RETRACTED ARTICLE: Improving the reconstruction of dental occlusion using a reconstructed-based identical matrix point technique

Abstract

Digital dental models are widely used compared to dental impressions or plaster-dental models for occlusal analysis as well as fabrication of prosthodontic and orthodontic appliances. The digital dental model has been considered as one of the significant measures for the analysis of dental occlusion. However, the process requires more computation time with less accuracy during the re-establishment of dental occlusion. In this research, a modern method to re-establish dental occlusion has been designed using a Reconstructed-based Identical Matrix Point (RIMP) technique. The curvature of the dental regions has been reconstructed using distance mapping in order to minimize the computation time, and an iterative point matching approach is used for accurate re-establishment. Satisfactory restoration and occlusion tests have been analyzed using a dental experimental setup with high-quality digital camera images. Further, the high-quality camera images are converted to grayscale images for mathematical computation using MATLAB image processing toolbox. Besides, 70 images have been taken into consideration in which 30 planar view images has been utilized for experimental analysis. Indeed, based on the outcomes, the proposed RIMP outperforms overall accuracy of (91.50%) and efficiency of (87.50%) in comparison with conventional methods such as GLCM, PCR, Fuzzy C Means, OPOS, and OGS.

Full text

Vol.:(0123456789)
1 3
Journal of Ambient Intelligence and Humanized Computing (2023) 14:1937–1950
https://doi.org/10.1007/s12652-021-03404-5
ORIGINAL RESEARCH
Improving thereconstruction ofdental occlusion using
areconstructed‑based identical matrix point technique
SukumaranAnil1,2 · SajithVellappally3· AbdulazizA.AlKheraif3· DarshanDevangDivakar3· WaelSaid4 ·
AzzaS.Hassanein5
Received: 26 October 2020 / Accepted: 15 July 2021 / Published online: 3 August 2021
© The Author(s) 2021
Abstract
Digital dental models are widely used compared to dental impressions or plaster-dental models for occlusal analysis as
well as fabrication of prosthodontic and orthodontic appliances. The digital dental model has been considered as one of the
significant measures for the analysis of dental occlusion. However, the process requires more computation time with less
accuracy during the re-establishment of dental occlusion. In this research, a modern method to re-establish dental occlusion
has been designed using a Reconstructed-based Identical Matrix Point (RIMP) technique. The curvature of the dental regions
has been reconstructed using distance mapping in order to minimize the computation time, and an iterative point match-
ing approach is used for accurate re-establishment. Satisfactory restoration and occlusion tests have been analyzed using a
dental experimental setup with high-quality digital camera images. Further, the high-quality camera images are converted to
grayscale images for mathematical computation using MATLAB image processing toolbox. Besides, 70 images have been
taken into consideration in which 30 planar view images has been utilized for experimental analysis. Indeed, based on the
outcomes, the proposed RIMP outperforms overall accuracy of (91.50%) and efficiency of (87.50%) in comparison with
conventional methods such as GLCM, PCR, Fuzzy C Means, OPOS, and OGS.
Keywords Dental occlusion· Camera images· Reconstruction· Grayscale images· Point classification
1 Introduction
Aesthetic and functional dental occlusion is the objective of
orthodontic treatment. The tooth size, jaw relation, and teeth
alignment are the important aspects of orthodontic manage-
ment (Svedström-Oristo etal. 2001). Examination of the oral
cavity, radiographic assessment, and evaluation of dental
casts are performed to acquire the necessary data during
the treatment planning (Rischen etal. 2013). However, the
visual examination has limitations to properly visualize the
palatal and lingual surface and the occlusion (Maspero etal.
2019).
Moreover, impression procedures can cause discomfort
to the patient and require longer chair time (Yuzbasioglu
etal. 2014). The plaster casts need physical storage space
in addition to the financial and logistical burdens. Further-
more, the visual inspection of dental plaster casts does not
enable clinicians to examine, measure, or track orthodontic
tooth movement and the surrounding bone’s root area (Li
etal. 2018). The application of orthodontic force through
the appliance shifts the teeth in incremental steps with
* Sukumaran Anil
drsanil@gmail.com
Sajith Vellappally
svellappally@ksu.edu.sa
Abdulaziz A. Al Kheraif
aalkhuraif@ksu.edu.sa
Darshan Devang Divakar
ddivakar@ksu.edu.sa
Wael Said
wael.mohamed@zu.edu.eg
Azza S. Hassanein
sa_azz@yahoo.com
1 Department ofDentistry, Oral Health Institute, Hamad
Medical Corporation, P.O. Box3050, Doha, Qatar
2 College ofDental Medicine, Qatar University,
P.O. Box2713, Doha, Qatar
3 Dental Health Department, Dental Biomaterials Research
Chair, College ofApplied Medical Sciences, King Saud
University, P.O, Box10219, Riyadh11433, SaudiArabia
4 Computer Science Department, Faculty ofComputers
andInformation, Zagazig University, Zagazig44511, Egypt
5 Biomedical Engineering Department, Faculty ofEngineering,
Helwan University, Cairo, Egypt
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1938 S.Anil et al.
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successive activation of the appliance (Cunningham etal.
2000; Harrison 2011).
In several aspects of dental care, accuracy is a significant
problem. To remove the hard dental tissue, an appropriately
designed prosthesis is required to avoid the destruction of
the existing structure (Aivatzidou etal. 2020; Perea-Lowery
and Vallittu 2018). Fixed partial dentures and complete den-
ture prostheses are particularly crucial if devices such as
designed teeth or implants can be precisely adapted. There-
fore, a highly precise reproduction is essential, particularly
in dental impressions and laboratory setup (Malachias etal.
2005; Moreira etal. 2015).
Current validation techniques provide centralized linear
measurements in all these areas through calipers or micro-
scopes. Such methods are limited to a small number of meas-
urement points and minimal data on 3D adjustments in the
testing area (Chandak 2020). The modern forms of measur-
ing include the optical or X-ray analysis of the whole object
test area. It tests the entire region or volume and shows it
on the computer screen as a 3D object (Erdelyi etal. 2020;
Oprea etal. 2008; Shimada etal. 2020). Linear comparisons
and overlaps between models with different scan times are
feasible. With this outline, it is possible to measure the sur-
face’s modifications at each scan point (Akyalcin etal. 2013;
Wiranto etal. 2013).
The clinical examination and the assessment of teeth and
fremitus mobility are the main methods used to rule-out of
occlusal pathology (Fan and Caton 2018; Ribeiro-Dasilva
etal. 2017). Many methods have been utilized to determine
the occlusal properties, such as using images, and occlusal
sonography (Agbaje etal. 2017).
However, conventional methods such as GLCM, PCR,
Fuzzy C Means, OPOS, and OGS methods have been uti-
lized to calculate occlusal properties shows less accuracy,
less efficiency and more computational time. These chal-
lenges have been resolved using RIMP which has been listed
as follows:
• To design a modern method to re-establish dental occlu-
sion using a Reconstructed-based Identical Matrix Point
(RIMP) technique.
• To achieve less computation time and more accurate dur-
ing the re-establishment
• To analyze satisfactory tests of restoration and occlu-
sion at the lab scale, which outperforms conventional
techniques.
The rest of the paper is organized as follows: Section2
discusses the background survey and its limitations. Sec-
tion3 analysis the mathematical modeling for the Recon-
structed-based Identical Matrix Point (RIMP) technique.
Section4 validates the results with simulation analysis.
Section5 concludes the research with perspective outcomes.
2 Literature survey
Veena et al. (2017) introduced two different dental
anomaly detection algorithms. The work provides a new
approach to the detection using hybridized negative trans-
formations of dental caries. The texture classification is
used for segmenting the objects based on the quality of
texture instead of attributes. Grey level Co-occurrence
Matrix (GLCM) is the texture of the panorama image.
The results obtained from both techniques correlate to the
orthopaedic radiologists’ diagnosis.
Kasai etal. (2016) present a system for estimating the
dental plaque adhesion area using a commercial camera
image for oral healthcare via management of the intraoral
environment. They suggestedan estimation procedure for the
volume of dental plaque applied for Plaque Control Record
(PCR) replacement. The relation between the PCR of the
front teeth was examined using the suggested method. The
test results indicate that the proposed method will estimate
the PCRs on all teeth from the front tooth’s details.
Yeesarapat etal. (2014) develop an automatic dental
fluorosis classification system using multi-prototypes
derived from the fuzzy C-means clustering algorithm. The
algorithms’ values are red, green, blue, hue, contrast, and
strength canals. Dental fluorosis requirements are often
specified for each class, depending on the number of pix-
els. In contrast to findings with two experts, they find that
the right pixel classification is about 92%on the data col-
lection and about 90%on the blind dataset.
Deng etal. (2020) suggested a three-stage method for
achieving the required dental final occlusion digitally and
automatically by considering the most common One-Piece
Orthognathic Surgery (OPOS). This approach consists of
three stages: removal points and teeth from two upper and
lower dental models, determination and precise align-
ment of the upper and lower teeth with normal pressure
between midline and canine Molar (M-C-M) according
to these three clinical principles of regions, and without
interrupting the established connection between M-C-Ms.
The approach was quantitatively and qualitatively tested
by 18 sets of dental models.
Seikaly etal. (2019) introduced the Alberta reconstruc-
tive techniques to performing the jaw reconstruction and
occlusion driven process. This process uses the free flap
reconstructive protocols along with Alberta reconstruc-
tive technique to examine the procedures for implementing
jaw reconstruction. The created system is performed with
a cohort study, and the system performs the jaw recon-
struction with the effective, accurate, cost-effective and
aesthetic process.
Seo etal. (2020) suggested a digital occlusion technique
applied in unilateral cleftOrthognathic Surgery (OGS).
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1939
Improving thereconstruction ofdental occlusion using areconstructed‑based identical matrix…
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Single orthodontics and a single surgeon with 2-jaw OGS,
utilizing three-dimensional surgical modelling, were used
to study 30 successive patients diagnosed with unilateral
cleft palate. According to this procedure, visual occlusions
were established with the 30 patients’ images, and accord-
ingly, quantitative (external group) data were gathered.
The findings were matched for two groups. All material
has been reviewed to optimize the procedure and identify
the final guidelines.
However, many conventional methods such as GLCM,
PCR, Fuzzy C Means, OPOS, OGS have been utilized to
calculate occlusal properties for digital dental models. How-
ever, conventional methods failed to focus on better accuracy
and computational time with improved efficiency. This has
been resolved in this research using a Reconstructed-based
Identical Matrix Point (RIMP).
3 RIMP mathematical modeling andanalysis
This paper developed a new approach called the Recon-
structed-based Identical Matrix Point (RIMP) method,
using the dentition’s symmetrical properties. Many simula-
tors can hardly import the external intraoral scanning solid.
The dental/stone casts used an intraoral scanner were used
for virtual models. Intraoral images were generated on the
virtual model using the geometry imaging method by plac-
ing the appropriate characteristics points in two-dimensional
and three-dimensional D models (with and without crowd-
ing) and patients with relatively toothed teeth with intraoral
images. Furthermore, RGB (red–green) colour information
and a grab error can be retrieved. Image-to-geometry, allow-
ing for mapping of colour information’s to 3D virtual den-
tal models in 2D and 3D images. The proposed method is
appropriate for all scanning systems. Colour models can be
obtained from steel and artificial photographic models that
allow colour information and beautiful smile matching. The
initial missing teeth, which may entirely fulfil the patient’s
anatomic specifications, are the most fitting for the partial
strength, in which the initial teeth do not exist. Since the
dental model is bilateral symmetric for most cases, sym-
metrical teeth maybe used to substitute the dental model
with the original teeth. Therefore, it is possible to expecta
customized dental reconstruction. Figure1 displays the pro-
posed solution flow diagram. In the initial step, the point
matching algorithm and distance mapping process has been
processed. For each tooth, the segmentation phase is done,
and the partially edentulous position of the dental model
is calculated by a pair of teeth to the right and left ends,
which are a variation of the mirror transition, rotation, and
transposition to decide the position of the implant accu-
rately. Here, the high-quality camera images are converted
to grayscale images for mathematical computation using
MATLAB image processing toolbox. Besides, the 3D rep-
resentation model has been created and processed based on
mathematical derivations for accurate tooth segmentation
from grayscale images.
3.1 Point matching algorithm
Let
(
aj)
M−1
p=1
and
(
bj)
K−1
q=1
be the 3D dental models of maxillary
and mandibular feature points are observed from camera
images based on grayscale conversion. Here
p
and
q
are the
maxillary models of the teeth, and
K
and
M
are the mandibu-
lar arches. In this case, the two series of points will be paired
with a technique that contrasts points based on the tooth
curves in line with MI’s dental models (Maximum Intercus-
pation). The point match algorithm is based on an advanced
function that utilizes weighted optimization of least squares
model (Chen etal. 2013). The original alignment will con-
sider a process of the energy feature, and a relationship
between the two points (
aj)
and (
bj)
. The energy function is
denoted as
npq
. It measures the rotation matrix
R
and the
relationship, which will reduce a translation vector
v
.
i,
and
j
are vertex points and
u,v
is the translation vectors.
InitializetargetpointsM,p,K,q;
Begin
If
(npq∕(aj−v−Rbj)2)
Matching
(check)∶
M−1
∏
p=1
K−1
∏
q=1
npq
(aj−v−Rbj)2−𝛽
M−1
∏
p=1
K−1
∏
q=1
npq (1)
Where
∏(M−1)
(p=0)npq ≥1, ∀p,∏(M−1)
(q=0)npq ≥1, ∀q,npq ∈(0, 1),∀p,q
elseIf
(npq(aj−v−Rbj)2)
Matching
(check)∶
M−1
∏
p=1
K−1
∏
q=1
npq(aj−v−Rbj)2−𝛽
M−1
∏
p=1
K−1
∏
q=1
npq (2
)
Where
∏(M−1)
(p=0)npq ≤1, ∀p,∏(M−1)
(q=0)npq ≤1, ∀p,npq ∈(0, 1),∀p,q
endif
endbegin
3.2 Algorithm.1. Point matching algorithm
𝛽
is the threshold that determines the objective and rejects
outliers. Where
(
a
j
−v−Rb
j)2
<0, n
pq
=
1
is preferred as
npq
=0
, if all the other parameters are zeros in the
pth
and
qth
rows, for decreasing the objective function. The pair
aj
and
bj
are not viewed as generally identical outliers.
In the point matching model,
M
denoted matrix and
m
denotes the number of iterations addresses the transition
(R, m). It can be conveniently used to evaluate the other
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1940 S.Anil et al.
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after either matrix or transformation is collected. Equa-
tion (1)’s energy function is reduced tooptimizationwith
a weighted leastsquare due to the accompanying matrix.
As shown in Eq. (2), the most challenging aspect of
minimization is finding a successful correspondence
matrix. To demonstrate the point match method, equali-
ties of Eq. (2) and a square matrix set are considered. The
correspondence matrix is a processing matrix with entries
in columns 0 and 1 in line and columns. Suppose the cor-
respondence matrix boundaries are reduced to positive real
constant numbers. The correspondence matrix is doubly
stochastic, with a combination of all positive continuous
rows and columns.
(3)
M
∏
p
=0
npq ≤1, 0 ≤p≤M−1
K
∏
q=0
npq ≤1, 0 ≤q≤K−
1.
To eliminate the outliers, the disadvantages of inequali-
ties must be recognized. The inequalities in (2) can be
updated by adding positive slack values
nMp
and
nKq
and it
is described in Eq. (3).
At the beginning of the Point matching algorithm, the
mapping matrix is unknown and must be correctly deter-
mined based on the dental occlusion criteria. Figure2 indi-
cates the correct situation when the point matching algo-
rithm on such specific points is performed. The collection of
features on the mandibular form’s arc matches the MI’s max-
illary model (maximum Intercuspation). It may be achieved
through estimation as the dental curves are very straight and
symmetricallyrelative to the central incisal midline. The
parameters can define the matrix even without the other
parameters of the whole model being taken into considera-
tion. They may be stopped during the initial configuration.
To avoid the case, the occlusal planes of the teeth are taken
into consideration.
Reconstructed
Image
Input Image
Disarticulation
of Maxillary
and
Mandibular
Model
Create a Dental
Model with
High
Intercuspation
Point Matching Algorithm
and Distance Mapping
Process
Tooth Segmentation
Dental Model
Reconstruction and
Transformation
Estimation using
RIMP
Parally
Edentulous
Posion
Feature Points
Matching
Fig. 1. Overall Architecture of the Proposed Framework
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1941
Improving thereconstruction ofdental occlusion using areconstructed‑based identical matrix…
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3.3 Distance mapping process
In the digital dental model of maxillary and mandibular,
(
cj)
M−1
p=1
and
(
dj)
K−1
q=1
will be two sets of the vertices of
M
and
K
. It assumes that the maxillary model is static. The pro-
cessing takes place according to the mandibular model.
The
Vq
is transformed as follows:
where
V′
q
is denoted as transformed vertex,
O
is indicated as
a rotation origin., the rotation matrix
R
, and
t
is the transla-
tion vector. When the two simulated dental models do not
differ, the maximization of the interface region is equivalent
to the maximization of the number of
D
vertices of the inter-
face.
uj
and
upq
is the pair of vertex points.
s
→
surface.
However, when the models are in the
MI
, not every
vertex of
vq
makes contact. Such areas of interaction are
much difficult to forecast correctly. Therefore, it models
the distance between the lower and upper teeth.
upq
is the closest point to
vq
and it is given as follows:
(4)
V�
q
(R,T)=R
(
Vq−O
)
+O+tv
,
(5)
s
=1
k
K−1
∏
q=0
(upq −vq)2
,
(6)
u
pq
=arg max
u∈(u
j
)
(u−V
q
).
Equation (6) has been described to measure the
distance between the lower and upper teeth. Where
pq∈(0,1, …,N−1)
,
N
indicates the amount of data. It is
that chances of achieving contact by minimizing distance
instead of directly maximizing
s
the interaction region.
The rotation origin
O
is suggested as follows,
The rotation origin comprises non-linear circumstances
that are linear by the approximation of small angles. As
the two dental models occlude, the improvement required
for the dental occlusion is gradually decreased. Therefore,
the errors produced by this estimation are less significant.
In Fig.3a, the upper and lower surfaces of the teeth
are on one side, similar to the other. The core of rota-
tion would be positioned closer by intuitively to enable
the lower tooth surface to be shifted closer to the teeth’
top. Denture rotation is known as intra-alveolar dent
displacement of the tooth around the longitudinal axis.
If your tooth is just slightly rotated, dental bonding will
fix it. It includes the use of a composite resin substance
of tooth colour. The composite is formed, hardened and
polished after it has been applied to the affected teeth.
Several factors such as spatial inadequacy, the irregular
sequence of the tooth eruption, and unwanted forces of the
tongue or lipped or the above combination are involved
in the rotation. Biomechanical concepts require the use
of one or more forces to correct rotation. Dynamic rotat-
ing adjustments can make it easier for the lower and top
(7)
O=arg min
v∈
(
v
j)(min
u∈
(
u
j)(p−q)).
Fig. 2 The dental models are accurately articulated when the feature points are matched from camera images
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1942 S.Anil et al.
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Fig. 3 a Upper and lower teeth at the front teeth are similar to the back teeth. A constraint is a half-space. bThe edge cannot be transformed in
the other half-space, such as the upper and lower teeth cannot be overlapped
Fig. 4 a Complete mandibular model. b Part of the mandibular model selected. c Base of triangular mesh. d Cloud Point as observed from
MATLAB image processing toolbox
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Improving thereconstruction ofdental occlusion using areconstructed‑based identical matrix…
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tooth surfaces to perfuse better as the tooth surfaces are
different. The most significant move of automated den-
tal occlusion is the application of collision constraints.
It builds a 3D dental data collection collision avoidance
system. Collision avoidance is known as restrictions and
is implemented into the optimization system. Figure3b
indicates how a constraint is applied from camera images.
3.4 Data processing
The Digital Dental System is shown in Fig.4. Figure4a dis-
plays a full, 3D laser surface scanner, a complete mandibular
model with a right lateral incisor that has been synthetically
missed. The aspect of the entire model used in the proposed
approach shows in Fig.4b. Figure4c shows the triangular
mesh region around the missing tooth. Figure4d displays
the point cloud of the model’s surface formed by the trian-
gular mesh vertices. The findings have been retained in the
form of stereolithography, which reveals a triangular mesh
modelling system consisting of facets and vertices for the
3D framework of each dental model Fig.4c. Every dimen-
sion has a popular basic external vector. The recognized
neighboring facets of each vertex are discussed. Across the
surface, the vertices compensate for a cloud label Fig.4d.
3.5 Dental segmentation
As shown in Fig.5a, a partially edentulous teeth pattern
will extract from the camera image grey value on each
pixel from the reference surface representing the height of
a specimen point on the tooth model. The black curve of
Fig.5b is a polynomial of the fourth order plated in the
dental arch curve. The dental arch curve is followed by a set
of candidates based on the dental arch’s edge. The dental
arch named the cross-points from the spokeintersection. A
direct spokes sequence is created by a point match algorithm
(Fig.5b). This raw sequence has been used to accurately
segmentation both neighboring teeth by a spoke, and it is
found accurately at the right-angle interstices. Missing or
malocclusion of the teeth can be caused by many causes,
including naturally weak bite, trauma, dental care including
fillings, crowns, bridges and orthodontic treatment, without
considering how the teeth connect properly, i.e. a healthy
bite. The crowns, bridges and fillings that do not fit consist-
ently up and down and about half of the patients treated
with symptoms undergo orthodontic therapy. Therefore, it
involves segmentation and processing throughout the tooth’s
surface to be sliced, resampled, and smoothed to create a
three-dimensional mesh. It is expected to be very sensitive
Fig. 5 Dental Image Segmentation a Image selection. b Raw Image. c Edentulous space. d Stretched Sequence
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1944 S.Anil et al.
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to triangle count and mesh resolution with very low resolu-
tions. Still, higher resolutions can be expected when surfaces
and tooth sizes (e.g. predicted dental area) converge.
Nevertheless, the limit between the partially edentulate
space has been analyzed when a whole dental model is pro-
duced, and many spokes are correctly placed in the partially
edentulate position. The two points articulated (Fig.5c) are
partially constant and numbered perpendicular to the curve
from the beginning to end lines. Any teeth can miss a par-
tially edentulous position as long as it continues.
Digital dental interface distance image in Fig.5a. The
sequence of raw spokes is shown in Fig.5b. Many spokes
are in part edentulous position by mistake, while others cor-
rectly indicate each tooth. Figure5c indicates the partially
edentulous location of the two articulated spokes (red). Fig-
ure5d demonstrates the polished spokes sequence (blueand
red), which separates the tooth correctly and the partially
edentulous position.
Finally, the raw sequence is mixed with partly edentulous
data to provide a refined expression sequence. It initially
filters spokes, all of which are false, in a partially edentulous
location. It separates the spokes from the beginning to the
end of their arch lines. And the two spokes are connected
to the sequence, and the arch lines connect the spokes. The
polished spokesequence is obtained (Fig.5d), which cor-
rectly differentiates the developing tooth from the partial
edentulous position. The dental arches are the two arches
of the teeth, one on each jaw, which form the dentition. The
upper (magical) arches of the dental arches are consider-
ably wider in humans and many other species than the lower
(mandible or lower) arches such that the teeth on both the
front and sides of the maxilla overlap slightly in the top
of the maxilla in a normal condition (lower jaw). Hence,
the masks’ approach and dentals when the mouth closes,
known as occlusion, determine the occlusal relationship of
opposite teeth and is maloccluded if facial or dental growth
is incomplete.
3.6 Reconstruction‑based digital dental occlusion
ofthepartially edentulous dentition using
RIMP
The dental model’s reconstruction is explicitly planned to fill
the edentulous gap of the symmetrical teeth on the other side
of the jaw. Every point of the transformed surface is modi-
fied in the same way. This information contributes to the
process of reconstruction of the tooth model. The complete
dentition dental model has to be computed.
Let
Cqand Dp
be the points of cloud for dental model.
(C
q
)1
≤
q
≤
U1
completely to the right or left of the dental model
which is the coordinates of a 3D set of vertices and the
(D
p
)1
≤
p
≤
V1
on the other half, the dental model is the coordi-
nates of vertices. The cloud points (
Cq)
is symmetric with
(
Dp)
in the potential ideal arrangement of completely mir-
rored points. With this intense, rigid transformation
𝛿
, it may
compare the two types of
R3→R3
performed on (
Dp)
.
The first stage of rigid transformation consists of a mirror
transformation that is performed on (
Dp)
as
𝛿1∶R3
→
R3
. The
transformation of a mirror is parameterized by a matrix of
3×3
reflection transformations M. (
Dp)
Coordinates are indi-
cated by
(Z
p
)1
≤
p
≤
V1
. Here
ZpistheimageofDp
by the effect of
transformation
𝛿1
, where
U
is the transformation matrix.
The second step is to introduce a transition of rotation and
transmission
𝛿2∶R3
→
R3
.
(Z
p
)1≤p≤V1
is transformed to

(
Z
p)
.
𝛿2
parameterizes
𝜃
, which is given as follows with
3×3
rota-
tion matrix R and a three-translation vector t:
where
𝜃
is the parameter for point registration, and p is the
vertex point. Point registration is an optimal alignment
between two set of points.
Zp,𝜃
may be transformed to
Cp
. It
demonstrates that one part of the
Zp
the dental model can be
transformed into another part
Cp
with the rigid
𝛿
transforma-
tion. It refers to their subsets,
T
denotes the time. A crowded
mouth with inadequate space to organize all teeth in one line
often leads to traumatic occlusion or illness. Another impor-
tant factor is the correct alignment of the upper and lower
jaw; if it is not properly closed while chewing, several other
oral disorders can occur later in life. The risks for periodon-
tal disease increase significantly if the traumatic occlusion
is not treated in good time. It is because the teeth are not
straight or aligned. The biting pressure of other teeth makes
them loose and ultimately sick. Orthognathic is the term
used to define the consistency of the upper and lower align-
ment of the jaw. This form of surgery aims not to straighten
the teeth and correct the bone connection.
(
C
�
u
)
1≤u≤U2
is a tooth in (
Cq)
,
(
D
�
v
)
1
≤
v
≤
V2
is in (
Dp)
and
symmetrical tooth of (
D�
p)
.
(D�
v),Cp,Dq
are denoted as dental
models and
(C�
u)
is a symmetrical tooth. It can be described as
(8)
(
Zp)=𝛿1∕
(
Dp,U
)
;where
(
Zp
)
1>p>V1
(Zp)=𝛿1
(
Dp,U
)
;where
(
Zp
)
1≤p≤V1
},
(9)
𝛿1(
D
p
,U
)
=UD
p.
(10)

(
Z
p
)=𝛿
2(
Z
p
,𝜃
),
(10)
𝛿
2
(
Zp,𝜃
)
=RZp+t,𝜃=(R,T)wherep >0
𝛿2(
Z
p
,𝜃
)
=Rc −t,𝜃wherep <0
},
(11)
𝛿2(
Z
p
,𝜃
)
=Rc −t,𝜃wherep <
0,
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1945
Improving thereconstruction ofdental occlusion using areconstructed‑based identical matrix…
1 3
To the same rigid
𝛿
transformation as shown in (5) and (6)
by
(U,R,t)
variables and it has:
where
Z
�
q
∈

(Z
p)
.
Z′
q
is a tooth in

(
Z
p)
. Where
(
Z
�
v
)
1≤v≤V2
is
the transition
𝛿
of the tooth
(
Z
�
v)
. It is a dental in

(
Z
p)
. In the
form of

(
Z
p)
matches (
Cq
),(Z
�
v)
and it matches (
C�
q)
.

(
Z
p)
is
denoted as a symmetrical tooth.
The same applies to a different
(
C
��
1
)
1
≤
l
≤
U3
in (
Cq)
tooth and
symmetrical tooth
(
X
��
g
)1
≤
g
≤
V3
in (
Xq)
:
where
(
Z
��
g)
1
≤
g
≤
V3
is the tooth (
Z��
g)
parameterized by
(U,R,t)
after transformation
𝛿
.
(C��l)
,
(
C
��l
),(D
��g
),(D
��v
),(Z
��
g)
is represented as a tooth.
According to (13) and (14), it is necessary to transform
𝛿
from
(U,R,t)
,
Z′
q
to match
C′
q
and
D′′
g
to
C′′
l
using the same
transformation. If
C′′
l
is missing, the partially edentulous space
requires to be filled with its symmetrical Z
′′
g
tooth and the
rigid transformation with another pair of teeth
C′
q
and
Z′
q
can
be estimated as long as it exists. It assumes that most patients’
teeth are symmetrical and can be controlled with the suggested
approach.
3.7 Estimation transformation withpartially
edentulous positions
At this point, the transition is determined for a set of symmetri-
cal teeth. In one dental model
Hq(q=1, ……., L)
,
L
indicates
the position length and there can be many partially edentulous
positions. On the one hand, all the partially edentulous posi-
tions may be filled with the same transition from the previous
topic with their symmetrical equivalents. However, it suggests
estimating the transformation for any partially edentulous
Hq
the position with the teeth close to
Hq
to improve the exact-
ness of the process. To illustrate the calculation, it proceeds to
use the dental model seen in Fig.3b. There is only one partly
edentulous position in this case, which is not ambiguous by
H
.
First, itwill evaluate the remaining teeth pair (
C�
p)
and
(
D�
q)
. On the same side of
H
, a continuous object (
C�
p)
with
one or several teeth can be chosen, whether its symmetrical
equivalent on the other side occurs. If (
C�
p)
, and it will be
perfect. The symmetric tooth on the left of the first premolar
is designated as (
D
�
q)
.
(12)
(
C
�
u)∈Cp
(
D�
v
)∈D
q.
(13)
Z�
q
=URD
�
v
+t
,
(14)
(
C
��
l)∈Cq
(
D��
g)∈Dp
(
Z��
g)=UR(D��
v)+
t
(
Z��
g
)
∈

(Zp),
A (
D�
v)
mirror transition would be able to turn the sym-
metric (
U�
v)
tooth on the same side. The mirrored (
Z�
v)
tooth
can be measured as follows:
where
U
=
⎛
⎜
⎜
⎝
−100
0 10
0 01
⎞
⎟
⎟
⎠
The crown of
(Z�
v)
and
(D�
q)
should be chosen; these are
all 3D points identified respectively as design points and
observation points. These three points are classified as the
initial concept points. The RIMP contrasts two different
types, but not the same, and their points are distributed
randomly.
The curve angle is not a spendingtime separating the
curve vertices that are difficult as the free curve, however
group the points in the spectrum along the Z-coordinate
and choose the upper vertices
1∕V
for the teeth and
1∕V
for the upper
1∕V
lower vertices. The top
1∕V
vertices
(
Z
′
v)
are chosen. Each set has different points. There is an
approximation of their 3D coordinates. The
𝜃
processing
parameters can be tested using a RIMP. There are two
main parts of a tooth – the crown and the root. The part
of a tooth that can be seen in the mouth is the clinical
curve, while by definition; the part that is not apparent is
the clinical base. Due to its shape and form of hard tooth
tissue covering the external surface, the crown and root
are anatomically distinguishable. The permanent teeth are
32 teeth in each arch, and 16 in each arch. Eight teeth
consist of two incisors, one canine, another two premo-
lars, and three molars in each quadrant. These teeth are
called numbers, 1 (centrally incised) to 8 (third molar or
"Weisheit" tooth).
In (16),
𝛽pq
is the regressive probability.
C�
p
−
𝛿2
is the
squared Mahalanobis distance. The 3D coordinates for the
transformed model points are defined as follows in the
𝛿2
(
𝜗�p
,
𝜃d)
iteration step:
R
and
t
can be given to initialize the identity matrix and zero
vector. With the current Registration parameter
𝜃d
the pos-
terior
𝛽pq
is evaluated in E-step. A reference point or outlier
class can be allocated to every observed point.
In Eq. (18)
Wq=p
specifies that
C′
p
matches
x′
p
and
W
q=
V2
V+1
specifies that
C′
p
is an outlier. The reflected
(Z�
v)
(15)
(
Z
�
v
)=
U
(
D
�
q
),
(16)
𝜃
v+1=argmin
𝜃1∕2
U2∕V
∏
q=1
V2∕V
∏
p=1
𝛽v
pq(C�
p−𝛿2(𝜗�
q𝜃d)
.
(17)
𝛿2(
𝜗
�
p
,𝜃
d)
=R
c
𝜎
�
p
+t
c,
(18)
W
q=argmax
p
𝛽
d
qp
.
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1946 S.Anil et al.
1 3
tooth may be transformed into the
(
D
�
q)
source tooth, as
seen in Fig.6c, with the RIMP, and the recording param-
eters
𝛽
are obtained in conjunction with transformation
𝜃
.
Themeshes are not entirely matched for two reasons. First,
there are various types of corrections added to each tooth.
Furthermore, the spokes that divide the dental model into
segments with an interstice resistance angle in opposite
directions differ in the left and right segmental limits of
each mesh. Such considerations may explain why only the
crowns are transformed.
The process with a pair of teeth is shown in Fig.6. Fig-
ure6b, where the right-side incisor is removed, reveals
a dental sequence that has been partly edentulous. The
source tooth and the symmetric tooth is calculated. Fig-
ure6a indicates the selection of the first right premolar
and the first left molar. Both teeth are symmetrical and
appeared on both ends. Figure6b transfers the balanced
tooth of the X–Y–Z plane over the mirrored tooth. The
mirrored tooth has been transformed to the original tooth
in Fig.6c. The parameters that characterize the transfor-
mation have been assessed. It is easier to establish occlu-
sion as a reference of one entity to another in the sense of
a complex link between mandibular to maxillary during
function while exploring various complete dental sys-
tem occlusal. Two individual entities that make up the
full dental occlusion are bilateral balanced occlusion and
unequalled occlusion. When simultaneous interactions
are achieved, both centrally and eccentrically, bilateral
equilibrate occlusion is observed. The affected areas are
highlighted by lines. In this method, the curvature of the
dental regions has been reconstructed based on distance
mapping to minimize the computation time, and an itera-
tive point matching approach is used for accurate reestab-
lishment. Satisfactory tests of restoration and occlusion
have been analyzed at the lab scale, which has been dis-
cussed as follows.
4 Results anddiscussion
This section discusses the effectiveness of the introduced
RIMP technique based dental occlusion process. In our lab-
scale experimental analysis, 70 images have been analyzed
with 30 consecutive patients based on high-quality camera
images. Among 70 images we have utilized 30 planar view
images for experimental analysis. Further, the scanning with
parts and a completely smooth maxilla were superimposed
on each other to validate data. Here, the high-quality camera
images are converted to grayscale images for mathematical
computation using MATLAB image processing toolbox. The
patient information is gathered from orthodontic treatment
and the 2-jaw surgeon process. The dental occlusion infor-
mation is collected, and the above-discussed procedures are
applied to perform the dental reconstruction process using
the matrix laboratory preprocessing tool for the 30 planar
view images.
Fig. 6 Estimation Transformation a Pair of Training. b Mirrored Image. c Matched Image
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1947
Improving thereconstruction ofdental occlusion using areconstructed‑based identical matrix…
1 3
4.1 Accuracy evaluation
In certain aspects of dental treatment, accuracy is a signifi-
cant problem. The reconstruction of the dental hard tissue
needs an accurate prosthesis to restore the existing structure.
In particular, fixed partial teeth and full prosthesis are essen-
tial if devices like teeth or implants can be modified accu-
rately. The accuracy of a test is the capacity to reconstruct
theteeth correctly. To measure the accuracy of a method,
the proportion of true positive, and true negative in all the
evaluated cases should be calculated. Based on the Eq. (19),
if the False positive value is high it shows decreased level
in the graphical structure. Further, If the True positive high
it shows increased range in the graphical structure. This can
be stated as in Eq. (19) (Alsiddiky etal. 2020):
This proposed Reconstructed-based Identical Matrix
Point (RIMP) technique achieves better accuracy in the
reconstructed dental model (83.51%) and partially edentu-
lous dental model (91.50%) when compared to the other
existing methods such as GLCM, PCR, Fuzzy C Means,
OPOS, and OGS that mentioned in the literature survey
section. Figure7a shows the reconstructed dental model’s
accuracy, and Fig.7b shows the partially edentulous dental
model’s accuracy.
4.2 Computational time evaluation
In the manual labelling step, time-consuming manual work
is required. Furthermore, the standard dental model based
(19)
Acccuracy
=
TruePositive
+
TrueNegative
TruePositive
+
TrueNegative
+
FalsePositive
+
FalseNegative
.
on manually appointed characteristics, determined from a
small number of dental shapes, is challenging to adapt to
individuals’ morphology. This proposed Reconstructed-
based Identical Matrix Point (RIMP) technique has less
computational time in reconstructed dental (30 s) and
partially edentulous dental models (19s) than the other
existing methods such as GLCM, PCR, Fuzzy C Means,
OPOS, OGS. Figure8a shows the computational time of the
reconstructed dental model, and Fig.8b shows the compu-
tational time of the partially edentulous dental model. The
two front teeth should be square rather than rectangular.
Teeth should be higher than wide and should be rectangular.
The two teeth (called lateral incisors) on both sides should
be smaller and the width of the two front teeth roughly 80%.
Small or ’peg-formed’ side incisors are a common concern.
The two sides should be half a millimetre higher than the
two sides. The canine teeth shouldn’t be too sharp because
people don’t like vampires! The dog’s teeth should be the
same as the two front teeth.
4.3 Mean andstandard deviation evaluation
The most accurate results of clinical alignment studies on
the maxillary scale are the 1stright molar crypt (A), the
1stleft molar tooth crypt (B), the 1stmedian tooth (C).The
coordinates of this position are reported to demonstrate the
simple truth. The coordinates of each symbol are contrasting
until the models come back from some initial positions. Each
of these models is reconstructed. It is described in Table1
Fig. 7 a Accuracy of the reconstructed dental model, b Accuracy of the partially edentulous dental model
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1948 S.Anil et al.
1 3
Finally, this strategy has a specific ultimate objective.
The preceding approaches are built to rework the tooth
for chewing. The technique will measure the artificial
tooth or repaired tooth crown in actual usage. However,
the goal is to restore dental occlusion. No physical res-
toration of missing teeth is possible in real surgery. The
partially edentulous mandibula or maxilla is positioned
without filling according to the occlusion plan to MI
(Maximum Intercuspation) location. This approach is
distinct from other approaches to dental occlusion. The
previous methods of occlusion will only match the man-
dible and the maxillary with full teeth. With the proposed
approach, it will effectively match the partly edentulous
dental model with MI. The correctness or efficacy of your
dental occlusion depends on if your face is symmetrical or
asymmetrical and whether your facial bone structure has
discrepancies or malformations that are the primary cause
of your malocclusion. If tooth wear is absent, an excessive
eruption could happen in patients due to a dent alveolar
development and an increase in face height in turn. One
should open the mouth between the edges of the lower
and upper incisors. The full depth is measured. Dentists
must justify the mandible deviation upon opening or shut-
ting of the jaw while conducting an extraoral examination.
The typical error of about 0:1mm in the recently acquired
tooth analysis can be compared to Table2.
4.4 Efficiency evaluation
Some existing results relate to the excellent compatibility of
the dental model reconstructed. The suggested RIMP would
Fig. 8 a Computational time of reconstructed dental model. b Computational time of partially edentulous dental model.
Table 1 Translational variations in the analysis of alignment with
biological structures that are partially edentulous and corresponding
reconstructed model
Marker Axis Reconstructed teeth Partially edentulous
teeth
Mean (mm) Standard
deviation
Mean(mm) Standard
deviation
A X −0.234 0.235 1.782 0.846
Y −0.256 0.263 1.672 0.673
Z −0.245 0.282 −2.342 0.762
B X −0.134 0.167 0.645 0.875
Y −0.145 0.178 0.428 1.987
Z −0.176 0.193 0.532 0.349
CX 0.054 0.183 −0.234 0.241
Y −0.145 0.172 −0.342 0.432
Z 0.017 0.195 −0.453 0.538
Table 2 Translation changes in the analysis by the original dental
models, which are partially edentulous and accurately reconstructed
Marker Axis Reconstructed teeth Partially edentulous teeth
Mean (mm) Standard
Devia-
tion
Mean(mm) Standard
deviation
A X −0.0035 0.0038 0.2452 0.0034
Y −0.0048 0.0026 0.3523 0.0053
Z −0.0231 0.0087 0.5638 0.0027
B X −0.0452 0.0051 0.9327 0.0072
Y −0.0342 0.0047 0.2455 0.0025
Z −0.0267 0.0038 0.6234 0.0043
C X −0.0145 0.0023 0.3762 0.0032
Y −0.0137 0.0072 0.3421 0.0056
Z −0.0321 0.0082 0.4422 0.0078
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1949
Improving thereconstruction ofdental occlusion using areconstructed‑based identical matrix…
1 3
substantially improve occlusion efficiency and implement
the appropriate operating strategy for partially edentulous
versions. This approach allows the maxillary and mandibular
models to be expressed efficiently with greater efficiency.
There is a small degree of variation is due to non region of
interest (ROI) unwanted pixels in this method among the
digitally articulated occlusion.
The proposed Reconstructed-based Identical Matrix
Point (RIMP) technique achieves better efficiency in the
reconstructed dental model (87.50%) compared to the
other existing methods such as GLCM, PCR, and Fuzzy
C Means, OPOS, OGS. Figure9 shows the efficiency of
the reconstructed dental model.
In the asymmetric circumstance, the virtual teeth gen-
eration from statistical modeling of dentures is proposed to
fill a partially edentulous region; alignment results could
be obtained using the RIMP technique.
5 Conclusion
This paper introduces an innovative Reconstructed-based
Identical Matrix Point (RIMP), enabling the partially
edentulous model to be appropriately replanted by virtu-
ally implanting the symmetric component into the some-
what endless space. The symmetric counterpart replaces
the missing teeth. The transition is determined from a sym-
metrical pair of teeth. The digitally restored versions are
capable of repairing optical dental occlusion. Satisfactory
restoration and occlusion tests for both synthetic and real,
partially edentulous tooth models have been demonstrated.
Here, the curvature of the dental regions has been recon-
structed based on distance mapping to minimize the com-
putation time, and an iterative point matching approach
is used for accurate reestablishment. Based on the above
results and discussion, the proposed RIMP outperforms
overall accuracy (91.50%) and efficiency (87.50%) in com-
parison with conventional methods such as GLCM, PCR,
Fuzzy C Means, OPOS, and OGS.
Acknowledgements The authors are grateful to the deanship of Scien-
tific Research, King Saud University for funding through Vice Dean-
ship of Scientific Research Chairs.
Funding Open access funding provided by the Qatar National Library.
Data Availability None.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long
as you give appropriate credit to the original author(s) and the source,
provide a link to the Creative Commons licence, and indicate if changes
were made. The images or other third party material in this article are
included in the article’s Creative Commons licence, unless indicated
otherwise in a credit line to the material. If material is not included in
the article’s Creative Commons licence and your intended use is not
permitted by statutory regulation or exceeds the permitted use, you will
need to obtain permission directly from the copyright holder. To view a
copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4. 0/.
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