10.18605/2175-7275/cereus.v13n3p68-82
<<Recebido em: 05/07/2021
Aceito em: 25/09/2021. >>
ARTIGO ORIGINAL
3D reconstruction method applied to sediment layers in computed tomography
geometry
Método de reconstrução 3D aplicados a camadas de sedimentos em geometria de
tomografia computadorizada
Joel Sánchez Domínguez1, Gabriela Hoff2, Joaquim Teixeira de Assis3, Antonio
Brunetti4, Susana Marrero Iglesias5
RESUMO
A obtenção de informações sobre o depósito de sedimentos é uma tarefa difícil devida
à fragilidade do meio analisado. A utilização de testes não destrutivos para produzir
dados confiáveis nesses ambientes está sendo avaliada por vários pesquisadores. O
presente estudo propõe a avaliação da geometria de irradiação de tomografia
computadorizada (TC) para obtenção de imagens das camadas de testemunhos de
sedimentos. Num primeiro estágio, imagens planares de objetos geométricos em
geometria centrada, similar a utilizada em processos de tomografia computadorizada,
foram simuladas usando o código dedicado X-Ray Monte Carlo (XRMC).
Posteriormente as radiografias foram processadas usando o algoritmo de reconstrução
Feldkamp, David e Kress (FDK) para gerar o volume tridimensional. O método FDK foi
avaliado para reconstrução de imagens definidas com 8 e 64 bits de cores. O método
de reconstrução apresentou-se adequado para reconstruir imagens usando 64 bits na
escala de cinza mostrando uma exatidão nas medidas dos objetos de contraste com
desvios máximos de 8%. Artefatos de imagens, vantagens e desvantagens do método
de reconstrução para o caso avaliado são abordados nesse artigo. Os resultados
obtidos mostram a possibilidade de aplicação da metodologia para produzir imagens
detalhadas de testemunhos de sedimentos coletados em lagos, rios ou tanques de
simulação de deposição.
Palavras-chave: Tomografia Computadorizada. XRMC. Algoritmo FDK. Imageamento
de Sedimentos.
ABSTRACT
Obtaining information on sediment deposition is a difficult task due to the fragility of the
analyzed medium. The use of non-destructive tests to produce reliable data in these
environments is being evaluated by some researchers. The current study proposes the
computed tomography (CT) irradiation geometry evaluation, for obtaining images of the
sediment deposition layers. As a first stage, planar images of geometric objects in
centered geometry, similar to those resulting from the CT processes, were simulated
using the dedicated X-Ray Monte Carlo (XRMC) code. Then, the x-rays were processed
using the Feldkamp, David and Kress (FDK) reconstruction algorithm to generate the
three-dimensional volume. Evaluating the FDK method for the reconstruction of the 8 to
64 color bits images, the obtained results were satisfactory for 64 bits grayscale images.
The method showed accuracy in the contrast objects measurements, presenting a
maximum deviation of 8%. This article discusses the constructed image artifacts and
also, the advantages and disadvantages of the reconstruction method. The results show
the feasibility of applying the methodology to produce detailed images of sediment
samples collected in lakes, rivers or deposition simulation tanks.
1
Doutor
em
Modelagem
Computacional pelo IPRJ/UERJ.
Instituto Politécnico Universidade
do Estado do Rio de Janeiro
https://orcid.org/0000-0003-43308593
E-mail: jsdominguez@iprj;uerj.br
2
Doutora
em
Biociências
Nucleares pela UERJ
Instituto Nazionale di Fisica
Nucleare (INFN) - Sezioni di GE
https://orcid.org/0000-0002-74608030
3
Doutor em Engenharia Nuclear
pela UFRJ.
Instituto Politécnico Universidade
do Estado do Rio de Janeiro
https://orcid.org/0000-0002-40276939
4
Doutor em Física Médica pela
USP.
University of Sassari, Italy
https://orcid.org/0000-0002-01161899
5
Doutora
em
Modelagem
Computacional pelo IPRJ/UERJ.
Universidade Estadual de Santa
Cruz, Ilhéus Bahia.
https://orcid.org/0000-0002-49556216
Keywords: Computed Tomography. XRMC. FDK Algorithm. Sediments Imaging.
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DOMINGUEZ, J.S; HOFF, G; DE ASSIS, J.T; BRUNETTI, A;
IGLESIAS, S.M
3D reconstruction method applied to sediment layers in computed
tomography geometry
1. INTRODUCTION
The characterization of regions using the computational simulation of the sediment
deposition process is widely used in geological studies (MIALL, 2006; BJORLYKKE,
2015). Nevertheless, as a result of the sediment deposition structures fragility, its
evaluation must be done through minimally invasive or non-invasive methods. This kind
of methods avoids destroying information from the unstable and delicate structure.
Computed tomography (CT) is a non-destructive test that allows to obtain images of
the axial sections from a set of an object x-rays (DOMINGUEZ, 2016). The transmission
and processing information about the planar images generate a stack of cutaway images
of the object. The internal structures can be characterized by the shade of gray and
position. CT is a widely accepted technology with numerous applications in medicine,
industry and scientific research (DOMINGUEZ, 2016).
The present study proposes to explore the 3D Feldkamp, David and Kress (FDK)
reconstruction method for the evaluation of collected sediment samples. These samples
are designed according the data collection geometry used in CT to obtain images of
sediment layers. The FDK reconstruction algorithm is a filtered back-projection algorithm
for tomographic images 3D reconstruction (DOMINGUEZ, 2016). In order to evaluate the
reconstruction method, it was used planar images generated by simulation with the X-Ray
Monte Carlo software (XRMC) considering radiographic images generated in a similar
geometry to those obtained using a CT equipment. In the following section we briefly
discuss some characteristics of CT, the reconstruction method and the XRMC package.
In section 3 we describe the methodology applied, including the data preparation and the
application of the reconstruction model. In section 4 we present the preliminary results for
the created images. Finally, we present the conclusions and the next steps in this
research.
2. COMPUTED TOMOGRAPHY AND THE RECONSTRUCTION METHOD
CT can be analyzed as a two-step process: the exploration of the samples through the
planar images generation and the axial cuts images reconstruction. Generally, in the
exploration step, a source/detector set is used to irradiate the studied object in different
angles, detecting the radiation amount that passes through the object (transmission study).
The result of this process are, flat images, for every irradiated angle. This set of images can
be obtained rotating the source/detector set around the body or otherwise by the object
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rotation in front of the emission source. The simulation process performed in this work to
obtain the planar images emulates the scanning, in which the object rotates and the
source/detector set is fixed. This type of exploration is similar to the irradiation geometry in
CT equipment for research and industrial applications due to its lower mechanical
complexity.
In the 3D reconstruction step of the CT process, a computational algorithm calculates
every planar image´s contribution for each volume point to be reconstructed. In this work,
the FDK algorithm (FELDKAMP et al., 1984) was used to do the reconstruction. The FDK is
an analytical reconstruction algorithm for cone beam, which has been the basis of the most
commonly used algorithms (KALENDER, 2011). The formulation is only valid for circular
trajectories of the radiation source. Variations of the algorithm were developed for helical
trajectories (OLIVEIRA, 2002). Equation 1 shows how the FDK algorithm calculates density
f(r) as a function of the filtered projections PΦ(Y,Z) from planar images.The subscripts i, r, k
reflects the discretization of these projections. Further details regarding the algorithm
mathematical basics can be consulted in (DOMINGUEZ, 2016) and (FELDKAMP et al.,
1984).
f (r ) =
1
4
2
i
d2
Pi (Yr , Z k )
(d + r xˆ ') 2
(1)
After axial planes reconstruction, the images can be stacked to visualize the volume
as a whole. The rendered volume can be manipulated with imaging tools to produce lateral
or sagittal plane images, and also, frontal or coronal planes.
The reason of the selection of the FDK algorithm in this work to perform the
reconstruction is that being an analytical algorithm its performance (time and processing) is
better when compared with other algorithms as the iterative ones. On the other hand, it
produces excellent results in different CT applications (KALENDER, 2011). However, it has
some limitations such the raising of computational cost when the image quality increases
(SHUNLI et al,.2018) and also the algorithm need a full exploration of the object (360o
images) to performs the study. These characteristics complicate its use for on-site studies
and real geometries (rivers, lakes and / or simulation tanks) when only some section's
radiographies are available for analysis. Nevertheless, for a sample study (geological
evidences), this method is a good alternative.
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3D reconstruction method applied to sediment layers in computed
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2.1. COMPUTATIONAL IMPLEMENTATION OF THE FDK ALGORITHM
To implement the FDK reconstruction algorithm, a C ++ program was developed. The
program input data included:
a) number of projections;
b) width and height of images projection;
c) images projections;
d)reconstruction initial and final plane.
The program output is a RAW file containing the reconstructed image, a volume with
a square base with a side equal to the width of the image projections and a depth equal to
the number of the reconstructed planes, the difference between the final and initial planes
of the reconstruction. The RAW format is used for digital images and contains all the
available image data. This format is used in TC to store images complete sequence obtained
from the sample exploration. Figure 2 shows the implemented program flow diagram to
execute the reconstruction process.
Figure 1. Software routine flow diagram developed for reconstruction process.
In this implementation, a background image (no object present) is used to compare the
maximum radiation at the detector with and without the sample. In 8-bit color images, this
background image had a fixed value in all of its pixels, however, using 64-bit color images
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tomography geometry
the fixed value in the background image produces distortions in the planar images. For that
reason, it was necessary to create a simulated background, an x-ray generated in the same
geometry but without the object. In the reconstruction final stage, a normalization of the
pixels in the volume was made using the images grayscale limits. In the 8-bit images these
limits were fixed from 0 to 256 but in 64-bit images, the maximum and minimum values
produced during the reconstruction were used, generating a better visualization of the low
contrast images.
3. SOFTWARE X RAY MONTE CARLO
The XRMC is a dedicated Monte Carlo code for precise simulation of images generated
by X-ray transmission and spectroscopy experiments in heterogeneous samples. The use
of the Monte Carlo method makes the code suitable for detailed simulation of complex
experiments in generic samples. The program is written in C ++ and has been tested on
Linux, Mac OS X and MS Windows platforms. The software package is being developed by
the University of Sassari researchers and is available for the scientific community use under
a general GNU license (GOLOSIO et al., 2013).
Approximations of the Monte Carlo method are often used to simulate the particles
interactions with the matter, under different experimental conditions. However, these
methods applied to X-ray imaging and spectroscopy experiments require a high
computational effort. Also, have some other limitations such as the inclusion of a limited
region of the space or photons produced by rare interaction in the final channels. To solve
these problems, the XRMC combines the Monte Carlo method with variance reduction
techniques, reducing by several orders the simulation times (OLIVA et al., 2015).
Several XRMC applications have been reported in the literature recently as (HOFF et
al., 2017; MANSO et al., 2015; BRUNETTI et al., 2016; HOFF et al., 2010). XRMC has a
user-friendly interface, with scripts to determine the devices that describe the geometry,
material, quantities to be simulated, and final results output format.
3.1. USE OF XRMC
Before running XRMC, is necessary to define the input files that describe the
experimental setup that you want to simulate. These files include a main input file, a
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parameter file, and some device files. Device files contain the necessary parameters for the
C ++ objects, used to perform the simulation. The main input file specifies the commands to
load all device files, to execute the simulation, and to save the output file (GOLOSIO et al.,
2013).
The typical configuration for X-ray imaging simulations or spectroscopy experiments
includes the following device files (GOLOSIO et al., 2013):
• source device;
• spectrum device;
• detector device;
• sample device;
• composition device;
• quadricarray device;
• geom3d device (three-dimensional description of object geometry).
3.2. SAMPLE EXPLORATION SIMULATION METHODOLOGY
As shown in section 2 the process of scanning CT samples consists of producing xrays of the interest object (in this case, sediment samples) from different angles, completing
a full turn over the object. In our simulation one x-ray is produced for each rotation angle,
totalizing 360 images for a complete rotation.
The XRMC software generates an image under the experiment specified conditions.
Then to simulate the CT scanning process, is necessary to rotate the sample under analysis
by running the simulation program for each set of input files. These input files represent the
different positions (data collection angles) in which the object planes´ images must be
produced. The methodology described is shown in figure 2.
The methodology execution, including the XRMC run and the input files update
process was performed using a Linux shell script, that allows to perform these two processes
at the same time. The modified input files were, the main file, to change the name of the
next output file and the quadricarry file to rotate the studied object.
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Figure 2. Flux diagram of the methodology to simulate CT samples exploration.
4. RESULTS
To represent the sediment layers in the XRMC, were simulated volumes with acetylene
(C2H2) as Base Material (BM) and acetylene with 10% Barium (C2H290% Ba10%) as
Contrast Object (CO) (HOFF et al., 2017). The BM object was a cube with side varying from
10 to 50 cm, to evaluate the method. As COs, different geometric shapes were placed in the
center of the cube. For samples with thicknesses up to 30 cm, a monochromatic photon
beam of 30 keV was used. However, for samples with 30 to 50 cm thicknesses, were used
a beam of photons of the Ir-192 spectra, generating satisfactory results.
Sediment imaging involves working with low contrast images. In initial tests, images
with 8-bit color, and 256 gray tones were used, and the BM was a 10 cm side cube. In all
simulations, the sample was placed in the center of the source-detector assembly. For 10
cm samples, the distance between the source and the detector was 40 cm. Figures 3 and 4
show an x-ray and a reconstruction plane for two COs, a 5 cm cube and a 2 cm radius
sphere.
Observing the reconstructed images in Figures 3 and 4 we can notice that some
artifacts emerge in the images. The visual analysis suggests reasonable quality images.
Nevertheless, a more accurate analysis using automated macros in Fiji to compare the
reconstructed volumes to the simulated volumes was unviable due to these artifacts and
also the noise in the images.
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Figure 3. CO 5 cm cube, BM 10 cm cube, 8-bit colors. (a) Simulated radiograph for 0°
observation angle, (b) central plane of the reconstruction.
Figure 4. CO 2 cm radius sphere, MB 10 cm cube, 8-bit colors. (a) Simulated radiograph
for 0° observation angle, (b) central plane of the reconstruction.
To overcome this problem, 64-bit color images were used, resulting in images with 1.8
x 1019 shades of gray. Figure 5 shows an X-ray and a reconstruction plane for a cubic OC
of 5 cm side and a 10 cm side's cube of MB, using a 64-bit color images.
The x-ray in Figure 5 (a) represents appropriately the explored volume, even though,
the low contrast between the BM and the OC in the image center difficult its detection
visually. In Figure 5 (b), the reconstructed image, using 64-bit color, presents the same
artifacts reported in the 256-grayscale images. However, in this case, the enhanced images
and the noise reduction allow the automatic processing for statistical analysis.
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tomography geometry
Figure 5. CO 5 cm cube, BM 10 cm cube, 64-bit colors. (a) Simulated radiograph for 0°
observation angle, (b) central plane of the reconstruction.
Figures 6, 7, 8 and 9 show axial, sagittal and coronal planes of the reconstructed
volumes center, for several COs with different dimensions' BMs using the 64-bit color
images. The simulated COs were elliptical base cylinder and also, different layers varying
its thicknesses and sizes. For samples of 30 cm side BMs the distance between the source
and the detector was 100 cm and, for 50 cm side BMs this distance was 200 cm.
Figure 6. Reconstructed volume central planes for a cylindrical CO with BM 10 cm cube
and 64-bit color images. (a) Axial plane, (b) sagittal plane and (c) coronal plane.
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tomography geometry
Figure 7. Reconstructed volume central planes for a layer CO with BM 10 cm cube and
64-bit color images. (a) Axial plane, (b) sagittal plane and (c) coronal plane.
Figure 8. Reconstructed volume central planes for a three-layers CO with a BM 30 cm
cube and 64-bit colors. Axial plane (a), sagittal plane (b), coronal plane (c).
Figure 9. Reconstructed volume central planes for a layer CO with BM 50 cm cube and
64-bit color images. (a) Axial plane, (b) sagittal plane and (c) coronal plane.
In figures 6 and 7, is possible to observe that in the three planes the COs have well
delimited edges without artifacts inside, and that several artifacts appear between the COs
and the BM. In Figures 8 and 9 the COs edges are well delimited but a discontinuity appears
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tomography geometry
in the center of the layers in the coronal plane resulting from the signal intensity decreasing.
Nevertheless, this artifact presence does not interfere in the automatic segmentation or CO
measurement. Using automated macros in Fiji, a statistical comparison was performed
between the simulated volumes (the expected object dimensions defined in the simulation)
and the reconstructed volumes (the reconstructed objects' measured dimensions), obtaining
errors less than 8%. The COs used on all samples had similar dimensions, the difference
observed between the COs sizes in the figures 7, 8 and 9 are due to the different distances
which detector were positioned to be able to irradiate the entire volumes.
In Figures 6 and 7 with smaller size samples and a lower energy beam the COs are
most notable in the images. When the size and the energy beam increase in Figures 8 and
9, the contrast between the COs and the BMs decreases. Nevertheless, is still possible to
differentiate the COs as a solid layer.
With these results, is possible to affirm, that the FDK algorithm was adequate to
perform the samples 3D reconstruction considering the analyzed imaging, producing the
axial images for the compared reconstructed volumes.
4.1. ARTIFACTS FOUND IN RECONSTRUCTED IMAGES
As can be noticed in the Figs (3-9), artifacts appear in all the reconstructed images
dependents on the object's geometry and its edges. The reconstruction basis of the FDK
algorithm is strongly linked with the object's edges, what is shown by the presence of these
artifacts in our reconstructions. The fact of having low contrast images seems to reinforce
this behavior. The mentioned artifacts are generated both in 8-bit color images, and in 64bit color images, however there are more evident in the 64-bit images. Nevertheless, in 64bit images, the signal intensity difference is greater in each region diminishing the artifacts
interference. This factor, prevents low-resolution images automatic processing and does not
jeopardize this process for high-resolution images.
It is important to point out, that the images were balanced (especially contrast and
brightness) in order to highlight the artifacts, making them more evident for this discussion.
The artifacts associate with the edges and are generated inside the cube that forms
the BM and also, inside and outside the COs. Figures 10 and 11 show, respectively, the
artifacts in the cubic OCs slices for 8-bit and 64-bit color images. In figure 11 the artifacts
appear sharper and are observed in larger quantity if compared with the figure 10. This is
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due to the better image, nevertheless, a detailed analysis showed similar artifacts in both
images. In the case of the cubic CO, the edges are located in the same positions for all the
slices in which the cube is present, for that reason, similar artifacts appear in these slices.
Regard the CO spherical geometry (figure 12) where the edges appear different in each
slice, the artifacts also differ between the different slices. All of these artifacts are generated
in a kind of ghost image where there is an object edge enhancement, but the signal strength
remains constant. This type of artifact appears a few slices (from 3 to 5) before that a
specific-material object appears and there are easily recognizable, if the contrast between
the materials is considerable (that is, greater than the statistical fluctuation for each material
signal).
Figure 10. Artifacts in a cubic OC for an 8-bit color image. Artifacts at the edges of the
outer cube (a), artifacts external to the OC (b), artifacts internal to the OC (c).
Figure 11. Artifacts in a cubic OC for a 64-bit color image. Artifacts at the edges of the
outer cube (a), artifacts external to the OC (b), artifacts internal to the OC (c).
Figure 12 shows the identified artifacts for a sphere's CO. In Figure 12 (a) only the
artifacts of the outer cube are observed, since the CO is far from the edge. In Figures 12 (b)
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when the OC begin to appear and 12 (c) 40% the OC appears, the artifacts are different
depending on the CO edges at different slices.
Figure 12. Artifacts in a spherical OC for 64-bit color. Artifacts at the edges of the outer
cube (a), artifacts in the slices that begin to appear the OC (b), artifacts in the slices where
40% of the OC appears (c).
Comparing the images, especially Figures 11 and 12, the image object format
influence on the generated artifacts is evident: straight lines or lines’ rays for straight-side or
with corners objects, and concentric circles for the circle objects case.
Figure 13 shows an artifact enlargement for the 1mm-layer OC. This enlargement
improves the observation of the artifact structure and their dependence on the object’s
edges. In the original images the artifacts are noticed, but, their signal intensity is smaller if
compared with the COs.
Figure 13. Enlargement of the spherical OC artifacts for 64-bit color image.
5. CONCLUSSIONS
This paper proposed a reconstruction method for computed tomography (CT) for
obtaining images of the sediment deposition layers. To test the methodology, planar images
of geometric objects in centered geometry, similar to those resulting from the CT processes,
were simulated using the dedicated X-Ray Monte Carlo (XRMC) code. With these generated
x-rays, using the Feldkamp, David and Kress (FDK) reconstruction algorithm threedimensional volume were generated.
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tomography geometry
The results show that CT geometry or industrial radiography, with X-ray sources or Ir192 seeds, are techniques that can be successfully applied to obtain sediment layers’
images. The use of these techniques preserves the material integrity and produces images
with information that would allow to locate or identify the several materials in the layers
accurately.
This work demonstrates that, due to the possible low contrast between the elements
present in this kind of samples, the images produced must be high quality to avoid their
noise contamination or artifact's appearance in the image processing. The use of the FDK
allows the method validation, however, as we analyze in section 4.1, this method produces
numerous artifacts. Nevertheless, for images with 64-bit color, the images automatic
processing is possible.
For future researches, the authors propose to evaluate pre and post processing
techniques in order to reduce the artifacts’ appearance in the reconstructed images as well
as the testing other reconstruction algorithms for field use, with image recollection in defined
solid angles.
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