Image Anal Stereol 2017;36:35-41 doi: 10.5566/ias.1631 
Original Research Paper 
APPLICATION OF IMAGE ANALYSIS METHODS FOR ISOCENTER 
QUALITY ASSURANCE IN RADIOTHERAPY 
MICHAŁ NIED ŹWIECKI
1
, MONIKA TOMASZUK
2
, DAMIAN KABAT
2
, ZBIGNIEW LATA ŁA
1
, 
KRZYSZTOF RZECKI
1
, ZBIS ŁAW TABOR

,1
 
1
Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland; 
2
Centre of Oncology, Maria 
Sklodowska-Curie Memorial Institute, Kraków Branch, Garncarska 11, 31-115 Kraków, Poland 
e-mail: nkg@pk.edu.pl, m.tomaszuk@gmail.com, z5kabat@cyf-kr.edu.pl, zlatala@mech.pk.edu.pl, 
krz@pk.edu.pl, ztabor@pk.edu.pl 
(Received September 22, 2016; revised December 21, 2016; accepted March 2, 2017) 
ABSTRACT  
One of the major procedures for testing the geometrical accuracy of devices used in radiotherapy treatments 
is the test of the geometrical position of the radiation isocenter. The importance of the test reflects the fact 
that geometrical position of the radiation isocenter generally affects the tumor targeting. At present the 
geometric accuracy is assessed with the Winston-Lutz test which checks the position of an image of a ball 
marker with the respect to the center of the radiation field as projected on a detector plane. Obviously, 
determination of coordinates of a single marker is not sufficient to fully account for a complicated geometry 
of a therapeutic device. The purpose of the study was to design a new image analysis tool to better determine 
the isocenter. The proposed automated procedure for determining isocenter position uses projection data 
acquired for a special cube phantom. The projection images of a phantom are acquired for various angles of 
rotation of the gantry. A procedure is proposed to extract some geometric characteristics of a therapeutic 
device from the projection images. 
Keywords: fiducials, isocenter, projection images, radiotherapy 
 
INTRODUCTION 
For all radiation dose delivery techniques in external 
beam therapy (EBT), the accuracy of the treatment is 
the ultimate goal. However, all assumptions of the 
perfect therapeutic procedure are in fact impossible to 
reach. Inevitable uncertainties always appear and 
could be identified at each step of the preparation and 
implementation of therapeutic process. Assessment of 
potential errors should include all aspects of overall 
performance of imaging devices used for patient posi-
tioning and target localization, accuracy of the treatment 
planning system, and geometrical precision of the treat-
ment device with meticulous check of dose delivery. 
Advanced modes of high-precision radiotherapy (e.g., 
intensity modulated radiation therapy IMRT or volu-
metric modulated arc therapy VMAT) allow confor-
mal delivery of radiation dose to a planned target 
volume while minimize exposure to organs at risk. 
On the other hand, the more advanced and precise the 
device or method is, the more attention should be paid 
to ensure its high accuracy and the lesser uncertainties 
are clinically accepted. Therefore, each radiotherapy 
department develops quality control tests to maintain 
high-level accuracy of the treatment. Various types 
and frequencies for providing such tests are recom-
mended by national legislations. One of the major 
geometric tests is the test of the geometrical locali-
zation of the radiation isocenter. 
The geometrical localization of the radiation iso-
center generally affects the tumor targeting and overall 
accuracy of the treatment (Du et al., 2010). On the 
other hand the mechanical isocenter of the linac is the 
point in space where rotation axes of gantry, collimator, 
and treatment table intersect (Lutz et al., 1988). 
Ideally these three elements rotate around one point 
which additionally coincides with the radiation iso-
center. Furthermore, this assumption implicates that 
the real position of radiation field during the treatment 
session is in accordance with a treatment plan. 
However, due to inaccuracies in the construction and 
real weights of device components (also the jaws of 
linac), the isocenter might slightly move in the space 
in a virtual spherical volume, which gives obvious 
mechanical limitation of the linac. Therefore, the test of 
radiation isocenter localization should be considered 
as very important. 
35 

NIED ŹWIECKI M ET AL: Quality assurance in radiotherapy 
At present the discrepancy between mechanical 
and radiation isocenter is tested using the Winston-
Lutz (W-L) test (Lutz et al., 1988). The W-L phantom 
is a small metallic ball representing the planned target. 
The phantom is positioned in 3D space using treat-
ment room lasers, which should ideally point to the 
radiation isocenter. Then, projection images of the 
phantom are acquired and discrepancy between radia-
tion and mechanical isocenter is reported whenever 
the center of the ball - as projected onto detector plane 
- deviates from the center of the radiation field. Mea-
surements are repeated for a few angular positions of 
a gantry of a therapeutic device (Rowshanfarzad et 
al., 2011).  
Obviously, comprehensive characterization of the 
geometry of a therapeutic device is not possible with 
a limited data provided by the W-L test. For example, 
the distance between the center of an image of a ball 
and the center of the radiation field depends on the 
distance between the source of ionizing radiation and 
the detector plane which is known only approximately. 
However, the images of a W-L phantom certainly 
contain more data than explored in a simple W-L test. 
Thus, the purpose of the study was to design a new 
image analysis tool to support the isocenter quality 
assurance by extracting additional parameters from 
images of a W-L phantom.  
 
Fig. 1. Axial cross-section of the geometry of a thera-
peutic device. 
METHODS 
The problem of determination of the position of an 
isocenter has been defined in a study of Du et al. (Du 
et al., 2016). According to (Du et al., 2016), for a set 
of gantry orientations (specified by an angle  of gantry 
rotation around a horizontal axis of a therapeutic device) 
a line referred to as a central axis (CAX), which is 
normal to the detector plane and passes through a 
source of ionizing radiation must be determined (Fig. 1).  
 
Fig. 2. Images of a ball marker and a source in the 
detector plane. 
Then the position P(x,y,z) of the isocenter is the 
solution to the following minimization problem (Du 
et al., 2016): 


i
CAX
i
z y x Q
CAX z y x Q d z y x P ) ), , , ( ( arg min ) , , (
2
) , , (
, (1) 
where d(Q(x,y,z), CAX
i
) is the distance from some 
point Q(x,y,z) in a 3D space to line CAX
i
 and the sum 
on the RHS of Eq. (1) is minimized over all possible 
3D points Q(x,y,z).   
All coordinates are computed in a natural frame 
of reference with the origin in the center of the ball 
marker and following three axes: horizontal axis of 
the gantry rotation, vertical axis and the third axis 
normal to the previous two. Then, the position of the 
36 

Image Anal Stereol 2017;36:35-41 
isocenter is calculated with the respect to the position 
of the ball center. Because in clinical settings the 
phantom is positioned using the treatment room lasers, 
the computations provide data sufficient e.g. to recali-
brate the lasers.  
CAX is fully specified by its orientation angle 
 (i.e. the gantry has only one rotational degree 
of freedom) and an anchor point A – a projection 
of the phantom ball marker onto CAX. Both the 
anchor point A and angle α must be determined 
from phantom image data to find the position of 
the radiation isocenter, according to Eq. (1). 
Denoting the source to detector panel distance by 
L, the ball to detector panel distance by L-l, and ball 
to anchor point A distance by d it follows from basic 
geometrical considerations that: 
 
L
D
l
d | sin | | | 
 , (2) 
where both D and  (Fig. 2) can be measured as in 
clinical settings the pixel size is known. 
Consequently, the coordinates of the CAX anchor 
point A are: 
) sin sin , cos sin , cos (      D
L
l
D
L
l
D
L
l
A  ,  (3) 
and the directional vector of CAX is fully specified by 
. Clearly, to find any CAX and to calculate the 
radiation isocenter from Eq. (1), both the ratio l/L and 
 must be determined from image data (Fig. 3). In the 
following we focus on solution to this problem.  
 
Fig. 3. A typical projection image of a cubic phantom 
with a ball marker inside. A radiation center is by 
definition the center of the crosshair. Any shift of the 
ball with the respect to the radiation center indicates 
imperfect geometrical conditions.  
The ratio l/L can be determined from the analysis 
of vertical profiles of projection phantom images (i.e. 
profiles parallel to the gantry rotation axis). Indeed, 
assuming geometry like in Fig. 4 (where s is the size 
of the cubic phantom and s
1 
+ s
2 
= s, and the phantom 
is not necessarily ideally positioned i.e., some shift 
from a CAX to the phantom center is accepted) it can 
be shown that the distance r(x), the ionizing radiation 
travels through the volume of the phantom is:  
 
2 2
1
1
2
) ( L x
x
s
l
L
x
s x r 














   . (4) 
 
Fig. 4. The geometry used for the calculation of the 
attenuation of the ionizing radiation along profiles 
parallel to the gantry axis. 
For x in the range specified in Fig. 4 by the 
dashed lines (i.e., from a minimal value x
min
 equal to 
) 2 / (
1
s L Ls  to a maximal value x
max
 equal to 
) 2 / (
1
s L Ls  ) and for l equal approximately to L 
(which is the case of clinical settings adopted in this 
study, as explained in the next section) the 
dependence of r(x) upon x can be reasonably assumed 
to be linear. Indeed, the extent of this range of x 
values is approximately equal to s
2
/L which for the 
adopted clinical settings is only a small fraction of s. 
Replacing in Eq. (4) x by x
min
+  and expanding r(x) 
around x
min
 with a Taylor’s series it can be shown that 
the nonlinear terms of the Taylor’s series can be 
neglected. Moreover, due to Beer-Lambert law the 
logarithms of gray values are proportional to r(x). 
Then it follows from triangles similarity that if we 
37 

NIED ŹWIECKI M ET AL: Quality assurance in radiotherapy 
measure the width Z of the vertical profile of the 
logarithm of gray values at the half of the profile 
height we have: 
 
l
L
s
Z
. (5) 
The rotation angle  can be determined from the 
analysis of horizontal profiles of projection phantom 
images (i.e., profiles normal to the gantry rotation 
axis). The geometry is however more complicated in 
this case (Fig. 5) as all possible scenarios of rays 
passing through the phantom must be considered. 
Although closed form expressions can be found also 
for this case we choose to approach the problem 
numerically by analyzing the limiting cases of X-rays 
sliding through the edges of the cube (dot-dashed 
lines in Fig. 5).  
 
Fig. 5. The geometry used for the calculation of the 
attenuation of the ionizing radiation along profiles 
normal to the gantry axis. 
It follows that the dependence of the distance 
r(x), the ionizing radiation travels through the volume 
of the phantom on the position along the horizontal 
profile can be approximated very well with a piece-
wise linear function (Fig. 6) and from the analysis of 
the asymmetry of the profile the rotation angle  can 
be extracted. 
 
r
position along horizontal profile
 
Fig. 6. Typical horizontal profile of the distance the 
ionizing radiation travels through the volume of the 
phantom. 
RESULTS 
In the study images of a phantom were acquired using 
PaxScan 4030 system and Acuity Simulation System 
(Varian Medical Systems, Salt lake City, Utah). The 
phantom was a cube with 70 mm edge length and 
2mm tungsten ball in the center. The system was 
operating at 60 kV, 80mA current, 5 ms exposition 
time and pixel size 0.194 x 0.194 mm. The spectrum 
of X-rays emitted by an X-ray tube fort such settings 
contains a strong characteristic line which justifies 
application of the Beer-Lambert low in the analysis 
of intensity profiles. The images were acquired for 
preset gantry rotation angles from 0 to 180 degrees 
with 15 degrees step. The values of rotation angles as 
displayed in the operator panel were different from 
the preset values by no more than 0.05 degree. The 
magnification of images was selected in the operator 
console of the simulator to achieve ratio l/L equal to 
1. For such settings the imaging system automatically 
resizes pixels of the acquired images to sizes 
corresponding to a panel detector crossing the center 
of a phantom. 
Sample vertical and horizontal profiles through 
the phantom before and after taking natural logarithms 
of gray levels are shown in Fig. 7 and Fig. 8, respect-
tively. Because the transition region between fore-
ground and background is very narrow for vertical 
profiles, in Fig. 7 we show for clarity only halves of 
the profiles. The shape of the profiles confirms quali-
tatively the analysis presented in the previous section.  
In the automated analysis of the profiles we 
focused on profiles crossing the center of the ball as 
projected onto the detector plane. The automated 
analysis started from extracting the position of the 
ball. The extraction of the ball was based on the histo-
gram-based (Fig. 9) segmentation of the phantom 
images. In all cases the histogram contained three 
modes corresponding to the background (low gray 
38 

Image Anal Stereol 2017;36:35-41 
levels), foreground (high gray levels) and phantom 
(intermediate gray levels) regions. 
 
 Gray level intensity
Position along a profile 
 
(a) 
 position along a profile
 log(gray level intensity)
 
 
(b) 
Fig. 7. Vertical profiles of a phantom image before 
(a) and after (b) taking logarithms of gray values. 
 
 gray level intnsity
 position along a profile
 
(a) 
 position along a profile
 log(gray level intensity)
 
 
(b) 
Fig. 8. Horizontal profiles of a phantom image before 
(a) and after (b) taking logarithms of gray values. 
Phantom images were segmented with threshold 
set to the value at the half distance between the two 
modes corresponding to the background and to the 
phantom. Then the ball was extracted as the black 
connected component closest to the center of mass of 
the white region. 
0 50 100 150 200 250
 
 
# of counts
gray level
 
Fig. 9. Histogram of gray levels of a phantom image. 
 
(a) 
 
 
(b) 
Fig. 10. An original (a) and a segmented (b) phantom 
image. 
Next, the center of mass C of the ball was computed 
and vertical and horizontal profiles crossing C were 
extracted from the original images and further analyzed 
after taking natural logarithms of gray levels. The data 
points inside black regions in segmented phantom 
images were discarded in the analysis. 
39 

NIED ŹWIECKI M ET AL: Quality assurance in radiotherapy 
The profile (either horizontal or vertical) was split 
into five regions: the left-most and the right-most 
modeled by a constant function and the middle three 
regions modeled by a linear function (Fig. 11). Prior 
to the split the phantom region was extracted from an 
original image by thresholding it with a threshold set 
in the middle between the histogram modes corres-
ponding to the foreground and the phantom regions. 
Then the split points P
1
, P
2
, P
3
, and P
4
 were found by 
a brute force search minimizing the total least squares 
fitting error under a constraint that the split points 
between constant and linear components of the model 
(P
1
 and P
4
) must be within the foreground region. 
0 100 200 300 400 500 600
9.3
9.6
9.9
10.2
10.5
10.8
11.1
 
 
ln(gray level)
position along a profile
 
Fig. 11. Logarithm of gray level intensity profile 
modeled as a piece-wise linear function. 
Given the split points P
1
, P
2
, P
3
, and P
4
 the height 
of the vertical profile was determined separately for 
the left and the right wing of the profile as the 
difference between ordinates of P
1
 and P
2
 and 
between P
3
 and P
4
. Then the width of the profile was 
set equal to the difference between the position of 
points at the half of the left height and at the half of 
the right height. The calculated values of the ratio l/L 
are shown in Fig. 12 for eleven tested gantry orien-
tations. On average the computed ratio l/L was equal 
to 0.999 with 0.0014 standard deviation compared to 
nominal value equal to one. 
The calculation of the rotation angle of the gantry 
required some more attention. For every angle in the 
range ±2 degrees around the nominal gantry rotation 
angles with 0.01 degree step we numerically generated 
profiles like in Fig. 6 but with a minus sign (to 
account for a minus sign present in the Beer-Lambert 
low). This process is straightforward as it requires 
calculation of coordinates of cube corners after rotation 
and calculation of the intersection points between the 
rays of ionizing radiation and phantom faces. In the 
calculations we used nominal values of L = l = 100 
cm which is the preset option in the PaxScan system 
for Winston-Lutz test and 70 mm phantom cube size. 
Then the generated profiles were compared with the 
profiles computed from the image. The angle corres-
ponding to the generated profile fitted best to the 
computed profile was selected as the calculated gantry 
rotation angle. The calculated values of the rotation 
angle are shown in Fig. 12 for eleven tested gantry 
rotations. The coefficient of correlation between no-
minal and computed gantry rotation angle was equal 
to 0.09997. The slope of the best fit line was equal to 
0.999 with 0.005 error. 
0 30 60 90 120 150 180
0.996
0.997
0.998
0.999
1.000
1.001
1.002
 
 
l/L
angle
 
P
4
 P
1
 
(a) 
0 30 60 90 120 150 180
0
30
60
90
120
150
180
 
calculated gantry rotation angle
nominal gantry rotation angle
 
P
2
 P
3
 
(b) 
Fig. 12. Ratio l/L (a) and rotation angle(b)as extra-
cted from the phantom images. 
DISCUSSION 
In the study we addressed the problem whether it is 
possible to extract some useful information about the 
geometry of a therapeutic device from projection 
images of a cubic phantom. In a clinical practice the 
only information extracted currently is the position of 
a center of a phantom as indicated by a ball marker 
with the respect to the center of the radiation field. 
We have shown that using still such a basic phantom 
additional information can be extracted, namely the 
ratio l/L and the gantry rotation angle . We have 
shown that there is a very good agreement between 
the nominal and calculated values of these quantities 
which is an important conclusion from the viewpoint 
of quality assurance. The calculated values of the 
ratio l/L and the gantry rotation angle  can be in turn 
used for more precise determination of the position of 
the radiation isocenter from Eq. (1) as the uncer-
tainties related to the discrepancy between preset and 
real values of these parameters may be eliminated 
this way. 
40 

Image Anal Stereol 2017;36:35-41 
41 
The developed method has been used for the 
analysis of phantom images acquired with a classical 
simulator which uses kV imaging. Although the method 
can be directly used for MV imagers of medical linear 
accelerators, the quality of MV images is worse than 
the quality of kV images. We expect however that the 
developed method can be still useful for MV images 
for example if the exposition time is increased to sup-
press noise. 
We have proposed an algorithm for automated 
analysis of the projection data to extract the afore-
mentioned quantities of interest. The algorithm is 
based on image analysis techniques. The results of 
the analysis can be further used to define axes of radi-
ation field and for the computation of the isocenter of 
radiation as defined in Eq. (1).  
The results of the study prove that it is possible to 
relax assumptions about an ideal geometry of a 
therapeutic device. It follows from the results of this 
study that analyzing projections of more than one 
phantom point we can subsequently extract informa-
tion about more geometric characteristics of the 
device. The amount of information about the geometry 
of a therapeutic device which can be extracted from  
 
images of commercially available phantoms used in 
routine clinical practice (e.g., the one used in the present 
study) is however limited to parameters evaluated in 
this study. 
ACKNOWLEDGEMENT 
The study was supported by NCBR grant No. POIR. 
04.01.04-00-0014/16. 
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