Electrochemical Coupling of Arylsulfonyl Hydrazides and Tertiary Amines for the Synthesis of β-Amidovinyl Sulfones

Article abstract of DOI:10.1002/ejoc.201901277

The reaction of arylsulfonyl hydrazides with tertiary amines provided β-amidovinyl sulfones in good yields under mild electrochemical conditions. The reactions were carried out using an acid, in a solution of nBu₄NBF₄ in dimethyl sulfoxide in undivided cells with graphite-platinum electrodes under a constant current. The arylsulfonyl hydrazides and tertiary amines were activated via a radical process by electrochemical oxidation and reacted to give the desired β-amidovinyl sulfones.

Full text of DOI:10.1002/ejoc.201901277

Dynamic focal plane estimation for dental panoramic radiography
Seungeon Kim, and Jong Beom Raa)
School of Electrical Engineering, KAIST, Daejeon, Republic of Korea
(Received 11 February 2019; revised 2 September 2019; accepted for publication 3 September 2019;
published xx xxxx xxxx)
Purpose: The digital panoramic radiography is widely used in dental clinics and provides the
anatomical information of the intraoral structure along the predefined arc-shaped path. Since the
intraoral structure varies depending on the patient, however, it is nearly impossible to design a com-
mon and static focal path or plane fitted to the dentition of all patients. In response, we introduce an
imaging algorithm for digital panoramic radiography that can provide a focused panoramic radio-
graphic image for all patients, by automatically estimating the best focal plane for each patient.
Methods: The aim of this study is to improve the image quality of dental panoramic radiography
based on a three-dimensional (3D) dynamic focal plane. The plane is newly introduced to represent
the arbitrary 3D intraoral structure of each patient. The proposed algorithm consists of three steps:
preprocessing, focal plane estimation, and image reconstruction. We first perform preprocessing to
improve the accuracy of focal plane estimation. The 3D dynamic focal plane is then estimated by
adjusting the position of the image plane so that object boundaries in the neighboring projection data
are aligned or focused on the plane. Finally, a panoramic radiographic image is reconstructed using
the estimated dynamic focal plane.
Results: The proposed algorithm is evaluated using a numerical phantom dataset and four clinical
human datasets. In order to examine the image quality improvement owing to the proposed algo-
rithm, we generate panoramic radiographic images based on a conventional static focal plane and
estimated 3D dynamic focal planes, respectively. Experimental results show that the image quality is
dramatically improved for all datasets using the 3D dynamic focal planes that are estimated from the
proposed algorithm.
Conclusions: We propose an imaging algorithm for digital panoramic radiography that provides
improved image quality by estimating dynamic focal planes fitted to each individual patient’s intraoral
structure. © 2019 American Association of Physicists in Medicine [https://doi.org/10.1002/mp.13823]
Key words: dental x-ray imaging, digital panoramic radiography, dynamic focal plane, focal plane
estimation, image enhancement
1. INTRODUCTION
empirically designed as an arch shape for describing the nor-
mal dentition, and the scan trajectory of the source detector
pair is correspondingly determined at each projection view
angle, while sliding the rotation center.
Digital panoramic radiography has been widely used in den-
tal clinics because it can immediately provide a clinical dental
image of a broad range of the jaw with a low radiation
dose.1–6 In particular, the objects of interest, such as the teeth,
residing on a focal plane, or focal trough, are clearly observed
in the panoramic radiographic image, while the other objects
out of the focal plane are blurred. Digital panoramic radiogra-
phy thereby improves diagnostic accuracy, compared to the
conventional X-ray projection radiography.
In a conventional panoramic radiographic imaging system,
the projection data are acquired at each view angle using a
rotating x-ray source and narrow slit detector pair around
sliding rotation centers.3 A panoramic radiographic image is
then obtained by shifting each projection data by predefined
amounts and accumulating them. Note that the shift amounts
at each projection view angle are calculated so that an object
of interest on the focal plane could be accumulated at the
same position in the panoramic radiographic image. There-
fore, the object on the focal plane appears focused in a
panoramic radiographic image, while the one outside the
focal plane appears blurred. In general, the focal plane is
As mentioned, a panoramic radiographic image is
obtained by focusing only the objects residing on a prede-
fined focal plane. Therefore, in order to provide diagnostic
image quality for the intraoral structure of a patient, the denti-
tion of the patient should coincide with the focal plane.3–7
Since the intraoral structure varies depending on the patient,
however, it is nearly impossible to determine a focal plane
that is commonly fitted to all different dentitions of patients.
In some cases, the patient’s dentition may deviate signifi-
cantly from the predefined focal plane, resulting in image
quality degradation of a panoramic radiographic image,
which may cause misdiagnosis.
Recently, a couple of algorithms that acquire a focused
panoramic radiographic image automatically have been
reported.4,6,7 In those algorithms, multiple panoramic radio-
graphic images are first obtained at different layers with vari-
ous depths,3,8 and then focused patches are selected from the
multiple images based on a sharpness metric. By stitching the
selected patches6 or performing the oriented planar image
1
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0094-2405/xxxx/0(0)/1/xx
© 2019 American Association of Physicists in Medicine
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2
Kim and Ra: Dynamic focal plane estimation
2
reconstruction,4,7 a focused panoramic radiographic image is
obtained. Since these algorithms are based on patch selection
among the patches with different depths; however, they
accompany a potential risk of unnatural artifacts near the
patch boundary, and the focusing accuracy may be bounded
by the patch size for the sharpness measurement.
In this paper, we propose a novel algorithm to obtain a
focused panoramic radiographic image by directly estimating
a 3D focal plane for a given patient. In the proposed algo-
rithm, the 3D dynamic focal plane is newly introduced. The
focal plane is then estimated on the basis of the matching
among the projection data of different view angles for each
patient. The panoramic radiographic image is then recon-
structed using the estimated patient-specific focal plane.
The remainder of this paper is organized as follows. In
Section 2, the overall structure of the proposed algorithm is
given and details of each module are described. In Section 3,
experimental results are provided for a numerical phantom
and clinical datasets. A discussion and conclusions are given
in Sections 4 and 5, respectively.
of interest, however, the back-projected data include the
boundary information of background objects, which mostly
lie on the opposite side of the objects of interest with respect
to a rotation center. Hence, the background objects have com-
pletely different registration relationships from the objects of
interest, and thereby tend to make the focal plane estimation
less reliable. In response, we preprocess the projection data
prior to back-projection, for more accurate and reliable focal
plane estimation by reducing the effect of background
objects.
For preprocessing, as shown in Fig. 2, we first apply a
log-transform to the acquired projection data to obtain line
integral values of attenuation coefficients, g.9,10 We subse-
quently reconstruct a 3D image, I, using the conventional
FDK algorithm.11 Note that in image I the back-projection is
performed only for the region between the detector and the
rotation center, where the objects of interest are located. In
order to determine whether the 3D position of each voxel, x,
is in between the rotation center and the detector at view
angle /i, we use the following equation:
ꢀ
ꢁ
S/ ðxÞ ¼ x ꢀ r/ ꢁ b/ ;
(1)
i
i
i
2. MATERIALS AND METHODS
where r/ denotes the 3D position vector of the rotation cen-
i
For the focal plane estimation, we first consider the rela-
tionship between the position of the focal plane and the image
quality of a panoramic radiographic image. Figure 1(a) shows
the data acquisition procedure for an object of interest, where
a source-detector pair is used at two different view angles. As
shown in Fig. 1(b), the object can be either focused or blurred
depending on the position of the accumulated plane. Based
on this observation, in order to obtain a focused panoramic
radiographic image, we propose a novel algorithm for esti-
mating the focal plane where back-projected boundaries of
the objects of interest are well aligned for all view angles.
ter of the source-detector pair at view angle /i, and b/
denotes a unit vector along the direction from the detector
center to source at view angle /i, as shown in Fig. 2. If
S/ ðxÞ is a negative value, x is considered to reside in
i
i
between the rotation center and the detector. Even though
tooth objects cannot be reconstructed completely due to lim-
ited view angles, it is observed in I that object boundaries
perpendicular to the projection direction can be well
defined.12–14 In order to reduce the intensity inhomogeneity
due to the data truncation arising from small detector width,
the intensity value of each voxel in I is normalized using the
angular span applied for the back-projection to the corre-
sponding voxel, and the normalized 3D image is illustrated as
IN. We then obtain the simulated projection data, G, by for-
ward projecting IN only from the rotation center to the detec-
tor, or only for the active region, at each view angle. Thereby,
the objects of interest are emphasized in G, while background
objects are de-emphasized. Finally, in order to make the fol-
lowing projection data alignment procedure more sensitive to
2.A. Focal plane estimation
2.A.1. Preprocessing
The proposed algorithm estimates a focal plane based on
the 2D registration of object boundaries among the back-pro-
jected data at different view angles. In addition to the objects
FIG. 1. (a) Projection data acquisition of an object of interest at two different view angles. (b) The object becomes focused or blurred in a panoramic radiographic
image depending on whether the object is placed on the focal plane.
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3
Kim and Ra: Dynamic focal plane estimation
3
object boundaries, we preprocess G using a 1D Laplacian fil-
ter and obtain the preprocessed projection data, P.
panoramic radiographic image domain, B denotes the 2D ten-
sor product of 1D cubic B-splines, and ds is a knot interval in
the space domain. Hence, the total number of knots, or con-
trol points, L, is {d(Nx/2)/dse 9 2 + 3} 9 {d(Ny/2)/dse
9 2 + 3} for a 2D panoramic radiographic image of
Nx 9 Ny pixels, where d⋅e denotes the ceiling operator. Note
in Fig. 3 that hj are illustrated for the example case of L = 15.
Also, vðxpanoÞ denotes a unit vector for the refinement of
Tðxpano; H ¼ 0Þ and can be obtained using a set of 3D unit
vectors from the source to array elements on the detector cen-
ter column at each view angle. Thereby, a dynamic focal
plane can be described using H.
2.A.2. Dynamic focal plane
In constituting a panoramic radiographic image in an ordi-
nary system, the imaging focal plane is usually set to be static
and may thereby cause out of focus areas depending on the
patient. Instead of using this static and patient-independent
focal plane, we suggest using a patient-dependent dynamic
focal plane, where all object boundaries are focused.
Figure 3 conceptually illustrates the proposed method to
derive a dynamic focal plane from the initial static focal
plane, which is a set of voxel points placed according to the
predefined fixed distance ratio from the source to the detector
plane. Note here that the static focal plane and the corre-
sponding scanning geometry of the source-detector pair are
assumed to be available in the imaging system. Let us assume
that a 2D pixel position in a panoramic radiographic image,
2.A.3. Definition of the cost function
In order to determine the optimal control point parameters,
hj, which can align the object boundaries back-projected from
different view angles to the focal plane, we define a data term
as the sum of differences between a pair of back-projected
data to the focal plane from neighboring view angles.
Namely,
x
pano, corresponds to a 3D voxel position xs on the initial
focal plane. We then consider that the voxel position xd on
the dynamic focal plane can be determined by properly refin-
ing xs.
X X
ꢄ
ꢀ
ꢀ ꢀ
ꢁ
ꢁꢁ
ꢄ
DðHÞ ¼
P/ A/ T xpano; H ꢀ r/
i
i
i
i
xpano2Xi
By adopting a B-spline based 2D interpolation model,15
the dynamic focal plane can then be described as follows:
ꢄ
ꢄ
ꢀ
ꢀ ꢀ
ꢁ
ꢁꢁ
2
2
ꢀ P/ A/ T xpano; H ꢀ r/
;
iþF
iþF
iþF
ꢀ
ꢁ
ꢀ
ꢁ
(4)
T xpano; H ¼ T xpano; H ¼ 0
ꢂ
ꢃ
X
ꢀ
ꢁ
where P/ denotes the preprocessed projection data at view
xpano
ds
(2)
i
þ v xpano
B
ꢀ j hj;
angle /i. In addition, Xi is a set of pixel positions, where the
back-projected data from view angles of i and i + F are over-
lapping in the 2D panoramic radiographic image domain.
Here, F denotes the view index interval for the comparison of
projection data, and an interval of 5 is used in this study.
Figure 4 shows the illustration of back-projection onto an
j
where
Tðxpano; HÞ ¼ xd; and Tðxpano; H ¼ 0Þ ¼ xs:
(3)
In Eq. (2), H denotes a set of L different hj, each of which
denotes a 2D B-spline coefficient at knot j in the 2D
ꢀ
ꢁ
arbitrary point, xd, [or T xpano; H in Eq. (4)] in the dynamic
FIG. 2. Flowchart of the proposed preprocessing method.
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4
Kim and Ra: Dynamic focal plane estimation
4
FIG. 3. An example illustration for describing the relationship between point xpano on a two-dimensional (2D) panoramic radiographic image and the correspond-
ing point xd which is considered to belong to the dynamic focal plane. By determining xd for all different view angles, a dynamic focal plane can be described.
Note that hj in the 2D panoramic radiographic image domain denotes a 2D B-spline coefficient at control point j.
focal plane, at view angle /i, as an example. Note here that
r/ and b/ are the same notations described in Fig. 2. As
Here, RSDD and RSAD denote the distances from the source to
detector and to r/ , respectively. Also, az denotes the unit vec-
i
i
i
shown in Fig. 4, A/ is the mapping function from 3D coordi-
nates xd to the 2D idetector coordinates at /i, which can be
written as follows:
tor along the z-axis, a/ represents a unit vector orthogonal to
i
az and b/ , and the superscript T denotes the transpose.
i
In addition to the data term, we adopt a regularization
term for robust parameter estimation by penalizing the exces-
sive difference between neighboring parameters, as follows:
ꢀ
ꢁ
RSDD
ꢀ
ꢁ
A/ xd ꢀ r/
¼
i
i
RSAD ꢀ xd ꢀ r/ ꢁ b/
i
i
X X
ꢄ
ꢄ
2
2
ꢅ ꢀ
ꢁ
ꢀ
ꢁ
ꢆ
ꢄ
ꢄ
T
RðHÞ ¼
hj ꢀ hk
;
(6)
xd ꢀ r/ ꢁ a/
xd ꢀ r/ ꢁ az
:
i
i
i
j
k2Kj
(5)
FIG. 4. An illustration of back-projection onto xd from the projection data at view angle /i.
Medical Physics, 0 (0), xxxx

5
Kim and Ra: Dynamic focal plane estimation
5
where Kj is a set of knot indices neighboring knot j. Using
Eqs. (4) and (6), we define a cost function C as (D + k R),
where k is a regularization parameter. The optimum
parameters can then be determined by minimizing C,
namely,
where
ꢀ
ꢀ
ꢁꢁ
T
UilðxpanoÞ ¼rP/ A/ xld ꢀ r/
i
i
i
RSDD
ꢀ
ꢁ
(14)
RSAD ꢀ xld ꢀ r/ ꢁ b/
i
i
ꢅ ꢀ
ꢁ
ꢀ
ꢁ
ꢆ
T
H ¼ argminfCðHÞg ¼ argminfDðHÞ þ kRðHÞg:
(7)
v xpano ꢁ a/ v xpano ꢁ az
:
i
H
H
Substituting Eqs. (13) into (4), we define the linearized data
term, DL as follows:
X X
2.A.4. Optimization
ꢄ
ꢄ
ꢀ
ꢁ
ꢀ
ꢀ
ꢁꢁ
DL DH; Hl
¼
P/ A/ xld ꢀ r/
i
i
i
The optimal parameters, which minimize C in Eq. (7), can
be determined in an iterative manner, based on both the
Gauss-Newton method16,17 and the optimization transfer
method.18–20 Using the Gauss-Newton method, the optimum
update amount at iteration step l can be determined as fol-
lows:
i
xpano2Xi
ꢀ
ꢀ
ꢁꢁ
ꢀ P/ A/ xld ꢀ r/
iþF
iþF
iþF
ꢀ
ꢀ
ꢁ
ꢀ
ꢁꢁ
þ Uil xpano ꢀ UilþF xpano
(15)
ꢄ
2
ꢂ
ꢃ
ꢄ
ꢄ
ꢄ
ꢄ
X
xpano
ds
B
ꢀ j Dh
:
j
ꢇ ꢀ
ꢁ
ꢀ
ꢁꢈ
j
2
l
l
^
DH ¼ argmin D H þ DH þ kR H þ DH
:
(8)
DH
Since DL is a non-separable function of multiple unknowns,
it is not suitable for parallel processing. We hence derive a
separable surrogate function of DL based on the optimization
transfer method. Namely,
For the linearization of D, we first rewrite Eqs. (2) and (5) as
follows:
ꢂ
ꢃ
ꢀ
ꢁ
X X X
T xpano; Hl þ DH ¼ xdl þ Dxd;
and
(9)
ꢀ
ꢁ
xpano
ds
DS DH; Hl
¼
B
ꢀ j
i
xpano2Xi
j
ꢄ
ꢄ
ꢀ
ꢀ
ꢁꢁ
 P/ A/ xld ꢀ r/
ꢀ
ꢁ
i
i
i
RSDD
A/ xld ꢀ r/ þ Dxd
¼
ꢀ
ꢀ
ꢁꢁ
ꢀ P/ A/ xld ꢀ r/
i
i
RSAD ꢀ ðxld ꢀ r/ Þ ꢁ b/ ꢀ Dxd ꢁ b/
iþF
iþF
iþF
i
i
i
ꢅꢀ
ꢀ
ꢁ
ꢄ
ꢄ
ꢀ
ꢀ
ꢁ
ꢀ
ꢁꢁ
2
2
xld ꢀ r/ þ Dxd ꢁ a/
þ Uil xpano ꢀ UiþF xpano Dhj
;
l
i
i
ꢁ
ꢆ
T
xld ꢀ r/ þ Dxd ꢁ az
(16)
i
which satisfies the following three conditions19,20
:
(10)
ꢉ
ꢉ
ꢀ
ꢁ
ꢀ
¼
ꢁ
DL DH; Hl
¼ DS DH; Hl
;
(17)
(18)
(19)
where
ꢉ
ꢉ
DH¼0
DH¼0
ꢀ
ꢁ
xld ¼T xpano; Hl and Dxd
ꢉ
ꢉ
ꢉ
ꢉ
ꢉ
ꢉ
ꢉ
ꢉ
ꢀ
ꢁ
ꢀ
ꢁ
d
d
dDH
ꢁ
DL DH; Hl
DS DH; Hl
;
ꢂ
ꢃ
X
ꢀ
ꢁ
xpano
ds
(11)
dDH
¼ v xpano
B
ꢀ j Dhj:
DH¼0
DH¼0
j
ꢀ
ꢁ
ꢀ
DL DH; Hl ꢂ DS DH; Hl :
Since RSDD [ RSAD ꢀ ðxld ꢀ r/ Þ ꢁ b/ [[ Dxd ꢁ b/ , we can
i
i
i
We can easily note that Eqs. (17) and (18) are satisfied. Since
the B-spline interpolation is a convex combination of B-spline
coefficients, we also note that Eq. (19) is satisfied.21 Mean-
while, the separable surrogate function of R can be written as
Ref. [20].
approximate Eq. (10) without loss of generality to
ꢀ
ꢁ
ꢀ
ꢁ
A/ xld ꢀ r/ þ Dxd ffiA/ xld ꢀ r/
i
i
i
i
RSDD
ꢀ
ꢁ
þ
ꢅ
(12)
RSAD ꢀ xld ꢀ r/ ꢁ b/
i
i
ꢊ
ꢆ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
ꢄ
T
X X
2
2
ꢀ
ꢁ
1
2
Dxd ꢁ a/ Dxd ꢁ az
:
RS DH; Hl
¼
\hl þ 2Dh ꢀ hl
i
j
j
k
j
k2Kj
Subsequently, we apply the first-order Taylor series expan-
sion to P/ in Eq. (4), as follows:
(20)
ꢋ
ꢄ
ꢄ
ꢄ
ꢄ
2
2
1
ꢄ
hl ꢀ h ꢀ 2Dhl
:
i
þ
ꢄ
k
j
k
2
ꢀ
ꢀ
ꢁꢁ
ꢀ
ꢀ
ꢁꢁ
P/ A/ xld ꢀ r/ þ Dxd ffiP/ A/ xdl ꢀ r/
i
i
i
i
i
i
Combining Eqs. (16) and (20), we can redefine the cost
function, which is suitable for parallel processing, as
ꢀ
ꢁ
þ Uil xpano
ꢂ
ꢃ
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
X
CS DH; Hl ¼ DS DH; Hl þ kRS DH; Hl :
By setting the partial derivative of Eq. (21) with respect to
each control point parameter to zero, the update amount at
(21)
xpano
B
ꢀ j Dhj;
ds
j
(13)
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6
Kim and Ra: Dynamic focal plane estimation
6
each iteration step l can be obtained concurrently at each con-
trol point as
201808-11-003). The information regarding the static focal
plane and the corresponding scanning geometry of the
source-detector pair is provided by the manufacturer. In the
numerical phantom study, the phantom is made using mathe-
matical ellipsoids of different shapes to simulate the human
dentition, and the corresponding datasets are generated based
on a simulated system with the same specifications as in the
clinical study. For each dataset, we reconstruct two panoramic
radiographic images using a conventional static focal plane
and the proposed dynamic focal plane, respectively. The
image size is commonly set to 2320 9 1280 with a pixel size
of 0.094 9 0.094 mm2. For the focal plane estimation, ds in
Eq. (2) is heuristically set to 27 pixels, which correspond to
approximately 5 mm. The total number of control points is
thereby 89 9 51 in 2D panoramic radiographic image
domain. The proposed algorithm is implemented using C and
CUDA on a GPU platform. In order to improve the visibility
of the dental structure, a simple unsharp masking scheme is
applied as post-processing on all panoramic radiographic
images.
D0 þ kR0
^
Dhj ¼ ꢀ
;
(22)
D00 þ kR00
where
ꢂ
ꢃ
X X
ꢀ
ꢀ
ꢁ
ꢀ
ꢁꢁ
xpano
ds
D0 ¼ 2
B
ꢀ j Uil xpano ꢀ UilþF xpano
i
xpano2Xi
ꢀ
ꢀ
ꢀ
ꢁꢁ
ꢀ
ꢀ
ꢁꢁꢁ
P/ A/ xld ꢀ r/ ꢀ P/ A/ xdl ꢀ r/
i
i
i
iþF
iþF
iþF
ꢂ
ꢃ
X X
ꢀ
ꢀ
ꢁ
ꢀ
ꢁꢁ
xpano
D00 ¼ 2
B
ꢀ j Uil xpano ꢀ UilþF xpano
ds
i
xpano2Xi
ꢀ
ꢀ
ꢁ
ꢀ
ꢁꢁ
Uil xpano ꢀ UilþF xpano
ꢌ
ꢍ
X
R0 ¼ 4
hlj ꢀ hkl and R00 ¼ 8NK :
j
k2Kj
(23)
In order to further reduce the computational complexity and
handle a large displacement problem in the iteration, we
adopt a multiresolution scheme.
3. RESULTS
2.B. Generation of panoramic radiographic image
3.A. Numerical phantom data
Once a dynamic focal plane is estimated by determining
the optimal parameters, as in the previous sub-section, a
panoramic radiographic image can be obtained via 3D back-
projection of log-transformed data P.9–11 Namely,
In this study, we design a numerical phantom using multi-
ple tilted ellipsoids. As shown in Fig. 5, the phantom includes
both normal and abnormal dentition models in the lower and
upper jaws, respectively. The abnormality of dentition in the
upper jaw is modeled by adjusting the tilting angle of two
ellipsoids.
Figures 6(a) and 6(b) show the panoramic radiographic
images obtained using the static and dynamic focal planes,
respectively. We can easily observe in the figure that the pro-
posed algorithm provides a panoramic radiographic image of
improved quality, where the boundaries of all ellipsoids are
well focused for both normal and abnormal dentitions of the
lower and upper jaws. The 1D intensity profiles in Fig. 7 also
demonstrate that the proposed algorithm improves the image
sharpness.
For further evaluation, we illustrate the static and the esti-
mated dynamic focal planes along with an image of the
numerical phantom, as in Figs. 8(b) and 8(d). We can easily
see that the estimated dynamic focal plane is nearly coinci-
dent with the abnormal dentition of the upper jaw, where
z = 96, as well as the normal dentition of the lower jaw,
where z = 32. Furthermore, 3D illustrations in Figs. 8(a)
and 8(c), which represents the depths from the plane of
y = 0 to the static and dynamic focal planes, respectively,
show how the estimated dynamic focal plane varies in the
3D domain.
ꢀ
ꢁ
1
P
fpano xpano
¼
D/i0
i02Kx
pano
X
ꢀ
ꢀ ꢀ
ꢁ
ꢁꢁ
P/ A/ T xpano; H ꢀ r/ ꢁ D/i;
i
i
i
i2Kx
pano
(24)
where D/i denotes the angular increment of the source at the
i-th view angle, and Kx denotes a set of view indices that
pano
contribute to reconstructing xpano. We note in Eq. (24) that
the proposed algorithm easily generates a panoramic radio-
graphic image corresponding to an arbitrary 3D focal plane
since it is based on 3D back-projection. Meanwhile, since the
filtering operation, such as Shepp-Logan filtering,9,10 is not
included in the image generation process, unlike in the con-
ventional 3D CT image reconstruction, the intensity value
may become higher as the projection data are accumulated.
To prevent this increase in intensity, a normalization factor is
used in Eq. (24).
2.C. Evaluation
We evaluate the proposed algorithm using a numerical
phantom dataset and four clinical datasets. The projection
data of clinical datasets are obtained using T1-CS of Osstem
Implant Co., Ltd., and the scan protocol utilized in this clini-
cal human study was approved by Korea National Institute
for Bioethics Policy (KONIBP), Republic of Korea (P01-
3.B. Clinical human data
In order to evaluate the proposed algorithm in a clinical
situation, we apply it to the following four clinical datasets:
H1 with the patient having a normal dentition, H2 with
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FIG. 5. Projection image of a numerical phantom along the y-axis; and two transaxial images of the phantom at upper and lower positions, respectively.
proposed algorithm estimates the dynamic focal plane well
such that it fits the patient’s intraoral structure. It thereby pro-
vides improved image quality, especially in enlarged areas in
Figs. 10(a) and 10(b).
(a)
Even though H3 includes multiple metallic objects, as
shown in Fig. 11, the proposed algorithm improves the image
quality by estimating the dynamic focal plane. The intraoral
structures, especially around the fore teeth in the enlarged
area, are blurred in Fig. 11(a), whereas those structures
become sharper and clearly visible in Fig. 11(b).
Panoramic radiographic images of a patient having severely
tilted teeth are obtained using H4, as shown in Fig. 12. As
expected, we can easily see that the image quality is consider-
ably improved using the proposed algorithm. Specifically, fore
teeth with a large tilting angle, as well as the other intraoral
structures, become sharper and more clearly visible.
(b)
For further evaluation, Fig. 13 shows 1D intensity profiles
on enlarged areas of the panoramic radiographic images
given in Figs. 9–12. It is noted in Fig. 13(c) that intensity pro-
files of the proposed dynamic focal plane provide higher res-
olution than those of ordinary static focal plane, especially at
the points depicted by arrows where edges and small struc-
tures are located. In addition, any shift and/or magnification
change are not noticeably observed between the intensity pro-
files of two images that are obtained using the static and
dynamic focal planes, respectively.
FIG. 6. Panoramic radiographic images of the numerical phantom obtained
using (a) static and (b) estimated dynamic focal planes, respectively.
dentition having baby teeth, H3 with dentition including mul-
tiple metallic objects, and H4 with dentition having severely
tilted teeth.
4. DISCUSSIONS
Figure 9 shows the panoramic radiographic images of H1
using the conventional static and estimated dynamic focal
planes, respectively. As shown in the figure, the conventional
static focal plane still provides acceptable image quality by
showing sharp object boundaries throughout the image,
because the intraoral structure of the patient in H1 is rela-
tively well fitted to it. The estimated dynamic focal plane,
however, provides further improved image quality in the
enlarged areas.
On the other hand, for H2, the panoramic radiographic
image of the conventional static focal plane fails to provide
sharp object boundaries, unlike the image of the estimated
dynamic focal plane, as shown in Fig. 10. This is because the
dentition of the patient of H2 is too complex to be well repre-
sented using a simple static focal plane. Meanwhile, the
In this paper, we propose an algorithm that can provide
clear and focused digital panoramic radiographic images for
patients having various dentitions. The proposed algorithm is
based on the observation that the boundaries of the objects of
interest, which are back-projected from each projection data,
should be well aligned at the focal plane in order to obtain a
clear and focused panoramic radiographic image. Accordingly,
we newly introduce a dynamic 3D focal plane, which is well
coincident with the objects, by describing its shape in the 3D
space with a high DOF. We then derive an optimization pro-
cess to determine the dynamic focal plane. In addition, for
more reliable focal plane estimation, we propose a preprocess-
ing method, which effectively alleviates undesirable effects of
background objects in the projection data. The proposed algo-
rithm is evaluated using simulation data and four clinical
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FIG. 7. Panoramic radiographic images of an enlarged region of interest that are obtained using (a) static and (b) estimated dynamic focal planes, respectively. (c)
One-dimensional intensity profiles along the dashed and solid lines in (a) and (b), respectively. For better comparison, the noise in the profiles is reduced by aver-
aging the intensities of 10 adjacent lines around the lines in (a) and (b), respectively.
FIG. 8. (a) Three-dimensional illustration of the static focal plane; and (b) its transaxial views at z of 32 and 96, along with the corresponding transaxial images
of the numerical phantom. (c) Three-dimensional illustration of the estimated dynamic focal plane; and (d) its transaxial views at z of 32 and 96, along with the
corresponding transaxial images of the phantom. Note in (b) and (d) that transaxial views of focal planes appear as lines and their accuracy can be examined by
referring to the transaxial images.
datasets. Experimental results show that the image quality is
highly improved using the proposed algorithm.
algorithm introduces a generalized focal plane with high
DOF in the 3D space by trying to align all boundaries of the
objects that are back-projected from different view angles.
Thereby, the proposed algorithm can improve the image qual-
ity throughout the image.
Meanwhile, a possible patient positioning error, which can
be another reason for image quality degradation, is not con-
sidered in this paper. Like the proposed algorithm which esti-
mates the patient’s dentition based on the projection data, an
advanced software approach may need to be developed to
estimate and correct the patient positioning error for further
improvement of image quality.
The proposed algorithm is suitable for parallel computing
based on the GPU platform, because the optimization process
consists of separable operations. The total computation time to
obtain a panoramic radiographic image using the proposed
algorithm is 6.5 s with a single GPU card, NVIDIA Tesla
K40c. The computation time is not considered long for
Most previous algorithms to improve the image quality of
panoramic radiography4,6,7 select focused patches from the
images, which are reconstructed at multiple parallel candidate
focal planes. Hence, they need to determine the patch size
and patch selection strategy, choose the number of candidate
planes and a depth interval between candidate planes, and
solve the discontinuity problem at the patch boundaries.
Meanwhile, the proposed algorithm first introduces a more
general focal plane model based on the B-spline and esti-
mates its optimal model parameters via a continuous opti-
mization. Hence, the proposed algorithm can guarantee a
well-focused image over the whole region.
As shown in the results, the proposed algorithm improves
the overall image quality by sharpening the boundaries of the
other intraoral structures, such as the temporomandibular
joint (TMJ), as well as the teeth. This is because the proposed
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Kim and Ra: Dynamic focal plane estimation
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(a)
(a)
(b)
(b)
FIG. 9. Panoramic radiographic images reconstructed from clinical data H1,
using (a) static and (b) estimated dynamic focal planes, respectively.
FIG. 11. Panoramic radiographic images reconstructed from clinical data H3,
using (a) static and (b) estimated dynamic focal planes, respectively.
(a)
(a)
(b)
(b)
FIG. 12. Panoramic radiographic images reconstructed from clinical data H4,
using (a) static and (b) estimated dynamic focal planes, respectively.
FIG. 10. Panoramic radiographic images reconstructed from clinical data H2,
using (a) static and (b) estimated dynamic focal planes, respectively.
practical use, even though it takes 60 ms to obtain a conven-
tional panoramic radiographic image in the same environment.
The feasibility and clinical applicability of the proposed
algorithm are proven through the experiments in this
paper. Nonetheless, for clinical use of the proposed algo-
rithm, it is desirable to validate the proposed algorithm
using extensive datasets with various clinical settings, as
further work.
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FIG. 13. Enlarged panoramic radiographic images for H1, H2, H3, and H4, which are obtained using (a) static and (b) estimated dynamic focal planes, respec-
tively. Note that the pixel size is 0.094 9 0.094 mm2. (c) The corresponding one-dimensional intensity profiles. For better comparison, the noise in the profiles
is reduced by averaging the intensities of 10 adjacent lines around the lines in (a) and (b), respectively.
5. CONCLUSIONS
CONFLICT OF INTEREST
We propose an algorithm that can provide clear and
focused panoramic radiographic images even for various
types of dentitions, by estimating an adaptive dynamic
focal plane. The proposed algorithm consists of three
steps: preprocessing, dynamic focal plane estimation, and
panoramic radiographic image reconstruction. The pro-
posed algorithm is evaluated using a simulation dataset
and four clinical datasets, and the results show that the
algorithm can dramatically improve the image quality
even for irregular dentitions.
The authors have no relevant conflict of interest to dis-
close.
Seungeon Kim is currently with Samsung Advanced Institute of Technology
(SAIT), Samsung Electronics Co., Suwon, Republic of Korea.
a)Author to whom correspondence should be addressed. Electronic mail:
jbra@kaist.ac.kr.
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