining symmetry by adding a blemish or nevus symmetrically
on the healthy side will not at all reduce disg-
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