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AB
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5 Morphometrics, Optical 3D Imaging, andMonitoring ofCraniofacial Development andMalformations
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59
straight line through the nasion point at a 90°
angle to the cranial width. Starting at the intersection of these two lines at a 30° angle to the
cranial length, two diagonals are drawn through
the cranial contour (Fig.5.5). The Cranial Vault
Asymmetry Index is then the relative length difference between these two diagonals, based on
CVAI
DiagonalDiagonal
AB
-
5.7.2 The 3D Asymmetry Index
(3DAI)
One approach for 3D symmetry analysis is based
on calculation of the mean distance between the
original 3D surface and its mirrored and matched
copy. It is a modication of a method proposed
by Benz etal. in 2002 [56].
The original surface and its mirrored copy are
matched (registered) employing the iterative
closest point (ICP) algorithm [57], thus minimizing the distance between them. This process is
repeated iteratively with rened mirror planes
calculated from the centroids of corresponding
points of the original surface and its mirrored
copy (Fig.5.6) [27, 58].
The nal symmetry plane is the estimated
median sagittal plane. The remaining asymmetries between the two surfaces can be visualized
by a pseudo-color scale as seen in Fig.5.6. An
asymmetry index 3DAI may be dened as
d
with d denoting the mean distance between the
two surfaces and D being the diagonal of the
bounding box that encloses the face [59].
´1000
the points of intersection with the outline of the
head [53].
It is calculated as the difference between the
length of the two diagonals multiplied by 100 and
then divided by the length of the longer diagonal.
The CVAI is given in percent. A CVAI >3.5% is
considered asymmetric [53].
´
100
>
if=
5.7.3 Landmarks
Morphometric landmarks can be dened as anatomical points located on the facial surface.
Landmarks occur either individually or in pairs.
In a right-left comparison, commonly used in
bilaterally symmetrical organisms, the individual
points are on the median sagittal plane, and the
pairwise points are about the same bilateral distance from it (Fig.5.7) [61].
A comparison of two similar faces or a symmetry calculation can be performed by measuring the deviation of each individual point from
the median sagittal plane and the difference in
distance of the paired points from that plane [62].
In addition, standards are dened by reference
values, giving the ratio or distance between certain points [63].
The analysis of the lateral cephalogram, which
works with landmarks, has been part of standard
diagnostics in orthodontics and combined dysgnathia surgery for almost 100 years [11]. This
complex analysis, which was previously carried out
manually, can now be carried out fully automatically by software that recognizes and analyzes landmarks [64]. Such an analysis can also be performed
with facial images [65, 66]. The manual setting of
60
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Fig. 5.6 Visualization
of the asymmetrical
areas of the face by
superimposing the
original face surface
with the matched
mirrored copy.
Pseudo-color scale with
distances in mm. The
symmetry plane is the
estimated median
sagittal plane
H. S. Visse et al.
2.883
2.162
1.442
0.721
landmarks on the patient can, however, improve the
precision of anthropometric software [28].
Modern 3D surface scanners offer a reliable
and accurate diagnosis of the soft tissue even
without additional hard tissue information [67].
The analysis of the hard tissue should not be used
to draw any direct conclusions about the soft tissue. Morphological differences between hard and
soft tissue should always be considered separately [68].
5.8 Shape Analysis
Within this context, shapes are described by a
xed arrangement of landmarks. This means that
the landmarks are ordered in a xed sequence (in
0.000
the example of Fig.
5.7 pairs of pixel coordi-
nates). When quantifying the differences between
two shapes, it must be taken into account that the
measured coordinates of the landmarks may be
provided in different scales and may be located
differently in space, which is not relevant for the
assessment of a shape. This means that the shapes
must rst be subjected to a transformation which
compensates for these irrelevant differences. For
example, in order to compare two different faces
dened by characteristic landmarks such as in
5.7, one of the faces must be transformed to
Fig.
look as similar as possible in size and shape to the
rst face, regardless of its position in the coordinate system. Two common methods for this are
the use of Bookstein coordinates and the
Procrustes transformation.
5 Morphometrics, Optical 3D Imaging, andMonitoring ofCraniofacial Development andMalformations
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Fig. 5.7 Facial
landmarks automatically
localized using a
machine learning
approach [60]
61
5.8.1 Bookstein Coordinates
A simple approach to the problem is the transformation proposed by Bookstein. In this method,
only the rst two landmarks are aligned by translation, rotation, and scaling. The remaining landmarks are then adjusted accordingly. This then
allows the calculation of (remaining) differences
[69, 70]. To illustrate this approach, Fig. 5.8
shows two shapes that represent similar anatomical features with different scales and positions. In
Fig. 5.9, the two shapes are transformed into
Bookstein coordinates.
5.8.2 Procrustes Analysis
The term Procrustes refers to a bandit from Greek
mythology who forced his victims into an iron
bed, stretching or cutting off their limbs when they
did not t. By analogy, in the Procrustes transformation, two shapes are brought into maximum
congruence through translation, rotation, and
scaling. A prerequisite for the meaningful application of this procedure is that the two objects to
be compared are similar [61]. Figure5.10 shows
the result of the Procrustes transformation of the
two shapes displayed in Fig.5.8. A simple mea-
62
−40 −20 02040
−40 −20 02040
180 200 220 240 260
360 380 400 420 440
−2 −1 012
−1.0 0.0 0.5 1.0 1.5 2.0
H. S. Visse et al.
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4
5
6
1
5
6
3
4
2
4
3
6
6
5
5
1
1
4
2
2
3
3
1
Fig. 5.8 Two shapes, each dened by a sequence of land-
marks. The lower one is taken from Fig.5.7 and represents the right eye, and the upper one is an arbitrary
eye-like shape
5
6
6
12
12
2
4
5
4
3
3
Fig. 5.10 Result of a Procrustes transformation of the
two shapes from Fig.5.8. All landmarks are brought into
alignment as much as possible using a regression
technique
5.8.3 Anthropometric Mask
The concept of landmarking was further developed by Claes et al. through the so-called
anthropometric mask. It consists of about 10,000
quasi-landmarks, which are placed automatically
over the face. By comparing the quasi-landmarks,
e.g., pre- and post-surgery, differences in facial
structures can be determined and displayed
graphically [71].
5.9 Conclusion
Fig. 5.9 The two shapes from Fig.5.8 transformed into
Bookstein coordinates. Only landmark one and two are
aligned by transformation
sure to quantify the residual deviation between
the shapes is the sum of the Euclidean distances
between corresponding landmarks.
Morphometrics and high-resolution optical 3D
imaging systems are powerful tools for documenting facial structures and their changes in
normal facial development and facial malformations. They can be used for a multitude of other
applications. In combination with radiological
layer systems (MRI, CT, CBCT), fundamental
insights in healthy or diseased states of patients
can be gained.
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63
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Classication ofCraniofacial
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Malformations
UlrichMeyer
6
6.1 Introduction
Classication of craniofacial malformations is
difcult to standardize. This is based on multiple aspects in disease development and disease
manifestation. Additionally, the border between
a disease and a norm variance is oating. Some
aspects have to be recognized: on one hand, the
determination of the disease and on the other
hand the documentation of the disease outcome.
Determination of a disease can be done on a
genetic or a clinical level; documentation can
be done on various imaging procedures (pictures, MRI, CT, CBCT, 3D scan, or sonographic
images). In order to elaborate a comprehensive
classication system for the broad range of craniofacial malformations, different issues have
to be considered: the development of classication systems, current concepts of disease classication, genetics and pathogenesis of head
malformation, and disease recognition and documentation. A new three-axis classication system
is proposed that comprehensively includes all
craniofacial malformations.
U. Meyer (*)
Craniofacial Center, Kieferklinik Münster,
Münster, Germany
University of Düsseldorf, Westdeutsche Kieferklinik,
Moorenstrasse, Düsseldorf, Germany
e-mail: info@kieferklinik-muenster.de
6.2 The Development
ofClassication Systems
Disease classications (taxonomies) are used
ubiquitously in academic medicine, human
genetics, the health industry, and economics.
Much like any library’s content catalogue, disease taxonomies strive to group together similar
entities for ease of access and analysis [1].
Historically, changes in these groupings have
reected a progression toward etiologic,
common- cause disease classications [2–6]. The
development of nosologies has closely paralleled
the evolution of methods designed for the reconstruction of the evolutional process (Fig. 6.1).
Approaches to species classications were
mostly subjective and made without any hint of
the common-origin interpretation. They utilized
only a small subset of all the visible morphological features of any given organism. Initially,
many of these groupings were largely arbitrary—
often guided by topographical or anatomical similarities. These early phylogenetic methods were
followed by the use of maximum parsimony
methods, explicitly minimizing the number of
differences between proximal taxonomy leaves.
Disease taxonomy plays an important role in
dening the diagnosis, treatment, and mechanisms of human diseases even now. The principle of the current clinical disease taxonomies,
in particular the International Classication of
Diseases (ICD) (Fig. 6.2), goes back to the
© Springer Nature Switzerland AG 2021
U. Meyer (ed.), Fundamentals of Craniofacial Malformations,
https://doi.org/10.1007/978-3-030-46024-2_6
67
68
New World monkeys
Organism
Archaebacteria,
a
https://t.me/medicina_free
Modern
humans
Orangutans,
Goillas
Great apes
Old World
monkeys
Tarsiers
Apes
Catarrhines
Haplorrhines
Rodents,
Lagomorphs
Xenarthrans
Marsupials
Birds
Bony fishes
Hagfishes
Tunicates
Echinoderms,
Hemichordates
Protostomes
Comb jellies
Trichoplax
Choanoflagellates,
Mesomycetozoea
Plants
Archaeplastida
Bacteria
Prokaryotes
Primates
Euarchonoglires
Placentals
Mammals
Tetrapods
Gnathostomata
Vertebrates
Chordates
Deuterostomes
Bilateria
Eumetazoans
Metazoans
Opisthokonts
Eukaryotes
Chimpanzees
Gibbons
Strepsirrhines
Treeshrews,
Colugos
Afrotherians,
Laurasiatherians
Monotremes
Amphibians,
Reptiles
Cartilaginous fishes
Lamprey eels
Cephalochordates
Xenoturbella
Orthonectida,
Acoelomorpha,
Dicyemida
Cnidarians
Sponges
Fungi
Amoebozoans,
Chromalveolata,
Rhizaria,
Excavates
U. Meyer
Fig. 6.1 (a) Taxonomy from simple organisms to the
human species. (b) Taxonomy at a precise level. (With
permission from Springer Nature: Nature, The global
diversity of birds in space and time, Jetz, W., Thomas, G.,
Joy, J. etal., 2012). Source: Reprinted from Peter Hermes
Furian/Shutterstock.com with permission
6 Classication ofCraniofacial Malformations
https://t.me/medicina_free
b
69
Fig. 6.1 (continued)
Fig. 6.2 International Classication of Diseases. Source:
Reprinted from hafakot/Shutterstock.com with permission
work of William Farr in the nineteenth century
and is primarily derived from the differentiation of clinical features (e.g., symptoms and
micro-examination of diseased tissues and
cells) [7]. Despite its extensive clinical use and
elaboration for economical reasons, this classication system lacks the depth required for precision medicine with the limitations of its rigid
hierarchical structure, and, moreover, it does
not exploit the rapidly expanding molecular
insights of disease phenotypes. Most recent
arrivals to disease classication are statistical
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