Geometric morphometric footprint analysis of young women

Abstract

Most published attempts to quantify footprint shape are based on a small number of measurements. We applied geometric morphometric methods to study shape variation of the complete footprint outline in a sample of 83 adult women.
The outline of the footprint, including the toes, was represented by a comprehensive set of 85 landmarks and semilandmarks. Shape coordinates were computed by Generalized Procrustes Analysis.
The first four principal components represented the major axes of variation in foot morphology: low-arched versus high-arched feet, long and narrow versus short and wide feet, the relative length of the hallux, and the relative length of the forefoot. These shape features varied across the measured individuals without any distinct clusters or discrete types of footprint shape. A high body mass index (BMI) was associated with wide and flat feet, and a high frequency of wearing high-heeled shoes was associated with a larger forefoot area of the footprint and a relatively long hallux. Larger feet had an increased length-to-width ratio of the footprint, a lower-arched foot, and longer toes relative to the remaining foot. Footprint shape differed on average between left and right feet, and the variability of footprint asymmetry increased with BMI.
Foot shape is affected by lifestyle factors even in a sample of young women (median age 23 years). Geometric morphometrics proved to be a powerful tool for the detailed analysis of footprint shape that is applicable in various scientific disciplines, including forensics, orthopedics, and footwear design.

Full text

M ET HODOLOGY Open Access
Geometric morphometric footprint analysis of
young women
Jacqueline Domjanic
1
, Martin Fieder
2
, Horst Seidler
2
and Philipp Mitteroecker
3*
Abstract
Background: Most published attempts to quantify footprint shape are based on a small number of measurements.
We applied geometric morphometric methods to study shape variation of the complete footprint outline in a
sample of 83 adult women.
Methods: The outline of the footprint, including the toes, was represented by a comprehensive set of 85
landmarks and semilandmarks. Shape coordinates were computed by Generalized Procrustes Analysis.
Results: The first four principal components represented the major axes of variation in foot morphology:
low-arched versus high-arched feet, long and narrow versus short and wide feet, the relative length of the hallux,
and the relative length of the forefoot. These shape features varied across the measured individuals without any
distinct clusters or discrete types of footprint shape. A high body mass index (BMI) was associated with wide
and flat feet, and a high frequency of wearing high-heeled shoes was associated with a larger forefoot area of
the footprint and a relatively long hallux. Larger feet had an increased length-to-width ratio of the footprint, a
lower-arched foot, and longer toes relative to the remaining foot. Footprint shape differed on average between
left and right feet, and the variability of footprint asymmetry increased with BMI.
Conclusions: Foot shape is affect ed by lifestyle factors even in a sample of young women (median age 23 years).
Geometric morphometrics proved to be a powerful tool for the detailed analysis of footprint shape that is
applicable in various scientific disciplines, including forensics, orthopedics, and footwear design.
Keywords: Foot asymmetry, Body mass index, Footprint shape, High heels, Semilandmarks, Shoe design
Background
The analysis of normal and pathological variation in
human foot morphology is central to se veral biomedical
disciplines , including orthopedics, orthotic design,
sports sciences , and physical anthropology, and it is
also important for efficient footwear design. Genetic
factors (including gender) as well as environmental and
lifestyle factors (e.g., body weight, shoe wearing habits)
have been shown to i nfluence adult foot morphology
[1-7]. Human foot shape changes in the course of post-
natal de velopment [8] and differs among certain ethnic
groups [1,9].
A classic and frequently used approach to study foot
morphology is the analysis of the two-dimensional foot-
print, despite the apparent loss of information along the
vertical dimension. Footprints are relatively easy to pro-
duce and to measure, and they can be preserved natur-
ally in different soils. In a forensic context, footprint
shape can be used in the identification process [2]. Foot
print shape is frequently classified into discrete types
such as pes planus (flat foot) and pes cavus (high-arched
foot) by visual inspection. There have also been pro-
posed a wide range of different quantitative measures
and indices of footprint shape, mainly based on the
geometry of the medial longitudinal arch. These parame-
ters have been used to create various foot typologies
[8,10,11]. Most of these quantificatio ns are based on a
small number of characteristics of footprint shape, such
as the areas of different parts of the footprint, the curva-
ture of the medial longitudinal arch, or the orientation
of the forefoot relative to the rearfoot. However, these
measures are insufficient to describe the entire footprint
shape and require an a priori sele ction of the shape
* Correspondence: philipp.mitteroecker@univie.ac.at
3
Department of Theoretical Biology, University of Vienna, Althanstrasse 14,
A-1090, Vienna, Austria
Full list of author information is available at the end of the article
JOURNAL OF FOOT
AND ANKLE RESEARCH
© 2013 Domjanic et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
Domjanic et al. Journal of Foot and Ankle Research 2013, 6:27
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features of interest (see [12-16] for more comprehensive
approaches).
In the present paper w e apply geometric morphomet-
ric methods to study the shape of the entire footprint
outline in a sample of adult women. Geometric mor-
phometrics (GM) is based on the Cartesian coordinates
of landmarks (measurement points) that are homolo-
gous across all measured individuals [17-19]. In contrast
to a small number of indices, the set of all landmark
coordinates preser ves the geometry of the me a sured
landmark configurations, and statistical results, such
as group means, regressions, or principal components,
can thus be represe nted a s a ctual shapes or shape de-
formations. Geometric morphometrics is of superior
statistical power than most traditional morphometric
approaches and is particularly effective for exploratory
studies [17-21].
Landmark configurations need to be registered
(superimposed) prior to any statistical analysis because the
coordinates not only contain information on the shape
of the measure d obje ct s, but also on their position,
scale, and orientation. The most common superimpos-
ition technique in geometric morphometrics is Gener-
alized Procrustes Analysis (GPA) [22,23], consisting of
three steps. All landmark configurations are (i) trans-
lated to have t he same centr oid (average landmark pos-
ition), (ii) scaled to have the same size, and (iii)
iteratively rotated to mi nimize the summed squared
distances between the landmarks and the correspond-
ing sample average. Overall size is measured as Cen-
troid Size, the square root of the summed squared
distances between the landmarks and their centroid
[17]. Procrustes registration is based on all landmarks
and o n their explicit correspondence (homology) across
specimens. It does not require the specification of
reference points or lines and is more stable than
simple principal component alignment (For maximum-
likelihood based versions of Procrustes registration see
[24,25]). The coordinates of the superimposed land-
mark configurations are called Procrustes shape coordi-
nates as they contain information about the shape of
the landmark configurations only. They are the basis
for further statistical analysis. Procrustes distance is a
measure of shape difference betwe en two obje ct s and i s
approximated by the Euclidean distance between the
two set s of shape coordinates.
Many biological structures, such a s footprint outlines ,
consist of relatively smooth c urves a nd lack homolo-
gous landmark points that can be identified in all
individuals. Semilandmarks are points along such
smooth outlines that are initially placed at approxi-
matel y co rresponding positions; their exact locations
are then estimated statistically in order to create geo-
metrically homologous landmarks that can be used in
thesubsequentanalysisasiftheywereanatomicalland-
marks. The most common algorithm for this purpose is
Figure 1 Landmark scheme for measuring footprint shape. (a) The footprint of one individual, extracted from a three-dimensional surface
scan, together with the landmarks and semilandmarks used for the morphometric analysis shown as gray and white points. (b) Landmark
configurations of all individuals after Procrustes superimposition. (c) Visualization of the average footprint shape (average shape coordinates) in
the sample.
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the sliding landmark algorithm [26,27], which itera-
tively slides the semilandmarks along their cur ves in
order to minimize local shape differences (the bending
energy of the thin-plate spline i nterpolation) between
each individual and the sample average.
In the present study, we extracted the footprint shape
from three-dimensional surface scan s of the feet (see the
methods section below), but geometric morphometric
methods can also be applied to other techniques for cap-
turing footprints, such as ink footprints or pressure
platforms.
Methods
The feet of 83 female individuals, aged between 19 and
36 years (median age 23 years), were scanned with a
“Pedus” laser foot scanner (Vitronic and Human Solu-
tions GmbH, Germany), located in the Department of
Clothing Technology at the University of Zagreb. A total
of four scans were made for each person, two of the left
foot and two of the right foot. Additionally, age, body
weight, body height, shoe size, sports activities, shoe
wearing habits, and handedness were recorded for each
person. According to their place of birth, the women
were grouped into four geographic categories: the con-
tinental (N=45), the Adriatic (N=20), and the Slavonian
region of Croatia (N=8), as well as a group of women
from other countries (Bosnia and Herzegovina, Kosovo,
France, and Austria; N=10). Participation in the survey
was entirely voluntary and based on written consent.
The study was approved by the Ethics Committee of the
Faculty of Textile Technology, University of Zagreb, on
July 18th, 2012.
Using the software Amira (Imersion Inc.), the scanned
surfaces were rendered and the footprints were extracted
by cutting off the lowest (plantar-most) 2mm of the foot
scan. The opacity of the remaining scan was reduced so
that the full outline of the foot was still visible. After
exporting a screenshot of the footprint and the foot out-
line, 85 landmarks and semilandmarks (Figure 1a) were
digitized using the software TPSdig 2.0 (James Rohlf). For
each toe, the outline of the distal element was digitized by
7 semilandmarks and 1 anatomical landmark at the distal-
most tip. The outline of the remaining footprint, including
the footpad, the midfoot, and the heel, was digitized by 34
semilandmarks and two anatomical landmarks at the two
medial-most positions. The medial outline of the foot
(starting and ending at the medial-most positions of the
footprint outline) was digitized by 9 semilandmarks.
We used the sliding landmark algorithm [26] to estimate
the position of the semilandmarks in all individuals, enab-
ling the joint analysis of anatomical landmarks and curves
(represented by semilandmarks). All landmark configu-
rations were superimposed by a Generalized Procrustes
Analysis [22], standardizing for position, size, and
PC 1
PC 2
Figure 2 Scatterplot of the first two principal components of footprint shape. The first principal component (visualized by the footprint
shapes along the PC 1 axis) is a contrast between flatfeet (low PC 1 sores) and high-arched feet (high PC 1 scores), whereas PC 2 (visualized by
the footprint shapes along the PC 2 axis) represents the differences between short and wide feet with short toes (low PC 2 scores) versus long
and narrow feet with long toes (high PC 2 scores). The symbol type reflects the geographical origin of the individuals: the continental (filled black
circles), the Adriatic (open black circles), and the Slavonian region of Croatia (filled red circles), as well as other countries (open red circles).
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orientation of the configurations. The resulting Pro-
crustes shape coordinates (Figure 1b) were used for fur-
ther statistical analysis.
We performed a principal component analysis (PCA;
also referred to as relative warp analysis by [17]) of these
shape coordinates to investigate the major components
of variation in footprint shape. The first principal com-
ponent (PC) is the shape pattern (linear combination of
shape coordinates) with maximum variance in the sam-
ple. It can be visualized as a shape deformation or a
series of shapes, and a score along the PC can be com-
puted for each individual. The second PC is geometric-
ally orthogonal (perpendicular) to the first one and
accounts for the second most variance, and similarly for
all subsequent components.
We further assessed the influence of body mass index
(body weight divided by squared body height), shoe size,
frequency of wearing high heels, age, and sports activ-
ities on footprint shape by multivariate regressions of
the shape coordinates on the respective variable. For
these analyses we averaged the two right footprints of
each person with the two mirrored left footprints so that
every person was represented by a single symmetric
footprint shape. Footprint asymmetry, i.e., the shape
differences between left and right footprints, were stud-
ied by comparing the right footprints with the reflected
left footprints [17-20,28,29]. Levels of statistical signifi-
cance were computed by permutation tests, using 5000
random permutations. Permutation tests do not require
normally distributed variables and can be applied to
multivariate datasets that are not of full rank, such as
Procrustes shape coordinates [30].
Results
The first four principal components (PCs) accounted
for 60.3% of total shape variation and are visualized in
Figures 2 and 3. PC 1 was a contrast between flatfeet
(pes planus; low PC 1 sores) and high-arched feet (pes
cavus; high PC 1 scores), whereas PC 2 represented the
differences between short and wide feet with short toes
(low PC 2 scores) versus long and narrow feet with long
toes (high P C 2 scores). PC 3 reflected variation in the
length and the shape of the toes. Individuals with a low
score along PC 3 had a long and narrow hallux relative
to the other toes (sometimes referred to as “Egyptian
foot”), whereas for individuals with high scores the sec-
ond toe was longer than the hallux (“Greek foot”). PC 4
mainly reflected the relative length of the forefoot.
PC 3
PC 4
Figure 3 Scatterplot of principal components 3 and 4 of footprint shape. The principal components are visualized by footprint shapes
along the two corresponding axes. Individuals with a low score along PC 3 have a long and narrow hallux relative to the other toes (“Egyptian
foot”), whereas individuals with a high score have a long second toe relative to the hallux (“Greek foot”). PC 4 mainly reflects the relative length
of the forefoot. The symbol type corresponds to the geographical origin of the individuals.
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Every symbol in the PCA plots represents the footprint
shape of one person. The four different geographic
groups (reflected by the symbol type) had a similar dis-
tribution alon g the PCs. Furthermore, pairwise permuta-
tion tests did not reveal any significant differences in
mean shape between the geographic groups (p>0.16 for
all tests).
We investigated the influence of different factors on
footprint shape by regressing the shape coordinates
on the respective variables (Figure 4). Body mass index
(BMI) had a significant effect on footprint shape
(p<0.001) and explained 2.8% of total shape variation. A
low BMI was associated with a more arched foot and a
high BMI with a flatter foot. BMI was further associated
with the relative width (length-to-width-ratio) of the
foot. Shoe size (measuring foot length) was significantly
related to footprint shape (p<0.001) and accounted for
2.4% of shape variation. Feet with a larger shoe size
tended to have an increased length relative to the width,
a lower-arched foot shape, and longer toes relative to
the remaining foot. The frequency of wearing high heels
significantly explained 1.8% of total shape variation
(p=0.003). People often wearing high heels tended to
have a relatively longer forefoot and a more anterior po-
sitioned hallux relative to the other toes. We further an-
alyzed the effect of age and sports activities on footprint
shape but found no significant relationships (p>0.26).
For all the above analyses, left and right footprints
were averaged for each individual, but they can also be
analyzed separately in order to investigate shape asym-
metry. Figure 5 shows the average left footprint and
the average right footprint (differing significantly at
BMI 15 BMI 30
never high heels often never × 3 often × 3
shoe size 33 shoe size 44
a
c
b
Figure 4 Visualization of the effects of body mass index (BMI), shoe size, and the frequency of wearing high heels on footprint shape,
estimated via linear regressions of shape on the corresponding factor. The displayed footprints are extrapolations of the actually occurring
range of variability in order to effectively visualize the patterns of shape difference. (a) Expected footprint shapes for BMI 15 and BMI 30.
(b) Expected footprint shapes for shoe size 33 and shoe size 44. (c) Average footprint shape for women never wearing high heels and for
women often wearing high heels, together with footprint shapes derived from a threefold extrapolation of these effects.
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p<0.001), along with extrapolations of the shape differ-
ences between them. Right footprints on average had
a slightly increased width relative to the length, and
the border between the forefoot and the midfoot was
more angulated in right feet than in left ones. We also
analyzed footprint shape asymmetry separately for left-
handed an d for right-handed persons but found no sig-
nificant difference.
In addition to the average pattern of asymmetry, we
further quantified the amount of asymmetry for every
individual as the Procrustes distance between the left
and the right foot. While the average amount of asym-
metry was not significantly related to any of the factors,
the variance of asymmetry was significantly lower for
women with BM I<21 as compared to women with
BMI>21 (p=0.006).
For every person two scans of the left foot and two
scans of the right foot were made and digitized with
landmarks, so we could also compute the repeatability
of the shape variables. The intraclass correlation coeffi-
cients (ICC) for the first four principal components were
0.95, 0.85, 0.85, and 0.88, respectively. Note that these
ICC coefficients reflect the repeatability of the actual
footprint (the way how people stand and how the foot
deforms under pressure), of the 3D surface scan and the
virtual ext raction of the footprint, and of the landmark
measurements.
Discussion
We applied geometric morphometric methods to study
variation of footprint shape in a sample of young adult
women. The outline of the footprint, including the
toes, was represented by a comprehensive set of land-
marks and semilandmarks , allowing for a detailed mor-
phological analysis without any prior selection of shape
features. The first four principal components of footprint
shape – the major axes of variation – represented crucial
aspect s of foot morphology: low-arched versus high-
arched fe et , long and na rr ow versus short and wide
feet, the relative length of the hallux, and the relative
length of the forefoot. These shape features varied in-
dependently across the mea sured individuals without
any distinct clusters or discrete types of footprint
shape. The distinction between different foot types,
which is very common in the literature [10], hence re-
mains p artly arbitrary: the definition of foot types can-
not be based entirely on biological variation, but must
be desig ned for specific pur pos es, s uch as shoe pro duc-
tion or clinical treatment. Different typological systems
based on different criteria are unlikely to match.
We investigated the influence of several lifestyle fac-
tors on footprint shape. A high BMI was associated with
wide and flat feet, which was also found by other re-
searchers. For example, Ashizawa et al. [1] and Mauch
et al. [6] reported an increase of relative foot width with
body weight.
A high frequency of wearing high-heeled shoes was as-
sociated with a larger forefoot area of the footprint and
a hallux exceeding the other toes in length. Heel eleva-
tion leads to increa sed pressure and shear stress on the
forefoot, particularly on the medial forefoot [31,32], and
several studies reported that older women who fre-
quently wore high heels had an increased prevalence of
hallux valgus [33,34]. Since our sample consists of young
women (median age 23 years), it is particularly surpris-
ing that we found a significant associat ion between foot
shape and shoe wearing habits already in this age range.
Right feet on average were slightly wider tha n left feet
and the outline of the medial longitudinal arch was more
angulated in right feet. Using elliptic Fourier analysis
Sforza et al. [13] reported a similar average shape differ-
ence between lef t and right footprints. We also found
left right left × 3 right × 3
Figure 5 Average left and average right footprint shape, together with footprint shapes derived from a threefold extrapolation of
these differences.
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that the sample variance of the amount of asymmetry in-
creases with BMI. A higher body weight might more
easily transform asymmetries of gait and behavior into
morphological asymme tries.
Larger feet (measured by shoe size) tend to have an in-
creased overall length relative to the width (length-to-
width ratio), a lower-arched foot, and longer toes relative
to the remaining foot. Such an association of overall size
and shape is referred to as allometry [17,23]. This has
profound consequences for shoe design: shoes differing
in size should also differ in shape, and shoes should not
be perfectly symmetric but should reflect the asymmet-
ries of the foot. We did not find differences in average
foot shape between the geographic regions covered by
our sample.
By applying geometric morphometrics to a compre-
hensive set of landmarks and semilandmarks along the
footprint outline, we were able to assess variation in
footprint shape at a very fine spatial scale. We could
confirm well-known patterns of shape variation, such as
variation in the curvature of the medial longitudinal arch
or in the size and orientation of the forefoot relative to
the rearfoot, without specifying these patterns prior to
the analysis by selecting corresponding measurements.
We were thus also able to discover novel patterns, e.g.,
details in the medial longitudinal arch shape and in the
relative size and shape of the toes. The convenient statis-
tical properties of geometric morphometrics together
with the effective visualization resulting from the large
number of landmarks allow for very powerful explora-
tory studies in various scientific disciplines, including or-
thopedics, forensics, and footwear production. The
manual measurement protocol used in the current study
might be too time-consuming for daily clinical routine,
but it is a powerful tool for scientific research and for
the generation and evaluation of simple indices of foot-
print shape. Geometric morphometrics of footprint
shape might be used complementary to plantar pressure
analysis [35], which typically aims at standardizing for
shape variation instead of analysing it.
Conclusion
We identified the major patterns of variation in foot-
print shape and estimated the effects of BMI, foot size,
shoe wearing habit s , and asymmetry on foot morph-
ology. Geometric morphometrics proved to be a power-
ful tool for assessing the shape of the complete
footprint outline. It should be the method of choice for
scientific research and for the evaluation of simple indi-
ces of footprint shape.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
JD carried out the surface scans, extracted the footprints from the surface
scans, digitized the landmarks, and participated in the data analysis and the
drafting of the manuscript. MF participated in the data collection and the
design of the study. HS participated in the design and coordination of the
study and helped to draft the manuscript. PM analyzed the data, wrote the
manuscript, and contributed to the design of the study. All authors read and
approved the final manuscript.
Acknowledgements
The research was supported by the Ministry of Science, Education and Sports
of the Republic of Croatia (MSES), Grant No. 117-1171879-1887, and the
OEAD project between Croatia and Austria: Anthropometry under special
consideration of life and early factors with an applied approach for the
garment industry. PM was supported by the Focus of Excellence “Biometrics
of EvoDevo” of the Faculty of Life Sciences, University of Vienna.
Author details
1
Department of Clothing Technology, University of Zagreb, Zagreb, Croatia.
2
Department of Anthropology, University of Vienna, Vienna, Austria.
3
Department of Theoretical Biology, University of Vienna, Althanstrasse 14,
A-1090, Vienna, Austria.
Received: 24 March 2013 Accepted: 17 July 2013
Published: 25 July 2013
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doi:10.1186/1757-1146-6-27
Cite this article as: Domjanic et al.: Geometric morphometric footprint
analysis of young women. Journal of Foot and Ankle Research 2013 6:27.
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