Orientation Optimization and Jig Construction for X-ray CT

10th Conference on Industrial Computed Tomography, Wels, Austria (iCT 2020), www.ict-conference.com/2020

Orientation Optimization and Jig Construction for X-ray CT scanning

Toshimasa Ito1, Yutaka Ohtake1, Hiromasa Suzuki1

1The University of Tokyo, Tokyo, Japan, e-mail: [email protected], [email protected],

[email protected]

Abstract

Recently, X-ray computed tomography (CT) scanners have become common in industry. However, artifacts resulting from the

orientation of the scanned object are often generated in industrial CT scanners. In this study, in order to improve the scan

result, we tried to search for an optimal object orientation. Using computer-aided design data, which are frequently generated

for designing industrial objects, we performed simulations of X-ray projections. We evaluated three types of artifacts in these

simulations: metal artifacts, beam hardening artifacts, and cone-beam artifacts. Each of these three artifacts was individually

minimized in the simulations. We the determined the overall optimal orientation via multiobjective optimization. In addition, CT

users often need to construct jigs to support objects in certain orientations. Accordingly, we proposed a method for construct a

jig to support objects in their optimal orientation. The scan results in the optimal orientation proposed by our method were better

than those obtained in the orientation proposed by a CT operator.

Keywords: Industrial CT scanner; scanning orientation; jigs; metal artifacts; beam hardening artifacts; cone-beam

artifacts

1 Introduction

Recently, X-ray computed tomography (CT) scanners have become common in industry [1]. In industrial CT scanners, especially

cone-beam CT scanners, X-rays are irradiated onto an object that progressively rotates in small increments. The collected

projection images are used to reconstruct the CT volume data (see Figure 1). Therefore, using an industrial CT scanner, the

internal structure of an object can be inspected without using invasive methods or destroying the object itself. However, artifacts

are often generated in industrial CT scanners [2], and these artifacts often depend on the orientation of the object. Several related

studies have attempted to reduce such artifacts by focusing on the orientation of the object. It is possible to reduce artifacts by

combining a few scanned results obtained from different orientations [3]. However, this method takes more time than a single

scan. It is also possible to calculate the optimal orientation for one type of artifact [4]. However, when using this method, there

is a possibility that another type of artifact will become more pronounced. In this study, we attempted to calculate the optimal

orientation for three types of artifacts during one scan. If we scan an object in the optimal orientation and obtain a good result

from this first scan, we can reduce the time and costs. Moreover, by automatizing the process of deciding the orientation, we

can consistently maintain the scan quality without depending on the user’s experience. In addition, CT users are often required

to construct jigs to support objects in a certain position. We herein proposed a method for automatically generating the required

shapes of the jigs to support the scanned objects in their optimal orientation.

1.1 Overview of the Proposed Method

We performed X-ray projection simulations using surface mesh data exported from the computer-aided design (CAD) data of

a scanned object as input data. We manipulated the vertices of the triangles and normal vectors of the triangles obtained from

detector

rotation table

X-ray

source

object

projection images

reconstruction

CT volume

Figure 1: Process of CT scanning.

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rotation axis

Figure 2: Projection simulation (left) and changing the rotation axis (right).

Jig for the orientation

Optimal orientationReducing metal artifacts

Orientation Optimization

𝑓mtl 𝜃, 𝜑 : The generalized

mean of the transmission length

Reducing beam

hardening artifacts

𝑓hdn 𝜃, 𝜑 : The variance

of the projection area

Reducing cone-

beam artifacts

𝑓fdk 𝜃, 𝜑 : The area of the faces

that do not satisfy the Tuy-Smith

sufficiency condition

Input data

Surface mesh data

from CAD data

CT Scanning

Minimizing 𝑚𝑎𝑥 ሚ𝑓mtl 𝜃, 𝜑 , ሚ𝑓hdn 𝜃, 𝜑 , ሚ𝑓fdk 𝜃, 𝜑

Constructing a jig to support an object in its optimal orientation

Projection simulation

Able to scan an object

in optimal orientation

Figure 3: CT scanning procedure at an optimal orientation.

the surface mesh data. As in actual CT scanning, the object was rotated incrementally in the simulation by rotating the vertices

and normal vectors of each triangle. Then, at each angle, the transmission length was calculated. Using this procedure, we

obtained the result of a projection simulation in a certain orientation (see Figure 2 left). We iterated the simulation by changing

the orientation of the object and the position of the rotation axis using two degrees of freedom, θ and φ . In this study, the rotation

axis rotates first around the x-axis, and then around the y-axis (see Figure 2 right). In each orientation, we evaluated three types

of objective functions related to metal artifacts, beam hardening artifacts, and cone-beam artifacts. Using the values of these

objective functions, we performed multiobjective optimization to determine the optimal orientation. However, even when the

optimal orientation is known, it can be difficult to support an object in this orientation. Therefore, we proposed a method for

constructing jigs to support objects in their optimal orientation. Using these methods, we were able to scan an object in its

optimal orientation (see Figure 3).

2 Orientation Optimization

2.1 Optimal Orientation for Reducing Metal Artifacts

Metal artifacts are often generated when X-rays penetrate thick metal parts of an object and nearly vanish. and almost vanishes

after the penetration. Therefore, we need to reduce the thickness of the object along the X-ray projections. Transmission length

is equivalent to thickness (see Figure 4); therefore, we defined the generalized mean of the transmission length as the objective

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X-ray source

detector

transmission length

Figure 4: Transmission length.

short length

large projection area

long length

small projection area

Figure 5: Relationship between the transmission length and the projection area.

function f mtl(θ ,φ). We then searched for the orientation that minimized the value of f mtl(θ ,φ). As demonstrated in the left

panel of Figure 7, when the object is in a vertically long orientation, the transmission length is reduced. The generalized mean

of the transmission length in the following equation (1). Here, xi is the transmission length of the ith pixel, n is the number of

pixels on the detector multiplied by the number of projection images, and m represents the type of norm of the generalized mean.

In this study, we determined the norm of the generalized mean to be 3.

f mtl(θ ,φ) = m

√

1

n

n

∑i=1

xmi (1)

2.2 Optimal Orientation for Reducing Beam Hardening Artifacts

Beam hardening artifacts are often generated when the variance of the transmission length during rotation is large and the

relationship between the X-ray attenuation and the material thickness is nonlinear. Here, we replaced the transmission length

with the projection area because when the transmission length is short, the projection area is large and vice versa (see Figure

5). In order to reduce the influence of beam hardening artifacts, we defined the variance of the projection area as the objective

function f hdn(θ ,φ). We then searched for the orientation that minimized the value of f hdn(θ ,φ). As shown in the middle panel

of Figure 7, the object needs ot be in an inclined orientation to reduce the variance of the transmission length. The variance of

the projection area is given in the following equation (2). Here, Amax and Amin are the maximum and minimum projection areas,

respectively, in the projection images in each orientation. In this study, the projection area was calculated by counting the number

of pixels with nonzero values on the detector in the simulation.

f hdn(θ ,φ) = Amax −Amin (2)

2.3 Optimal Orientation for Reducing Cone-Beam Artifacts

When the cone angle increases, the number of planes that do not satisfy the Tuy-Smith sufficiency condition [5] increases, which

increases the reconstruction error. Accordingly, cone-beam artifacts are often generated when the planes fail to satisfy the Tuy-

3


X-ray

source

trajectory of

X-ray source

intersecting point

plane including a mesh triangle

Figure 6: Schematic of the Tuy-Smith sufficiency condition.

Figure 7: Projection images of orientations that minimize the value of f mtl(θ ,φ) (left), f hdn(θ ,φ) (middle), or f f dk(θ ,φ) (right).

Smith sufficiency condition, a condition that need to be met for actual reconstructions. More specifically, if there exists at least

one cone-beam source point on every plane that intersects an object, then the object can be reconstructed. In this study, we

checked this condition for each triangle on the surface mesh data; the flat shape of the triangle can be accurately reconstructed if

the plane including the triangle intersects the circular trajectory of the source (see Figure 6). We defined the area of the faces that

fail to satisfy the Tuy-Smith sufficiency condition as the objective function f f dk(θ ,φ). We then searched for the orientation that

minimized the value of f f dk(θ ,φ). As shown in the right panel of Figure 7, when the object is in a horizontally long orientation,

the cone angle is reduced. The area of the faces that fail to satisfy the Tuy-Smith sufficiency condition is given in the following

equation (3). Here, M is the number of the triangles that do not satisfy the Tuy-Smith sufficiency condition and D j is the area of

the jth triangle that does not satisfy the Tuy-Smith sufficiency condition.

f fdk(θ ,φ) =M

∑j=1

D j (3)

2.4 Optimal Orientation via Multiobjective Optimization

Unfortunately, these objective functions have a trade-off relationship. Therefore, there is no ideal orientation in which the

values of all the functions are minimized. Accordingly, we determined the optimal orientation using multiobjective optimization

of f̃ mtl(θ ,φ), f̃ hdn(θ ,φ), f̃ f dk(θ ,φ), where the functions are normalized and the values range from 0 to 1. In this study, we

normalized the functions according to the following epuation (4). Here, the subscripts "max" and "min" represent the maximum

4


ground pointMoment: maximum

Figure 8: Projection images in the optimal orientation (left) and the first (middle) and second (right) pattern papers.

or minimum values, respectively, in all orientations.

f̃ ∗(θ ,φ) =f ∗(θ ,φ)−min{ f ∗(θ ,φ)}

max{ f ∗(θ ,φ)}−min{ f ∗(θ ,φ)}, (4)

where∗= {mtl,hdn, fdk}.When the value of the normalized function is close to 1, the possibility of more pronounced artifacts is high. Therefore, we need

to avoid such an orientation. Accordingly, we determined the optimal orientation by minimizing the maximum value among

f̃ mtl(θ ,φ), f̃ hdn(θ ,φ), and f̃ f dk(θ ,φ) (see Figure 8 left).

3 Automatic Generation of Jigs

We herein propose a method to create a jig to support objects in their optimal orientation. We used Styrofoam as the material

for the jig because X-rays can easily penetrate it and it has a minimal influence when scanning an object. In addition, Styrofoam

can easily be obtained and cut using a heat Styrofoam cutter. In this study, we output pattern papers that describe how to cut a

Styrofoam square in two directions using a Styrofoam cutter.

We designed the first pattern paper to support the direction in which the object is prone to falling, that is, the direction in which

the moment of force around the ground point becomes maximum (see Figure 8 middle). Then, to allow cutting the Styrofoam

square in two directions perpendicular to each other, the second pattern paper was rotated by 90◦ around the rotation axis from

the direction of the first pattern paper (see Figure 8 right).

We disigned the first pattern paper by drawing the outline of the upper part of the object (see Figure 8 middle) and the second

pattern paper by drawing the outline of the lower part of the object (see Figure 8 right). By drawing the outlines of the upper and

lower parts separately, we could support the upper and lower part of the object separately without interference. In this study, the

green areas indicate the jig parts.

In the following, we present the procedure for creating a jig.

1. Print the first and second pattern papers drawn using our method (see Figure 9 left top).

2. Cut the pattern paper along the edge of the green area and place it on the Styrofoam square (see Figure 9 right top).

3. Cut the Styrofoam square along the edge of the first pattern paper using a Styrofoam cutter (see Figure 9 left bottom).

4. Cut the Styrofoam square along the edge of the second pattern paper using a Styrofoam cutter (see Figure 9 middle bottom).

5. Place the object on the jig in its optimal orientation (see Figure 9 right bottom)

4 Experiment and Results

We scanned two aluminum parts (see Figure 10 left, and 11 left) with complex shapes twice: once in the optimal orientation

supported by the jig proposed by our method (see Figure 10 right, and 11 right) and once in the orientation proposed by a CT

operator (see Figure 10 middle, and 11 middle). We used a Carl Zeiss METROTOM 1500 CT scanner with a tube voltage of

150kV. No prefilter was used to evaluate the effectiveness of the beam hardening artifact reduction. We evaluated the histogram of

the scanned CT volume using separation metrics, related to the quality of the histogram. Higher values of the separation metrics

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1. 2.

3. 4. 5.

Figure 9: Procedure for constructing a jig.

indicate that the histogram is more clearly saparated into two classes. We determined the threshold between the air class and the

material class using Otsu’s method [6]. In Otsu’s method, the threshold is defined automatically at the point where the value of

the separation metrics becomes maximum. the separation metrics is represented by S = σ2b /σ2

w, where σ2b is the between-class

variance and σ2w is the within-class variance. We determined the between-class variance and within-class variance using the

following equation (5). Here, w{1,2} is the number of voxels in each class, m{1,2} is the mean of the value of the histogram in

each class, σ2{1,2} is the variance of the value of the histogram in each class, and the subscripts "1" and "2" indicate the air class

and the material class, respectively, in the histogram of the CT volume.

σ2w =

w1σ21 +w2σ2

2

w1 +w2, σ2

b =w1w2(m1 −m2)

2

(w1 +w2)2

(5)

We calculated the separation metrics using the CT volume data (see Figure 12, and 13). In the optimal orientation, the value of

the separation metrics was 12.169. In the operator’s orientation, the value of the separation metrics was 8.401. This indicates that

our optimal orientation is quantitatively better than that of the operator. The results of the CT volume indicates that the artifacts in

the CT volume of the optimal orientation are smaller than those of the operator’s orientation (see Figure 12, and 13). Moreover,

we could better define the isosurfaces of the CT volume in the optimal orientation compared to the operator’s orientation (see

Figure 14 top, and 15 top). Further, the deviations of the isosurfaces and the surfaces obtained by an optical scan (using an ATOS

Core 300) were smaller in the optimal orientation than in the operator’s orientation (see Figure 14 bottom, and 15 bottom).

5 Conclusions and Future Work

We iterated X-ray projection simulations using surface mesh data exported from the CAD data of a scanned object as input data.

Using these simulations, we evaluated three types of objective functions related to metal artifacts, beam hardening artifacts, and

cone-beam artifacts. Using the values of these objective functions, we performed multiobjective optimization and determined

the optimal orientation. In addition, we proposed a method for constructing jigs to support objects in their optimal orientation.

Using these methods, we scanned objects in their optimal orientation and found that the scan results were better in the optimal

orientation than in the operator-chosen orientation.

We also searched for the optimal orientation using two degrees of freedom. However, it may be possible to improve the quality

of the optimal orientation if we search using five degrees of freedom: two degrees of freedom of orientation and three degrees of

freedom of position. Moreover, the optimal orientation of an object made of two materials could also be calculated.

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Figure 10: Image of the first aluminum sample (left) and projection images of the first sample in the operator’s orientation

(middle) and in the optimal orientation (right).

Figure 11: Image of the second aluminum sample (left) and projection images of the second sample in the operator’s orientation

(middle) and in the optimal orientation (right).

References

[1] Simone, C., Wim, D., & Richard, L. Industrial X-Ray Computed Tomography. Springer, 2018.

[2] Hsieh, J. Computed tomography: principles, design, artifacts, and recent advances. SPIE The International Society for

Optical Engineering, 2003.

[3] Grozmani, N., Buratti, A., & Schmitt, R. H. Investigating the influence of workpiece placement on the uncertainty of

measurements in industrial computed tomography. iCT 2019 (2019).

[4] Amirkhanov, A., Heinzl, C., Reiter, M., & Groller, E. Visual optimality and stability analysis of 3DCT scan positions.

IEEE Transactions on Visualization and Computer Graphics 16.6 (2019), 1477-1486.

[5] Smith, B. D. Image reconstruction from cone-beam projections: necesarry and sufficient conditions and reconstruction

methods. IEEE transactions on medical imaging, 4. 1 (1985), 14-25.

[6] Otsu, N,. A threshold selection method from gray-level histograms. IEEE transactions on systems, man, and cybernetics,

Vol .9, No. 1 (1979), pp. 62-66.

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Figure 12: CT volume images and histogram of the first sample in the operator’s orientation (upper) and in the optimal orientation

(lower).

Figure 13: CT volume images and histogram of the second sample in the operator’s orientation (upper) and in the optimal

orientation (lower).

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Figure 14: Isosurfaces of the CT volume of the first sample in the operator’s orientation (upper left) and the optimal orientation

(upper right), and deviations of the isosurfaces and the surfaces obtained by an optical scan in the operator’s orientation (lower

left) and the optimal orientation (lower right).

Figure 15: Isosurfaces of the CT volume of the second sample in the operator’s orientation (upper left) and the optimal orientation

(upper right), and deviations of the isosurfaces and the surfaces obtained by an optical scan in the operator’s orientation (lower

left) and the optimal orientation (lower right).

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Orientation Optimization and Jig Construction for X-ray CT