3D Cephalometrics and morphometrics /certified fixed orthodontic courses by Indian dental academy

Three Dimensional
Cephalometrics,
Morphometrics and
other recent
advances
www.indiandentalacademy.com

Introduction
►Over the years, diagnosis and
treatment planning in
orthodontics and dentofacial
orthopedics has relied substantially
on numerous technological aids.


►The gold standard that these aids
(imaging, articulators, jaw tracking and
functional analyses) attempt to achieve is
the accurate replication or portrayal of
the “anatomic truth”.

►The anatomic truth is the accurate
three-dimensional anatomy, both static
and functional, as it exists in nature.

►The ultimate goal of the clinicians is to
use these technologies, either alone or
in various combinations, to delineate
this anatomic truth.

►Imaging is one of the most ubiquitous
tools that orthodontists use to measure
and record the size and form of
craniofacial structures.

►Imaging has been traditionally used in
orthodontics to record the status quo of
limited anatomic structures.

►While the use of imaging in orthodontics
has been relatively adequate, the
fulfillment of ideal has been limited by
the available technology & the quality of
the database.

►These desired goals of craniofacial
imaging are closer to being achieved than
ever before.

►We will be seeing in detail about the
Three dimensional cephalometrics,
Morphometrics & other advances in
imaging which takes us a step closer to
the realization of our goal.

Three Dimensional Cephalometry


►Facial evaluation begins with a
systematic, three-dimensional
assessment of the frontal & profile
views in three planes.

►The deformities can then be described
three dimensionally in the frontal and
profile views as excessive, normal, or
deficient.

►Earlier orthodontists paid little attention
to the PA view ‘coz the clinical problems
encountered were symmetric & appeared
to be adequately recorded by the lateral
view alone.

►Recently, as orthodontists have become
"craniofacial orthopedists" treating more
severe, often asymmetric craniofacial
anomalies; the limitations of the lateral
cephalogram have become obvious.

►The Broadbent-Bolton cephalostat
produces intrinsically three-dimensional
information about cranial form.

►Yet in the clinical setting, this
information has been used primarily two
dimensions at a time in the separate
study of lateral or posteroanterior
cephalograms.

►From the very first introduction of the
cephalostat, Broadbent and Bolton
stressed the importance of coordinating
the lateral with the PA films to arrive at a
distortion-free craniofacial form.

►For this purpose they described the
Orientator,an exploitation of the
geometry of the cephalostat to simulate
stereophotogrammetry.

►Orientator, is an acetate overlay placed
over both cephalograms (LAT and PA)
after they were oriented jointly along their
common Frankfort horizontal plane.


History
►The earliest three dimensional
measurements of the skull were made by
researchers in anatomy & anthropology,
primarily on dried specimens.
►The reference planes of Frankfort, His,
and Camper and most of the anatomic
landmarks that we currently employ were
defined and measured directly prior to
1900.

►The most widely known system for
measuring the spatial relationships
between the teeth and the skull in vivo
was that of P.Simon, during 1920’s.

►His system, like that of his predecessor
Van Loon; was essentially mechanical. It
included a maxillary clutch and a frame.


►By means of this
apparatus & a wax
‘check bite’, it
was possible to
locate the dentition
within the skull
anteroposteriorly,
vertically & with
respect to the
occlusal plane
orientation.

►Simon’s conceptions of gnathostatic
measurement were essentially sound,
but the technical procedures were quite
demanding.

►Simon's system is important in that it
focused sharply than did subsequent xray methods upon the location of
structures that interest Orthodontists
most— the teeth & alveolar process.

►In the exposure of a pair of
cephalograms the patient's head is not
turned, but instead the cephalostat
itself. The LAT and PA films would
occupy positions at 90° to each other.

►By keeping the films with respect to the
head, one can draw the rays connecting
the x-ray source to each landmark of
either film as threads in space.

►The result is a pair of pyramidal sprays
of thread, intersecting at approximately
90° throughout the interior of the space
occupied in reality by the patient's head.


►The films can be flattened into one
plane by unfolding them along the
"corner", with each bundle of threads
(x-ray paths) flattened to the side of the
other film at the appropriate distance.

►The Orientator is the diagram of the
flattened threads. When superimposed
over the abutted pair of films, the
points in each film that correspond to
any locus in the other can be visualized.

►Broadbent & Bolton used Orientator to
correct for distortion inherent in the
spread of cephalometric x-ray beam.

►In 3D cephalometry we are instead truly
reconstructing the location of landmarks
in space. The principle of the Orientator
then is identical with the ray intersection
method, a photogrammetric tool.

►For a radiographic landmark to be
locatable in the space of head, it must be
connected to the x-ray source in two
different projections: the LAT & PA views.

►The best landmark candidates for such
points are structures defined by means
of the vertical coordinate, which is
shared between the two views.

►Many landmarks are conventionally
defined as the "top" or "bottom" points
of structures: menton, condylions,
superior and inferior orbital rims, and
cusp tips.

►Points uppermost or lowermost in the PA
ceph may not represent precisely the
same points in space uppermost or
lowermost in the lateral ceph.

►The typical lateral tracing includes eight
landmarks conventionally taken to lie on
the midsagittal plane: S,N, ANS,
supradentale, upper & lower incisal
edge, menton, and pogonion.

►Of these, supradentale is visible in the
PA film, as are the averaged incisal
edges and menton.

►Sella, nasion, ANS, & pogonion have little
visibility, if any, in the PA film.

►With two of their coordinates supplied
by the lateral film, the third may be
taken to correspond to the apparent
position of the midsagittal plane at the
appropriate depth in the frontal film.

►Any three-dimensional reconstruction
will proceed more accurately if the
bilateral landmarks on the lateral film
have not been averaged.

►Instead they should be identified
individually by a careful consideration of
study models, dental landmarks, and
auxiliary cephalometric films.

►3D ceph
landmarks
x, y, & z
coordinates
found in the
LAT and PA
cephalogram
using which
the 3D points
are
reconstructed.

Registration of the
films
►The theory of the cephalostat treats
projections of the head in a pair of views
precisely to the FH plane & separated by
a 90° rotation about the vertical plane.
►But the real data is more or less
divergent from the ideal.


►Practically heads cannot be placed
precisely in the FH plane, nor can the
subject hold a fixed orientation while
rotated 90° within the cephalostat.

►In true Bolton system, the images at 90°
simultaneously by are generated almost
the use of 2 x-ray systems that are
themselves at 90°. Modern cephalostats
have lost this crucial capability.

►In particular, there is usually some
element of rotation about the ear rods,
away from the FH plane in one or both
images.

►Modest amounts of such positioning
error may be routinely corrected by
simple computations before one
proceeds to actual 3D reconstructions.

►The films corresponding to LAT and PA
projections of the same head are
digitized separately.

►The digitized LAT cephalogram is
rotated so that the point midway
between the two porions lies on a
horizontal line with the midpoint of the
two orbitales .

►The PA film is rotated so that the line
between the two porions is precisely
horizontal.

►This film is then subjected to a
computed shear correcting for failure of
the midorbitale point to lie precisely on
the horizontal line between the two
porions.

►Each landmark locatable on both films is
sheared by an amount corresponding to
its AP separation from porion as scaled by
the AP separation of midorbitale from
midporion in the LAT.
►This is a satisfactory approximation to
correct the procedure, a threedimensional rotation, for all angles of
rotation small enough to be encountered
in practice.

The ray intersection
method
►After this calibration step, we may
imagine that the landmark locations
correspond precisely to the nominal
geometry of the cephalostat.
►Each lies on one of a pair of film planes
in precisely known spatial relation at 90°
to each other.

►The landmark images are at a known
distance from x-ray source whose central
rays are at 90° to each of the films &
which intersect in space, exactly halfway
between the pair of porions.
►As in Orientator, each landmark location
on film is now replaced by the path in
space that the x ray must have followed
to arrive there: a thread connecting that
digitized location to the source.

►In this way the distortion
inherent in each
cephalometric projection
is corrected by the
combination of points
from both films.
►This three-dimensional
constellation of
landmarks may be joined
by straight lines and
rotated for viewing in all
directions.

Advantages
►The 3D method supports the usual
biometrics of landmark locations & takes
advantage of a normative data base that
is suited for semiautomatic analysis of
syndromic data.
►In comparison with CT, it involves low
radiation dose, simpler to obtain, has an
available normative data base, & is more
practical for long-term serial analysis.

►When compared with conventional
cehalometrics, the 3D evaluation for one
new methodology, (Acuscape & Sculptor)
was more precise within approximately
1mm of the gold standard.
►The sculptor program was found to be
4 to 5 times better than the 2D
approach.


Disadvantages
►The principal drawback of the method is
its inability to represent curving form in
three dimensions.

►One fundamental difficulty is associated
with the assumption that
"corresponding" landmarks in LAT and
PA films actually pertain to the same
three-dimensional point on the skull.

►Some inherent flaws and errors of this
scheme include tracing and digitizing
errors, failure of the porions to
superimpose in the lateral film, and the
finite size of the x-ray source.
►It is difficult to compensate for the
differences in enlargement (termed
"projective displacement'') of structures
which lie at different distances from the
frontal and lateral film surfaces.

►Empirical problems have prevented the
routine clinical use of this Broadbent’s
"biplanar" 3D method, notwithstanding
its obvious conceptual brilliance.
►To overcome the problems Sheldon
Baumrind and colleagues at the
University of California devised another
method, The Three-dimensional x-ray
stereometry from paired coplanar
images.

►The two basic and important problems
faced by the biplanar method of
Broadbent were:
►1.Difficulty in identifying the same
landmarks in both films with confidence.
and
►2. Projective displacement.


►Since both the LAT & PA are taken at 90o
to each other i.e, biplanar the same
anatomic structures take up different
size and shape, making it difficult to
precisely identify the landmark.

►This was overcome by this coplanar
method where both the films are taken
more or less in the same plane making
landmark identifications lot easier.

►It is difficult to
compensate for the
differences in
enlargement
("projective
displacement'') of
structures which lie
at different distances
from the frontal and
lateral film surfaces.


►That is to say that all the anatomic
structures lying in each "para-film" plane
will have the some magnification factor,
no matter what their anatomic nature.

►Conversely, if two planes are at different
distances from the film surface, their
enlargement factors will be different, no
matter what the anatomy.

►Broadbent system is in essence a spatial
and temporal composite of the two
views.

►It follows that the enlargement factor for
any given anatomic landmark will differ
from the lateral projection to the frontal
projection unless by coincidence that the
structure is at same distance from both
the film surfaces.

►In order to deal with the problem of
differential enlargement, a number of
investigators have constructed
specialized mechanical devices.

►These include the "orientator" of
Broadbent, the "compensator" of Wylie
and Elasser, and the "modified
compensator" of Vogel.

►This new method put forward by
Baumrind to overcome these difficulties
was based on an engineering tool called
Photogrammetry.

►Photogrammetry -- discipline devoted to
solving the problems of making 3D
measurements from paired 2D images,
esp. used for reconstructing terrestrial
maps from photos taken from space.

►The basic principle is the stereoscopic
vision used by eye to recognize the 3D
information of the object.

►When we view points at some distance
from us, our eyes rotate slightly to align
and focus on the points.


►Line segments can
readily be drawn
from each point
through the optical
center of the lens of
each eye. The
included angle
between the pair of
such lines is known
as the "parallactic
angle'' of the point.

►Points at different distances will have
different parallactic angles. Differences
in parallactic angle are interpreted by
the brain as differences in distance.
►The alternative way of measuring the
parallax is by using linear rather than
angular measurement. The distance
between two points on the connecting
lines in the same plane will also depict
the parallax of the point.

►In other words viewing the points along
the line with each eye focusing only on
one points, the brain will perceive it to
be a single point at the actual depth.

►Similarly, looking at a same point in two
pictures, with each eye concentrated on
one point, the brain will perceive the
depth of the structure.

►But this procedure puts extensive strain
on the eyes and though with dificulty the
clinician can assess the 3D info in mind,
it is not possible to quantify the
information and set up a database.
►To overcome this, Photogrammetry uses
STEREOSCOPE for viewing the picture
and then by calculating the distance
between the points, i.e, parallex the
depth information is quantified.

►Each matched pair of photographs is
called a stereopair or a diapositive.

►When this technique is used for
quantitative purposes, the distance
between each matched (or "conjugate")
pair of points is measured with a device
known as a "parallax bar“.

►The focal spot of x-ray tube is equivalent
to the optical center of camera lens. In
each case, the radiation travels in straight
line between the object & the nodal point.

►Thus, a conventional single x-ray film is
the geometric equivalent of a single
conventional photograph except that the
subject lies ''within" the camera instead of
beyond it.

Making of the stereopairs
►The subject would be positioned in a
head holder; and an exposure would be
made from "camera station L1.''
►The central ray would pass through the
porion-porion axis, the focal spot to
"midsagittal plane" would be maintained
at 60 inches, and a length scale would be
incorporated upon the film surface.

►Immediately after exposure, the film
would be removed and a new film would
be shifted into the same position by
some cassette-changing device.
►The second film would then be exposed
from "camera station L2.
►This produces a stereopair, one of which
is a standard cephalogram. This
procedure produces a coplanar image.

►The advantage of the coplanar image
over the biplanar is that both x-rays are
more or less similar & hence landmark
identification is a lot easier & reliable.
►Though the biplanar images have the
strongest mathematical correlation, its
advantage is offset by the projection
error and landmark identification.
►As we will be seeing the coplanar images
still retain a strong correlation.

►A – biplanar system
with rays orthogonal
and film in 2 planes.
►B – films placed in
single plane.
►C – head is rotated by
90o. Both are not
standardized films.
►D – orthogonal rays
are made to be acute.


►One of the systems dedicated for
producing coplanar images for 3D
stereometry with 2 cassette holders.

►The following parameters must be
known if 3D maps are to be made from
pairs of two-dimensional images:
►1. The principal point of both the films.
►2. The distance between the two stations
( L1 and L2 called base B).
►3. The perpendicular distance from the
film to the source.

►1.Principal point -- The location on the
film of the point of contact of central ray
from x-ray. The principal point of L1 is
needed to define the origin of coordinate
system. L2 is needed to define X axis.

►2.The perpendicular distance from each
exposure station to the film plane is
designated "H" (for height) & should, in
simple case, be equal for both x-rays.

►Knowing these values, by using simple
mathematical calculations the three
coordinates for the points are measured,
and using these coordinates a 3D wire
diagram is reconstituted.

►The origin of the coordinates can be
controlled, and the reconstituted figure
can be standardized, for future
comparison and evaluation.

Advantages
►More precise than the Broadbent and
Bolton system.
►Errors from patient movement can be
corrected by using reference landmarks,
whose definite relation we know.
►The projective displacement is not there.
►Can take use of the available normative
database.

Disadvantages
►Again cannot represent curving forms.
►Needs a dedicated special x-ray
apparatus with precise calibration.

►Needs complex patient positioning
arrays to avoid errors.
►Without calibration the reliability
degrades rapidly.

Morphometrics


Introduction
►Analysis of size and shape for diagnosis,
evaluation, comparison, and future
reference forms an integral part of
orthodontic diagnosis.
►The methods currently available to
evaluate craniofacial from include
Anthropometry, Photogrammetry,
Cephalometry, Computed tomography,
magnetic resonance imaging, etc.

►Invariably cephalometry continues to be
the most versatile technique for
investigation of the craniofacial skeleton
because of its validity and practicability.

►Despite the inherent distortion and
differential magnification, in comparison
with newer imaging techniques the
cephalogram produces a high diagnostic
yield at a low physiological cost

►There are 2 distinct groups of analytical
methods used in cephalometry:
►Landmark based techniques and
►Boundary outline methods.
►Landmark-based techniques are
dependent on cephalometric landmarks.
►Boundary outline techniques survey only
the perimeter of the structure.

► The use of algebraic measurements in
traditional ceph analyses is known as
conventional ceph analysis (CCA).
► It is a landmark based technique.

► Linear distance measurements between
two landmarks.
► Angles,
► Areas & ratios are the parameters used
by CCA.

Limitations of CCA
►Relies on the use of a reference
structure for orientation and
superimposition: that is assumed to be
biologically constant but in reality not
so.
►Measurements calculate the magnitude
of vectors between landmarks, ignoring
their direction.
►www.indiandentalacademy.com measured, not the shape.
Only size is

►To overcome all these, newer methods
of cephalometric analysis were
developed in place of CCA.
Morphometrics is one such.
►Morphometrics = morph + metrikos (Gr).
form + measurement.
Morphometrics = Measurement of form.

►In reality it consists of procedures which
facilatate mapping of visual information
into a mathematical representation.

►Morphometrics is measurement of form.
What is form?
►Form, fundamentally is the displacement
of space by area or volume due to an
object that is subject to scale difference.
►Simply stated,
Form = Size + Shape + Structure.

Types of morphometrics
►Morphometrics in representation of
form, mapping of visual information into
a numerical representation, viable for
statistical analysis.
The different types are:
►1.
►2.
►3.
►4.

Multivariate Morphometrics.
Co-ordinate Morphometrics.
Boundary Morphometrics.
Structure Morphometrics.


Multivariate
Morphometrics
►This type of morphometrics is applied to
datasets composed of distances, angles
and ratios.
►Multivariate Morphometrics (MM) is
defined as the use of quantitative
methods to discover the structure of
interrelationships of multiple
measurements.

►MM evolved to meet the need for
procedures aimed at measuring the
degree of similarity within and between
two or more forms using multiple
measurements.
►It is based on the concept that
simultaneous utilization of numerous
variables provides more information than
a large number of individual variables
being assessed seperately.

►Usually MM are based on measurement
system composed of distances, angles
and ratios, the Conventional Metric
Approach (CMA).

►MM (CMA) does not quantify the form
boundary or textural considerations.
►Used as an adjunct to Co-ordinate
Morphometrics.

►This method is extremely useful for
gaining insights about :

►1. How variables are structured?
►2. How the groups are related?


Some applications include :
►1. Establishing the similarity between
different forms.
►2. Measuring the variation that is present
using set of uncorrelated variables.
►3. Investigating the structure of
measurements used to describe form.
►4. Identifying the components of size and
shape.

Four commonly used methods for dealing
with form difference between groups
are:
►1.
►2.
►3.
►4.

Discriminant functions.
Mahalanobis D2 statistic.
Canonical variate analysis.
Cluster analysis.


Discriminant functions
►This assist in placement of unknown
specimens in to known groups.

►This is done by increasing the
discrimination between groups based on
a set of commonly held measurements.

►Discrimination is achieved by finding a
transformation in form which maximizes
between group differences while
minimizing within group variation.

►Group identity and membership within
the group must be known in advance
otherwise cluster analysis is indicated.

►The discriminants were computed to
maximize the between group variance
relative to the within group variance.
►The discriminant function for the
specimen is the sum of all linear distance
of how far apart, each multiplied by a
weighing co-efficient.
►Each discriminant function score is
orthogonal with respect to all others.

Mahalanobis D statistic
2

►The distance between groups is measure
and squared .
►This squared distance between groups is
termed the “generalized distance” or “D2
statistic of Mahalanobis".
►It describes the relatedness or similarity
between forms based on multiple
uncorrelated measurements.

Canonical variate analysis
►The form of an subject to be assessed is
taken, rotated through an axis so that
within group variation is minimized.

►The image is rescaled, transformed and
deformed until within group variation is
made circular.

►The image or the form is rotated again
through an axis this time such that
between group variations is maximized.
►Both the rotated & rescaled axis is called
the “Canonical Axis” for that image.
►These axes are orthogonal to each
other. They are in fact the representation
for the image or the group.

Cluster analysis
►This method deals with the identification
of group structures.
►That is given a collection of objects are
there recognizable subgroups?
►More than one clustering method has to
be used to get a reliable result.

There are two methods to find the
difference within groups:

►1. Factor analysis.
►2. Principal component analysis. (PCA).


►Both of these deals with differences and
interrelationships within the variables
themselves.
►These give an idea about the structure of
the underlying variables and how they
vary with each other.
►Identify which of those uncorrelated
variables are in turn the primary
determinants of form and reduce the
statistical load.

Procrustes
superimposition

►It is a variant of the landmark based
morphometric method, and a
superimposition method.
►Procrustes a robber in Greek mythology,
belived his iron bed to be unique and as a
standard of length.
►His victims if small were stretched, those
taller were chopped off their legs to fit the
size of the bed.

►His “one size fits all” concept was
utilized in the superimposition method.

►Each form is represented by a series of
landmark co-ordinates forming a figure
known as configuration.

►Each configuration is scaled first to the
same size.

►The Procrustes superimposition
algorithms translate the configurations
to superimpose the centroids and rotate
the configurations to minimize the
differences.

►This is essentially the position of ‘bestfit’. After the superimposition, the mean
configuration called the consensus is
computed.

►For each land mark the Procrustes
residual is calculated as the diff between
the location of landmarks in each form,
and its position in the consensus.
►These can be plotted to display the
shape variance.
►Procrustes superimposition has been
used for evaluation of normal and
syndromic craniofacial growth.

Co-ordinate
morphometrics
►Based solely on the data points
composed of 2D or 3D co-ordinates,
usually in the Cartesian system.
►It ignores the boundary of the form.
►Most of these are based on D’Arcy
Thompson’s Transformation grids.

This includes the following methods:

►1. Conventional Metric Approach (CMA)
including the Conventional Ceph Analysis.
►2. Biorthogonal Grids (BOG).
►3. Finite Element Method (FEM).
►4. Thin Plate Spline Analysis (TPS).
►5. Euclidean Distance Matrix Analysis

(EDMA).

Conventional Metric
Approach
►Based on distances, angles and ratios.
►Homologus points should be taken for
plotting.
► CMA and its CCA both are incomplete
mapping, not describing the shape or
shape changes.

Biorthogonal grids
►The BOG is developed by Bookstein.
►This also uses the homologus point
representation.
►The foundation of the BOG method is
comparison between two 2D forms.
►One form is designated as the base form
and the other as one which reflects the
shape changes from the base form.

►The shape changes are viewed as
deformations from the basic form.

►The base form is constructed with
landmarks of our interest, whose shape
change we are going to study.

►The base form is usually a triangle,
though any polygon can be used.

►The triangle is constructed and a circle
is drawn inside the triangle touching the
boundary.
►Once this triangle transforms in to
another triangle, the circle gets
transformed in to an ellipse.

Base triangle

Deformed triangle

►The major and minor axes of the ellipse
and the corresponding diameters of the
circle are the representations of shape
changes.

►They represent the “principal dilatations”
or estimates of maximum stretch or
shrinkage due to the deformation.


►The cross denoting the centre of the
ellipse with its major and minor axes
represents a tensor for that shape
change.

►The ratio of major axis to minor axis is
considered as the estimator of shape
change.

►The BOG is used by Bookstein for
studying shape changes in craniofacial
anomalies.
►When BOG is used for biological subjects
it is called “Tensor Biometrics”.

►The disadvantage is that it measures
shape change rather than the shape as
such.
►Like CMA it cannot represent curves.

Finite Elements Method
►This is similar to BOG if not identical.
►It is also based on homologus landmarks
and is invariant with respect to the coordinate system.
►Very similar to BOG, but that many
triangles (Finite Elements) are
constructed.

►The average shape change of all the
triangles is computed for the shape
change for the whole form.
►The principal dilatations in BOG are
called as “strain measures” here.
►The triangles are the basic forms used in
2D FEM.

►The triangles are replaced by
hexahedrons in 3D FEM.
►Each cube is represented by 8
homologus points in the Cartesian
system.
►The cubes are non-homogenous unlike
triangles and hence represent spatially
varying tensor fields.

FEM on Face

FEM on Tooth

FEM based Ceph analysis
►Discretization of
the craniofacial
complex in to
finite elements
based on the
normal biometric
landmarks.


FEM depicting
size and
shape changes
using colour
coding for
easy
comprehension


Thin Plate Spline Analysis
►TPS analyze shape change using theory
of surface spline interpolations.
►The TPS function colloquially known as
“bending energy” is visualized as an
infinetely thin metal sheet draped over a
set of landmarks, extending infinitely in
all directions.

►The configurations of two forms are
matched exactly to minimize the
bending energy.
►If two forms are identical bending
energy is zero.
►The magnitude and location of bending
energy can be identified depending upon
the size and position of the deformation
of the plate.

►The thin plate
where shape
changes, i.e,
“bending energy”
is depicted by the
colour gradient.


►In affine transformations the parallel
lines in the plate remain parallel.
►The bending energy of the affine
transformation is zero and only the
tilting of the plate may occur.
►In non-affine transformations the there
will be local deformations, these are
represented as “partial warps”.

►Shape changes can be statistically
analyzed using multivariate statistical
techniques, based on partial warp scores.
►TPS has been applied to three dimensions
for studying changes in cranial base.


Euclidean distance matrix
analysis
►This was developed by Lele at the
John Hopkins.
►Utilizes 3D Cartesian co-ordinates of the
homologus points to identify local areas
of shape change.

►Initially a ‘mean form’ from distances of
all possible landmarks is computed.
►These distances are the EDM
representations which is averaged to
yield a mean matrix for the sample.
►Calculation of a distance difference
matrix using ratio of similarity between
forms on pair wise distances is
calculated.

►This distance difference matrix is then
sorted to identify the areas of maximum
and minimum change.
►These EDMA does not distinguish
between size and shape individually.
►The results obtained are similar to FEM.


Boundary morphometrics
►These techniques takes boundary
outlines, and not points.
►Very useful in assessing shape where
landmarks are scarce.
►Indispensable if boundary outline is the
primary area of interest.

The advantages of boundary outline
methods are that:

►Recreation of the boundary precisely is
possible.
►It is an information preserving method.
►A combination of boundary outline form
can incorporate homologus points also.

There are six boundary outline methods:

►1.
►2.
►3.
►4.
►5.

Median Axis Function.
Fourier Descriptors.
Eigen Shape Analysis.
Fourier Transforms.
Wavelets.


Median Axis Function
►It is also called as symmetric axis or line
skeleton.
►MAF is defined as the locus of points
which lie in the interior of the form,
exactly equidistant from the border of
the outline.

►It is a method of collapsing of a 2D
outline in to a curve or a line.
►Consists of embedding a series of
overlapping circles or discs that touch
the outline such that they are tangential
to the borders of the outline.
►The centers of those circles now define
those two points and when we join the
centers we get a stick figure.

Stick figure of a mandible
using MAA


►The circle usually touches two points in
the periphery.
►If it touches three points it encloses a
bifurcation.

►The circles contains two variants
(determinants) :
►The structure of the median axis
(stick figure).
►Radius of the circle i.e, width of MAF at the
tangent points.

►Circles are used in a 2D structure, where
as it can converted to spheres and used
in 3D measurements.
►MAF is not unique, it is possible for
classes of similar shapes to have an
identical medial axis.
►The radius function must be computed
regularly to have an individual
representation.

Conventional Fourier Descriptors
►The approach of Fourier analysis can be
viewed as a transformation of data from
one domain to another.
►In biology it refers to the transformation
from spatial domain to the frequency
domain.

►This is also termed as decomposition of
the spatial configuration (Boundary) in to
frequency components (amplitude &
phase relationships).
►This procedure of decomposition is called
“Fourier analysis” or “Harmonic analysis”.
►The inverse process of recreation of an
image from data is called “Harmonic
synthesis”.

►Two types of FD approaches have been
widely used, both convert the data to
polar co-ordinates prior to analysis.
►One is based on measurements from a
center within the form, preferably a
centroid.
►The other uses angular functions based
on points located on the outline.

►How many harmonics are needed to
achieve a satisfactory fit of the FD as an
expected function to the boundary
outline (observed form).
►The residual of fit is calculated and is
used for comparison between FD’s.
►Elliptical Fourier Functions have now
superseded the conventional FD’s.

Eigen Shape Analysis
►The use of ESA facilitates the reduction
of the morphological shape space to a
comparatively few dimensions that
contain most of the differences in shape.

►So it is claimed to have reduced the
minimum number of factors necessary
for recognizing subtle shape differences.

►This utilizes Fourier functions using
tangent functions.
►So basically uses angular measurements
when compared to Conventional FD’s
which utilizes the sine and the cos data.
►There is no need for centroid, and is
basically a single valued function.

Elliptical Fourier Functions
►EFF is also a type of pattern recognition.
► The EFF technique was developed
originally for military aircraft
identification and like conventional
Fourier functions is a curve-fitting
procedure.

►The basic principle involves embedding
a set of closely spaced observed
measurements on an object’s boundary
into a mathematical function.

►EFF is a parametric solution to shape
description, deriving a pair of equations
as functions of a third variable


►The first harmonic represents an ellipse,
with higher harmonics detecting
increasingly localized shape differences.

►The accuracy of the procedure can be
determined by calculating a residual
value-the difference between the
observed data & the predicted values
derived from the EFF.

►EFF is very loyal in representing the
shape and shape differences.
►It is one of the most commonly used
boundary representation method.
►Though currently it is used only for the
2D data, it has been developed for use in
3 d forms also.

Fourier Transformations
►These are the recent developments of
the Conventional Fourier descriptions.
►There are 2 types of Fourier
transformations
1. Discrete Fourier transform (DFT).
2. Continuous Fourier transform
(CFT).

►FT’s are bit complicated in their
calculations, but software has developed
to compute them automatically.
►They have the ability to reproduce even
minor details of shape changes.
►To reduce the computer computation
times, newer tech like Fast Fourier
Transform (FFT) & Short Time Fourier
transform (STFT) are developed.

Wavelets
►These are similar to the FT’s.
►Unlike the FT’s which are continuous
representations over the period -∞ to
+∞, wavelets are limited duration.
►Similarly they are of two types
►1. Continuous wavelet transform (CWT).
►2. Discrete wavelet transform (DWT).

►Though both FT’s and the wavelets are
the currently developed geometric
morphometric methods which are highly
versatile, their regular use in biologic
morphometrics is yet to be realized.
►Both can represent many functions and
characteristics of the object, rather than
like the primitive methods.

Structural Morphometrics
►These are techniques that numerically
describe the characterizing of the
surface or the internal structure of the
form.

►Structure is also that, which is inside the
boundary outline.

►It can be both internal or external
structure of the object.
►It can be either surface texture or
roughness, or the internal structures like
the bony trabaculae, or the chemical
structures the crystal lattices.


There are three approaches:

►1. Fourier Transforms.
►2. Wavelets.
►3. Optical Data analysis/ Coherent
Optical Processing.
They are also yet to influence the field of
biologic morphometrics.

Recent Advances


►Change is the only thing that does not
change.
►Yes there are many recent advances in
the field of Orthodontics and especially
in the area of Craniofacial Imaging.
►Few of them have really a great potential
to be developed especially for
Craniofacial imaging.

Digital Imaging
►The interest in digital imaging has
resulted due to a number of different
reasons.
►In terms of necessity, utilization of
digital imaging provides the ability for
the computer to manipulate data to allow
complex introduced techniques may
reduce patient radiation exposure.

►The elimination of hard-copy X-ray film
may decrease storage needs and enable
teleradiology, or the transmittance, of
images over the phone and internet.

►The digital process is a collection of
information of binary form, resulting in
the construction of a computerized
image.

►In most types of digital radiography,
electromagnetic energy (X-radiations) is
converted to an electrical charge by an
X-ray sensor.

►These sensors include charge-coupled
devices (CCDs), amorphous silicon and
amorphous selenium chips are arranged
in an array when used in large X-ray
applications.

►Another method of converting the X-ray
into an electrical charge for digital use is
the storage based phosphor plate.
►These plates are thin, wireless, flexible
plates similar to intensifying screens.
►The re-usable phosphor plates store the
energy from X-ray beam, and are then
“read” by a laser scanner which detects
the intensity & location of the stored
energy.

►Once the X-ray energy has converted to
an electrical charge, a computer with a
frame-grabber circuit board (digitizer)
sample the photosensor value (voltage)
and converts (digitizer) them into a
picture element array (pixels).
►Since the information is in digital form,
it can be integrated together with other
digital information such as intraoral &
extraoral photographs & tomographs to
form composite profile.

Teleradiology
►Early 1982 marked the initial meeting of
the First International Conference and
Workshop on Picture Archiving and
Communications Systems (PACS) for
Medical Applications.
►This electronic transport of the images
will continue to meet challenges as new
technology surface

3D CT
►The CT images can be manipulated to
undergo a three-dimensional
reconstruction of the image.
►The final image can be fed through a
computer aided design system and either
viewed on a computer screen or
processed into plastic via milling
machines or laser stereolithography.

►The technique is sophisticated enough to
be able to extract an element out of the
image, such as the mandible, and view it
in isolation from other structures.


Microcomputed Tomography
►MicroCT is principally the same as CT
except that the reconstructed cross
sections are confined to a much smaller
area.
►The future of microCT lies in being able
to sample data over a much smaller
volume than full body volume, thereby
significantly reducing the radiation
exposure to the patient.

►This technique can now measure bone
connectivity in all three dimensions and
even record anisotropy, both of which
are not possible even with histology.

►This method has been used clinically to
evaluate osteoblastic/osteoclastic
alveolar remodeling as well as bone
dehiscences and root resorption.

Tuned-aperture Computer
Tomography
►TACT system is able to convert multiple
two-dimensional images created from
multiple arbitrary projection source
positions into a three-dimensional image.
►The future of TACT will lie in its ability
to assist in the evaluation of alveolar
bone & detection of root resorption.

MR Spectroscopy
►MRI works by obtaining a resonance
signal from the hydrogen nucleus, and
therefore is essentially an imaging of
water in the tissue.

►MR spectroscopy works in a similar
manner, but allows the imaging of any
molecule or compound in the tissue.

►MR spectroscopy is useful for the study
of skeletal muscle physiology.
►This approach has been applied for the
study of phosphate metabolism in
muscles of children with bruxism.
►They have applications to a better
understanding of changes in muscle
functions.

Structured Light
►Structured light scanning enables the
topology of the face to be digitized
simply, and without ionizing radiation.

►The result is a three-dimensional “shell”
of the patient’s face, viewable on a
computer monitor.

►The eventual goal of this technique is to
merge the facial “shell” and underlying Xray data from other sources to complete
the 3D structure for diagnosis, treatment
planning and assessment.

►3D facial analyses are now a possibility,
and 3D superimposition revealing
treatment effect & outcome will soon be a
reality.

Cone Beam Computerized
Tomography
►It is a type of CT that is more or less
similar to the DPT in function.

►This has tremendous potential to be
used in orthodontics, and is expected to
replace all other imaging modalities in
the near future.

►In contrast to the CT it uses a low energy
fixed anode tube with a cone shaped Xray beam.

►The image sensors used are solid state
image sensor or an amorphous silicon
plate.


►CBCT uses 1 rotation sweep of the
patient similar to the DPT. Image data
can be collected for a complete
maxillofacial volume or limited areas.

►The accuracy is very high coz the
projection is orthogonal and the rays are
parallel with each other. The object is
also very near to the sensor producing a
1 to 1 measurements.

Picture of a CBCT image

Discussion
►What is an ideal imaging?
The underlying principle of ideal imaging
is the determination of anatomic truth in
terms of accurate portrayal of spatial
orientation, size, form, and relationship of
desired structures of features.


The ideal imaging modality is the
one which maximizes the desired
information and minimizes the
physiological risk and economical
cost to the patient.



c
o
n
c
l
u
s
i
o
n

►Despite the inherent distortion &
differential magnification, in
comparison with newer imaging
techniques, the cephalogram
produces a high diagnostic yield at a
low physiological cost, the ideal with
the techniques available now.


►The newer techniques has to be
simplified for the practicing orthodontist
to emerge as an alternative to
cephalmetrics.

►For the every day clinician cephalogram
will continue to be the imaging tool,
where newer methods are useful for
research and study of ethnographical
data.

References
►Morphometrics for the life sciences ----- lestrel.
►AJO_DO OCT 1983 – 3D Ceph.
OCT 1988 – 3D Ceph.
MAY 2004 – morphometrics.
SEPT 2004 – 3D imaging.
DEC 1981 – Photogrammetry.
►AO
1999 NO 6 – review of imaging.
1994 NO 5 – FEM based Ceph Analysis.
►EJO
2003 25 – size and shape
measurements.

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