Computed Tomography Image Reconstruction in 3D VoxelSpace

International Journal of Modern Research in Engineering and Technology (IJMRET)
www.ijmret.org Volume 3 Issue 11 ǁ November 2018.
w w w . i j m r e t . o r g Page 1
Computed Tomography Image Reconstruction in 3D
VoxelSpace
M.S.M. Yusoff*, R. Sulaiman*, K. Shafinah**, R. Fatihah***
*Institute of Visual Informatics, National University of Malaysia (UKM), 43600 Bangi, Selangor, Malaysia.
**Faculty of Agriculture and Food Sciences, Universiti Putra Malaysia Bintulu Sarawak Campus, Nyabau
Road, P.O. Box 396, 97008 Bintulu, Sarawak.
***Faculty of Computer Science and Information Technology, Universiti Malaysia Sarawak (UNIMAS), 94300
Kota Samarahan, Sarawak, Malaysia.
ABSTRACT : The aim of the study was to investigate the relationship between 2D gray scale pixels and 3D
gray scale pixels of image reconstructions in computed tomography (CT). The 3D space image reconstruction
from data projection was a challenging and difficult research problem. The image was normally reconstructed
from the 2D data from CT data projection. In this descriptive study, a synthetics 3D Shepp-Logan phantom was
used to simulate the actual data projection from a CT scanner. Real-time data projection of a human abdomen
was also included in this study. Additionally, the Graphical User Interface (GUI) for the application was
designed using Matlab Graphical User Interface Development Environment (GUIDE). The application was able
to reconstruct 2D and 3D images in their respective spaces successfully.The image reconstruction for CT in 3D
space was analyzedalong with 2D space in order to show their relationships and shared properties for the
purpose of constructing these images.
KEYWORDS: - Computed Tomography, DICOM, Image reconstruction, Pixels, Voxels,
I. INTRODUCTION
This research focuses on aspects of image
reconstruction for computed tomography (CT) in
3D space.Sinogram images are a raw projection of
data from the CT scanner that is plotted to show a
graphical view of the projection data. These images
were often incomprehensible and useless especially
for applications in industrial business or in vitro
medicine.Should it be possible to reconstruct these
images rigorously through the application of
suitablealgorithms, then the invaluable hidden
properties and informationcontained within the
images ofthese internal object structures could be
displayed as real world images.
The transformation of sinogram data into
an ontological cross-section image is often labeled
as image reconstruction in computed
tomography[1].Fig. 1 shows a simple illustration of
the physical schematics of a CT scanner.They
consist of an x-ray source, detector assemblyarray,
radiation collimators and apatient bed conveyor.
They were set-up and aligned to measure the
heterogeneous density of x-ray readings after
penetrating the object. According to [2]the log-
attenuation count was a sinogram or projection data
that consistsof a multiple 2D cross-section
arrangement.
Figure 1: A simple model of a CT scanner
[2]

II. RESEARCH METHOD
According to [3] research, the 3D
sinograms wererebinding into 2D projections to
perform the forward and backprojection operations,
but were converted back into 3D sinograms in
between each iteration. Also, according to [4], the
3D cone-beam projections of N x N x M pixels
were decomposed to separate the 2D parallel-beam
projections.
The FDK method is a notable algorithm
that reconstructs a 3D volume from multiple 2D
projections. In this method, each of the 2D
projections were weighted, filtered and back-
projected, then constructed in a solid 3D form [5].
This optimization method was unavoidable in CT
image reconstruction due to the large size of
thevolumes.It holds millions of voxels and the
sinogram may consist of millions of projection
measurements [6].
2.1 Radon Transform
The projection problems in CT scans were
mathematically explained by the function of Radon
transformation[7]. Therefore, many difficult
computational methods have been developed to
solve the reconstruction problems of the inverse
Radon transformation[8].The image reconstruction
begins with data collection. This study used
theDigital Imaging and Communications in
Medicine (DICOM) data format[9]which
wascreated or collected within the study period. In
order to create and built a DICOM data, the raw
data wasinitially transformed into a 1D vector and
then reshaped into the desired 3D format.
2.2 The pixels and voxels
The standard terms of pixels and voxels
are widely used to represent the basicmeasurements
of a picture. Pixels were defined as an element that
has two dimensions, the horizontal dimension
representing the element’s x-axis and the vertical
dimension representing the element’s y-axis.
Concurrently voxels or 3D pixels were defined as
having a 3D spatial resolution which were stored in
the sequence of x-y-z[10]. Fig. 2 shows the
differences between these three types of image
space. First, the image in 2D pixels as shown in Fig.
2(a) and Fig. 2 (b), secondly the image in 3D pixels
as shown in Fig.2 (c) and Fig. 2(d) and finally, the
image in voxels as in Fig. 2(e) and Fig. 2(f).
Figure 2: The 2D pixels, 3D pixels and voxels
model
Voxelsare often illustrated as a solid
rectangular model, its dimensions were measured
by the reconstruction field-of-view (FOV) and slice
thickness [11]
2.3 The basic concept of cross-sectional
planes
The human body can be viewed as three
sets of cross-sectional universal planes [12]. The
first plane is the top view plane, which runs parallel
to the ground. Itis referred to by several different
names such as the transverse plane, horizontal
plane, axial plane, transaxial plane or x-z plane.The
second plane is the side view plane which is often
referred to as the sagittal plane, lateral plane or y-z
plane. Finallythe third plane known as the front
view plane and often referred to as the coronal
plane, frontal plane or y-x plane. Fig. 3 shows the
diagram of axial, sagittal and coronal cross-section
planes of the human body.
Figure 3: The diagram of axial, sagittal and
coronalcross-section planes

2.4 Conceptual of CT Data visualization
In science and engineering, data points are
commonly acquired through sampling and
experimentation. These function as plots to
construct a rough figure.However, through
numerical analysis known as the interpolation
method,additional datacan be generated to plot a
smoother graphical image. This is known as curve
fitting or regression analysis [13]. Fig. 4 shows the
fundamental flow diagram of a 3D image
reconstruction[14].Theimage interpolation
algorithm of the 3D image reconstruction was
carried out from original images by adhering to the
fundamental flow diagram.
Figure 4: The fundamental flow diagram of 3D
image reconstruction[14]
2.5 2D Pixel-BasedMethod
The pixel building blocks were established
from two common parameters, namelythe image
length and width[15].Table 1 shows a simple
concept of 2D numerical raw data intensity. The
table’srows consist of ninepixel elements
representing thedimension’s length, similarly the
table columns consist of ninepixel elements
representing the dimension’swidth. The rows and
columns represent a slice in 2D pixels. As for
thisstudy, the zero value will be represented using
the color the black’sdensity and the one value will
be represented by the density of the color white.
The zeroscan be visualized as a plus sign image
from theraw dataitself. The raw data can then be
saved in a file or stored within the database system
for easy retrieval in the future.
Table 1: The raw numerical data represent intensity
in 2D
1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1
0 0 0 0 0 0 0 0 0
1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1
Table 2 shows the addresseslocation of the
pixels’for the 2D pixels from the raw data intensity
as shown in Table 1. Thelocation wasspecifically
used to display the corresponding pixel intensity on
the computer screen.
Table 2: The addresses of the 2D pixels’location of
the raw data intensity as shownin Table 1
(1,1) (1,2) (1,3) (1,4) … (1,9)
(2,1) (2,2) (2,3) (2,4) … (2,9)
(3,1) (3,2) (3,3) (3,4) … (3,9)
(4,1) (4,2) (4,3) (4,4) … (4,9)
(5,1) (5,2) (5,3) (5,4) … (5,9)
(6,1) (6,2) (6,3) (6,4) … (6,9)
(7,1) (7,2) (7,3) (7,4) … (7,9)
(8,1) (8,2) (8,3) (8,4) … (8,9)
(9,1) (9,2) (9,3) (9,4) … (9,9)
Finally, Fig. 5 shows a 2D image that was
reconstructed from the data in Table 1 using
MATLAB numerical computing language. This 2D
image was significant to further the knowledge
forthe reconstruction of the targeted 3D imageused
in the present study.
Figure 5: The 2D image constructed from the raw
data intensity in Table 1
2.6 3D Pixel Method
In contrastto the 2D pixels, the 3D pixels
building blocks were established from three
parameters consisting of the length, width and
height data.Table 3(a) and (b) showsa concept of
the 3D raw numerical data intensity.The rows in
the table represent the dimension’s length and the
columns represent the dimension’swidth
similarlyto those of the 2D pixels. Therefore, 3D
data consisted of a collection of 2D data. Hence,
3D data blocksrequired two or more 2D datasets to
reconstruct a 3D image. Again, in 3D space, the

value of zero are represented by the intensity of the
color black and the value of one was represented by
the intensity of the color white.
Table 3: The raw numerical data representing data
in 3D space
1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1
a) First 2D Slice b) Second 2D
Slice
Table 4 and Table 5show the3D pixels
address locations from the raw data intensity shown
previously in Table 3(a) and (b). Thelocation
wasspecifically used to display the corresponding
pixel intensity on the computer screen.As in Table 4
and Table 5, there are three values in each cell of
3D pixels representing each corresponding row,
column and depth.
Table 4: The location address of the first slice of
the raw data intensity as shown in Table 3(a)
(1,1,1) (1,2,1) (1,3,1) … (1,9,1)
(2,1,1) (2,2,1) (2,3,1) … (2,9,1)
(3,1,1) (3,2,1) (3,3,1) … (3,9,1)
(4,1,1) (4,2,1) (4,3,1) … (4,9,1)
(5,1,1) (5,2,1) (5,3,1) … (5,9,1)
(6,1,1) (6,2,1) (6,3,1) … (6,9,1)
(7,1,1) (7,2,1) (7,3,1) … (7,9,1)
(8,1,1) (8,2,1) (8,3,1) … (8,9,1)
(9,1,1) (9,2,1) (9,3,1) … (9,9,1)
Table 5: The location address of the second slice of
the raw data intensity as shown in Table 3(b)
(1,1,2) (1,2,2) (1,3,2) … (1,9,2)
(2,1,2) (2,2,2) (2,3,2) … (2,9,2)
(3,1,2) (3,2,2) (3,3,2) … (3,9,2)
(4,1,2) (4,2,2) (4,3,2) … (4,9,2)
(5,1,2) (5,2,2) (5,3,2) … (5,9,2)
(6,1,2) (6,2,2) (6,3,2) … (6,9,2)
(7,1,2) (7,2,2) (7,3,2) … (7,9,2)
(8,1,2) (8,2,2) (8,3,2) … (8,9,2)
(9,1,2) (9,2,2) (9,3,2) … (9,9,2)
Finally, Fig. 6 shows the image plot using
3D data fromTable 3(a) and (b) using MATLAB
numerical computing language.
Figure 6: Images of 3D density plot fromTable 3(a)
and (b)
2.7 Voxel-Based Methods
The voxels were 3D coordinates in spatial
space similar to the 3D pixels which were also
established from the three basic parameters of
length, width and height. The voxelmethod consists
of 3D pixels in the shape of 3D cubeswhich
formedthe complete objects. According to
[16]eachvoxel infrastructure can be recognized asa
3D pixel which was similar to the dimensions of a
cube. Fig. 7 shows the result of voxels produced
through the use of MATLAB add-on application
GIBBON created by [17]. The images
wereconstructed from ahomogeneous intensity data
to show a 3D concept through the voxel-based
method.

Figure 7: Voxels[17]
The voxel-based method can easily be
understood by viewing their appropriate sketches.
Figure 8 shows MATLAB dimension cube of the x,
y and z dimension from the origin of point (0, 0, 0).
This singleton cube is the conceptual building
block of a much larger voxel dimension with
contrasting intensities.
Figure 8: MATLAB dimensional cube

III. RESULTS AND ANALYSIS
The prototype application was developed
based on the MATLAB script program and
information from previous literature dedicated to
3D image reconstruction of computed tomography.
The 3D data projection was obtained from an
online research platform (with consent to use
obtained for research purposes).Figure 9 shows the
axial, coronal and sagittal views of a 3D Shepp-
Logan phantom. These images were built with a
similar program as those discussed in the
methodology section, but with the addition of a 3D
phantom in DICOM format. The axial, coronal and
sagittal views were changed and
correspondedaccordingly to the x,y mouse location
on a picture canvas.Figure 10shows the internal
properties of ahuman abdomen from a DICOM
data projection in 3D.
Figure 9: Axial, Coronal and Sagittal Views
Figure 10: 3D Images Slices of Axial, Coronal and
Sagittal
Additionally,Figure 11 show slices of 2D
axial views from a synthetic 3D Shepp-Logan
phantom data projection. These slices were
displayed using afour times four grid. The images
werecreated using MATLAB script function of
phantom3dasproposed by Matthias Christian
Schabel of the Department of Radiology, University
of Utah. There are several free and paidtoolsrunning
on various platformswith the capability to slice a 3D
image into 2D slices, for example 3Dslicer, OsiriX,
SliceOmatic and Seg3D.
Figure 11: 2D Slices of Axial Views

Fig. 12 shows a 3D voxel-based
imageplotted using MATLAB add-on application
GIBBON. Fig. 12 a) shows the 3D slicer tool usedto
slice the object visually in 3D space; while Fig. b)
shows a 3D Shepp-Logan phantom image; and last
of all, Fig. 12 c) shows a 3D gray scale of a human
heart. The slicer can move in the x-axis, y-axis and
z-axis to perform the task of slicing.
a) 3D slicer tool
b) 3D phantom image
c) 3D gray scale of a human heart
Figure 12: 3D views a) 3D slicer tool b) 3D
phantom image c) 3D gray scale of a human heart
The experiments in the present study were
conducted on computers running theWindows 7 and
Windows 10 operating system with a minimum
hardware requirement of Intel Core i5-2410M,
CPU (2.3GHz), 4GB DDR3 RAM and 750 GB
HDD. Themajor application software utilized for
the purposes of the study was Matlab version 2008a
with image functionality capabilities.
IV. CONCLUSION
The image reconstruction for CT in 3D
space was studied along with 2D space to show the
shared properties they hold to build an image. The
3D images could be used to represent a real image
that will help people to recognize the scan’s object
without requiring a detailed description.
REFERENCES
[1] Quinto, E. T. An Introduction to X-ray
tomography and Radon Transforms. In
Proceedings of the Proceedings of
Symposia in Applied Mathematics The
Radon Transform, Inverse Problems, and
Tomography. American Mathematical
Society, Atlanta, 2006, 1-23.
[2] Karimi, S. Metal Artifact Reduction in
Computed Tomography. Ph.D., University
of California, San Diego, Ann Arbor, 2014.
[3] Keesing, D. B. Development and
Implementation of Fully 3D Statistical
Image Reconstruction Algorithms for
Helical CT and Half-Ring PET Insert
System. Dissertation, Washington
University, All Theses and Dissertations
(ETDs), 2009.
[4] George, A. K. Algorithms for tomographic
reconstruction: Fast backprojection and
cardiac computed tomography University
of Illinois Urbana, Illinois 2007.
[5] Leeser, M., Mukherjee, S. and Brock, J.
Fast reconstruction of 3D volumes from 2D

CT projection data with GPUs. BMC
Research Notes, 7(1), 2014, 1-8.
[6] Jørgensen, J. S. H., Per Christian; Schmidt,
Søren Sparse Image Reconstruction in
Computed Tomography. PhD, Technical
University of Denmark, 2013.
[7] Clackdoyle, R. and Noo, F. A large class of
inversion formulae for the 2D Radon
transform of functions of compact support.
Inverse Problems, 20(4), 2004, 1281-1291.
[8] Gottleib, D., Gustafsson, B. and Forssen, P.
On the direct Fourier method for computer
tomography. Medical Imaging, IEEE
Transactions on, 19(3), 2000, 223-232.
[9] Flanders, A. E. and Carrino, J. A.
Understanding DICOM and IHE. Seminars
in Roentgenology, 38(3), 2003, 270-281.
[10] Mueller, K. Fast and Accurate three-
dimensional reconstruction from cone-
beam projection data using algebraic
methods. PhD, The Ohio State University,
1998.
[11] Hsieh, J., Nett, B., Yu, Z., Sauer, K.,
Thibault, J.-B. and Bouman, C. A. Recent
Advances in CT Image Reconstruction.
Current Radiology Reports, 1(1), 2013, 39-
51.
[12] Ohnesorge, B. M., Flohr, T. G., Becker, C.
R., Knez, A. and Reiser, M. F. Multi-slice
and Dual-source CT in Cardiac Imaging
(Springer Berlin Heidelberg, 2007).
[13] Xu, J. Data Interpolations. Apress, 2010.
[14] Xueli, Z., Wanggen, W., Zhenghua, Z.,
Rui, W. and Feng, Q. A novel interpolation
algorithm for 3D reconstruction of medical
images. In Proceedings of the Audio
Language and Image Processing (ICALIP),
2010 International Conference, 2010, 797-
801.
[15] Smith, S. and Ray, A. A Pixel Is Not A
Little Square, A Pixel Is Not A Little
Square, A Pixel Is Not A Little Square!
(And a Voxel Is Not A Cube)”. Microsoft
Technical Memo 6. Microsoft. 1995.
[16] Chan, L. H. Synthetic three-dimensional
voxel-based microstructures that contain
annealing twins. Ph.D., Carnegie Mellon
University, Ann Arbor, 2010.
[17] Moerman, K. M. GIBBON (Hylobates Lar).
Zenodo, 2016.

Computed Tomography Image Reconstruction in 3D VoxelSpace

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