Customised 3D Tooth Modeling by Minimally Invasive Imaging

Modalities

Sandro Barone, Alessandro Paoli and Armando Viviano Razionale

Department of Civil and Industrial Engineering, University of Pisa, Largo Lucio Lazzarino 1, 56126, Pisa, Italy

Keywords: Customised Tooth Reconstruction, Panoramic Radiograph, Discrete Radon Transform, Digital Cast.

Abstract: Dental panoramic tomography represents a standard imaging modality in dentistry since it provides a

convenient and inexpensive method to visualize anatomic structures and pathologic conditions with low

radiation doses. However, this technique does not provide comprehensive 3D geometries of dental shapes

which are conventionally demanded to computerised tomography (CT) techniques. In this paper, a tooth

reconstruction process is presented by integrating patient-specific information with general dental templates.

A 2D panoramic radiograph and the digitised patient plaster cast are used to customise both shape and

orientation of teeth templates thus allowing a consistent 3D tooth reconstruction with minimally invasive

imaging modalities. The proposed methodology does not make any assumption about the tomographic

device used to collect the panoramic radiograph.

1 INTRODUCTION

Orthodontics is the branch of dentistry concerned

with the study and treatment of irregular bites and

deals with the practice of manipulating patient

dentition in order to provide better functionalities

and appearances.

Detection and correction of malocclusion

problems caused by teeth irregularities and/or

disproportionate jaw relationships represent the most

critical aspects within an orthodontic diagnosis and

treatment planning. The most common

methodologies for non-surgical orthodontic

treatments are based on the use of fixed appliances

(dental brackets) or removable appliances (clear

aligners) (Kuncio et al., 2007). In clinical practice,

the conventional approach to orthodontic diagnoses

and treatment planning processes relies on the use of

plaster models of the patient’s mouth which are

manually analyzed and modified by clinicians in

order to simulate and plan corrective interventions.

These procedures however require labour intensive

and time consuming efforts which are mainly

restricted to highly experienced technicians. Recent

progresses in three-dimensional surface scanning

devices as well as CAD (Computer Aided

Design)/CAM (Computer Aided Manufacturing)

technologies have made feasible the complete

planning process within virtual environments and its

accurate transfer to the clinical field. In particular,

orthodontic alignment procedures greatly benefit

from the combined use of CAD/CAM

methodologies which are used to produce custom

tight-fitting devices worn by the patients (Boyd,

2007). In this context, the accurate and automatic

reconstruction of individual tooth shapes obtained

from digital 3D dental models is the key issue for

planning customized treatment processes. Optical

scanners may be used to digitize plaster models thus

providing geometric representations of tooth crowns.

However, even if both clear aligners and brackets

accomplish the treatment plan only by acting onto

the tooth crown surfaces, a correct orthodontic

treatment should also take into account tooth roots in

terms of position, shape and volume. In particular,

position and volume of dental roots may cause

dehiscence, gingival recession as well as root and

bone resorption when teeth undergo movements

during therapy. Cone beam computed tomography

(CBCT) can provide comprehensive 3D tooth

geometries. However, concerns about radiation

doses absorbed by patients are raised. For this

reason, the use of computed tomography as a routine

in orthodontic dentistry is still a matter of

discussion. Even if CBCT has greatly reduced the

dose of absorbed x-rays, compared to traditional

computed tomography (CT), it still produces a

greater x-ray dose than a panoramic radiograph

Barone S., Paoli A. and Razionale A..

Customised 3D Tooth Modeling by Minimally Invasive Imaging Modalities.

DOI: 10.5220/0004912400700075

In Proceedings of the International Conference on Bioimaging (BIOIMAGING-2014), pages 70-75

ISBN: 978-989-758-014-7

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

(PAN).

2-D panoramic radiographs are a routine

approach in the field of dentistry since they

represent an important source of information. In

particular, they are able to inexpensively record the

entire maxillomandibular region on a single image

with low radiation exposure for the patient.

However, they are also characterised by several

limitations such as: lack of any 3D information,

magnification factors which strongly vary within the

image thus causing distortions, patient positioning

which is very critical with regard to both sharpness

and distortions. As a result, not only 3D

measurements are impaired, but also reliable 2D

dimensions cannot be retrieved.

The present paper is aimed at investigating the

possibility to recover 3D geometry of individual

teeth by customising general templates over patient-

specific dental anatomy. Information about patient

anatomy is obtained by integrating the optical

acquisition of plaster casts with 2D panoramic

radiographs. Even if the reconstruction of patient-

specific 3D dental information from 2D radiographs

and casts represents a challenging issue, very few

attempts have been made up to now within the

scientific community (Pei et al., 2012, Mazzotta et

al., 2013). Moreover, these studies greatly rely on

the knowledge of the specific tomographic device

used to acquire the PAN image. The present study is

focused on the formulation of a general solution

which could infer tooth roots shape without any

assumption on the specific hardware as well as

parameters used to collect patient data anatomy.

2 MATERIALS AND METHODS

In this paper, whole 3D teeth shapes are

reconstructed by integrating template models with

3D crowns data deriving from the optical acquisition

of plaster casts and 2D data deriving from PAN

radiographic images.

An optical scanner based on a structured light

stereo vision approach has been used to reconstruct

both template dental models and patient’s dental

casts.

Panoramic radiographs have been captured by

using a Planmeca ProMax unit (Planmeca Oy,

Helsinki Finland); whose data are stored and

processed in DICOM format.

2.1 3D Data Acquisition System

The optical scanner (Figure 1) is composed of a

monochrome digital CCD camera (1280 × 960

pixels) and a multimedia white light DLP projector

(1024 × 768 pixels) which are used as active devices

for a stereo triangulation process. In this paper, a

multi-temporal Gray Code Phase Shift Profilometry

(GCPSP) method is used for the 3D shape recovery

through the projection of a sequence of black and

white vertical fringes whose period is progressively

halved (Barone et al., 2013). The methodology is

able to provide n

= l

× l

measured points (where l

is the horizontal resolution of the projector while l

is the vertical resolution of the camera) with a spatial

resolution of 0.1 mm and an overall accuracy of 0.01

mm.

Figure 1: Optical scanner during the acquisition process of

a tooth template.

The optical devices are integrated with two

mechanical turntables (Figure 1) which allow the

automatic merging of different measurements

collected from various directions conveniently

selected.

2.2 Input Data

The methodology requires three different input data:

1) general dental CAD templates, 2) dental crowns

shape and 3) a PAN image. Crowns shape and PAN

image are patient-specific data while teeth templates

can be obtained from existing libraries.

2.2.1 Dental CAD Templates

Teeth template models are composed of complete

teeth crowns and roots and are placed in adequately

shaped holes within transparent plastic soft tissue

reproduction (Figure 2). Teeth can be easily

removed from their housing in order to allow full

reconstructions through the 3D scanner without

optical occlusions.

Customised3DToothModelingbyMinimallyInvasiveImagingModalities

Figure 2: Example of superior and inferior dental arch

templates.

2.2.2 Patient Crowns Reconstruction

The patient dental crowns geometry can be acquired

by scanning the plaster cast. Figure 3a shows the

final digital reproduction of the patient tooth crowns

with surrounding gingival tissue (digital mouth

model) as obtained by merging twelve acquisitions

of the superior plaster cast captured by different

views. Tooth crown regions are segmented and

disconnected from the oral soft tissue by exploiting

the curvature of the digital mouth model. This model

contains ridges and margin lines, which highlight the

boundaries between different teeth, and between

teeth and soft tissue. Regions with abrupt shape

variations can be outlined by using curvature

information (Barone et al., 2013). Segmented crown

shapes are finally closed by using computer-based

filling tools (Figure 3b).

(a)

(b)

Figure 3: (a) Reconstruction of the superior plaster cast as

obtained by the optical scanner and (b) segmented patient

crowns geometries.

2.2.3 Panoramic Radiograph

Dental panoramic systems provide comprehensive

and detailed views of the patient maxillo-mandibular

region by reproducing both dental arches on a single

image film (Figure 4).

A panoramic radiograph is acquired by

simultaneously rotating the x-ray tube and the film

around a single point or axis (rotation centre). This

process, which is known as tomography, allows the

sharp imaging of the body regions disposed within a

3D horseshoe shaped volume (focal trough or image

layer) while blurring superimposed structures from

other layers. The rotation centre changes as the film

and x-ray tube are rotated around the patient’s head.

Location and number of rotation centres influence

both size and shape of the focal through which is

therefore designed by manufacturers in order to

accommodate the average jaw.

2.3 Methodology

The proposed methodology is based on scaling the

tooth CAD template models accordingly to the

information included within the patient segmented

tooth crowns shape and the PAN image.

Segmented crown models are used to determine

the axis of each patient tooth. Teeth templates are

then linearly scaled by using non-uniform scale

factors along three different dimensions (Figure 5).

In particular, the tooth width (taken along the

mesiodistal line) and the tooth depth (taken along

the vestibulo-lingual direction) values are directly

determined from the patient crown geometries. The

tooth height (taken along the vertical direction of the

panoramic radiograph) is rather estimated by using

the PAN image.

Figure 4: Panoramic (PAN) radiograph.

The height estimation process, which represents the

core of the proposed method, is based on the

reconstruction of a synthetic PAN image from the

3D patient crowns geometries. A panoramic

radiograph essentially represents the sum of x-ray

attenuation along each ray transmitted from the

BIOIMAGING2014-InternationalConferenceonBioimaging

Figure 5: Tooth dimensions used to scale CAD templates.

source to the film (Tohnak et al., 2006). The

attenuation is due to the x-ray absorption by tissues

along the ray. For this reason, it is possible to

emulate a panoramic radiograph by taking 2D

projections through a data volume. In this paper, the

Discrete Radon Transform (DRT) is used to

calculate finite pixel intensity sums along rays

normal to a curve which approximate the medial

axis of the crowns arch.

The whole methodology can be summarized in

the following steps:

 Uniform scaling of the complete dental

template arch by using the patient digitised

cast (Figure 6a);

 Alignment of each tooth template on the

corresponding patient tooth crown geometry

in order to determine the orientation and

position with respect to the bone structure;

 Non-uniform scaling by using the tooth width

and depth values (Figure 6b);

 Tooth height estimation from the PAN image

by simulating the panoramic radiograph

process through the Discrete Radon

Transform applied on the reconstructed patient

crowns model.

The first three steps are quite straightforward and

can be accomplished by using any CAD software.

The last step is fully detailed in the following

section.

2.3.1 Tooth Height Estimation

The 3D patient crowns model must be spatially

oriented, by a rigid motion, in order to make its

projection consistent with the corresponding crowns

region in the PAN radiograph.

A set of n corresponding markers [P

PAN

 (x

PAN

, y

PAN

), P

 (x

, y

, z

)] is interactively selected on

crown regions of both PAN image and segmented

crowns model. A rigid motion, applied to the 3D

model and described by a rotation matrix (R) and a

translation vector (T), is then determined by

minimising an objective function defined as:

(,)

AN cr

fRT z z



 



(1)

(a)

(b)

Figure 6: (a) Uniform scaling of the complete dental

template arch and (b) two examples of non-uniform tooth

scaling by using width and depth values.

This transformation guarantees the alignment

between the 3D patient crowns model and the

radiograph along the z-direction (Figure 7). A

further transformation is then required in order to

project the 3D model onto the panoramic image.

This process is accomplished by computing multiple

parallel-beam projections, from different angles,

using the DRT. In particular, a 2D image is firstly

created by projecting the crowns model onto the X

plane (Figure 8). A fourth order polynomial

curve (



) is then determined by interpolating the

projection of the selected P

 (x

, y

) points.

The 3D model is vertically sliced with the same

vertical resolution of the PAN image. For each

horizontal slice, crown contours are projected along

the direction normal to



in correspondence of each

curve point by using the DRT (Figure 8). The curve

point sampling (s

) is piecewisely estimated by

matching the number of samples between two

consecutive P

points with the number of pixels

along the X

PAN

direction between the corresponding

PAN

points. Figure 9a shows the DRT results for the

projection of the crowns model illustrated in Figure

3b, while Figures 9b and 9c show its

superimposition on the original PAN image.

Tooth heights are then extracted from the PAN

image by the selection of root tips which are back-

projected onto the 3D model. This back-projection is

performed by considering the coordinates of the root

tip in the PAN image. The z-coordinate, up to a scale

Customised3DToothModelingbyMinimallyInvasiveImagingModalities

Figure 7: Alignment between 3D crowns model and PAN

image along the z-direction.

Figure 8: Projection scheme of the 3D patient crowns

model.

factor, is used to identify the slice to which the 3D

root tip belongs:

tip

cr z

PAN

zscalez

(2)

The x-coordinate is instead used to retrieve the

curvilinear coordinate along the



curve by:

tip

PAN

sx

(3)

The line normal to



and passing from s

tip

describes the projection ray through the root tip. It is

then possible the spatial identification of a direction

on which the 3D root tip must certainly lie

(constraint line). The template tooth model, already

scaled by considering width and depth values can

then be finally scaled along the height direction in

order to approach the above outlined constraint line.

Clearly, an indetermination about the root

inclination still remains since the tooth root could be

indifferently oriented to the buccal or lingual side of

dentition. However, the preventive alignment of the

tooth template on the patient crown model should

guarantee the correct orientation of the reconstructed

tooth.

3 PRELIMINARY RESULTS

The feasibility of the proposed methodology has

been verified by reconstructing some teeth of a

female patient superior dental arch. Figure 10 shows

two views of the CAD templates aligned and scaled

(using tooth width and depth values) on the crowns

model, along with the directions on which respective

root tips should lie. CAD templates are then further

scaled along the tooth heights while tooth axes are

oriented in order to intersect the respective

constraint lines (Figure 11). Crown geometries,

acquired by the optical scanner, and root geometries,

estimated by scaling CAD templates, are then

merged together thus creating the final digital tooth

model (Figure 12).

The reconstructed tooth shapes can be compared

to those obtained by processing volumetric data

from patient CBCT scans. In this case, segmented

tooth geometries from CBCT data (Figure 13a) can

be used as ground truth to assess the accuracy of 3D

models reconstructed by using minimally invasive

imaging modalities (Figure 13b,c).

(a)

(b) (c)

Figure 9: (a) DRT projection of the 3D patient crowns model, (b) superimposition of the projection on the PAN image

along with a detail (c). The crowns model projection is highlighted with a transparent cyan colour.

BIOIMAGING2014-InternationalConferenceonBioimaging

Figure 10: CAD templates aligned and scaled on the

crowns model with the respective constraint lines for root

tips.

Figure 11: Final height scaling and orientation (green

model) of the tooth CAD template (blue model).

Figure 12: Merging between crown geometry (gray

model) and scaled tooth CAD template (green model).

4 CONCLUSIONS

In the field of orthodontic dentistry, one of the main

challenges relies on the accurate determination of

3D dentition geometries by exposing the patient to

the minimum radiation dose. In this context, the

present paper outlines a methodology to infer 3D

shape of tooth roots by combining the patient digital

plaster cast with a panoramic radiograph. The

method investigates the possibility to adapt general

dental CAD templates over the real anatomy by

exploiting geometrical information contained within

the panoramic image and the digital plaster cast. The

proposed modelling approach, which has showed

encouraging preliminary results, allows a

generalised formulation of the problem since

assumptions about the tomographic device used for

radiographic data capturing are not required.

Many are the variables involved in the adopted

formulation. In particular, key issues are represented

by the optimization of the



curve, whose slope

determines the orientation of root tip constraint

lines, and the accurate evaluation of magnification

factors along the z-direction of the PAN image.

(a) (b) (c)

Figure 13: (a) CBCT tooth ground truth, (b) overlapping

between CBCT and reconstructed tooth model, (c)

discrepancies between the two models.

These topics certainly require further research

activities taking also into account, for example,

additional information which could be extracted by

supplementary lateral radiographs.

REFERENCES

Barone, S., Paoli, A. & Razionale, A. 2013. Creation of

3D Multi-Body Orthodontic Models by Using

Independent Imaging Sensors. Sensors, 13, 2033-

2050.

Boyd, R. L. 2007. Complex orthodontic treatment using a

new protocol for the Invisalign appliance. Journal of

Clinical Orthodontics, 41, 525-547.

Kuncio, D., Maganzini, A., Shelton, C. & Freeman, K.

2007. Invisalign and traditional orthodontic treatment

postretention outcomes compared using the American

Board of Orthodontics Objective Grading System.

Angle Orthodontist, 77, 864-869.

Mazzotta, L., Cozzani, M., Razionale, A., Mutinelli, S.,

Castaldo, A. & Silvestrini-Biavati, A. 2013. From 2D

to 3D: Construction of a 3D Parametric Model for

Detection of Dental Roots Shape and Position from a

Panoramic Radiograph—A Preliminary

Report. International Journal of Dentistry, 2013, 8.

Pei, Y. R., Shi, F. H., Chen, H., Wei, J., Zha, H. B., Jiang,

R. P. & Xu, T. M. 2012. Personalized Tooth Shape

Estimation From Radiograph and Cast. IEEE

Transactions on Biomedical Engineering, 59, 2400-

2411.

Tohnak, S., Mehnert, A., Crozier, S. & Mahoney, M.

2006. Synthesizing panoramic radiographs by

unwrapping dental CT data. 2006 28th Annual

International Conference of the IEEE Engineering in

Medicine and Biology Society, Vols 1-15, 1484-1487.

Customised3DToothModelingbyMinimallyInvasiveImagingModalities