Investigation of Non-circular Scanning Trajectories in Robot-based

Industrial X-ray Computed Tomography of Multi-material Objects

Peter Landstorfer

, Gabriel Herl

and Jochen Hiller

1,2

Fraunhofer Application Center CTMT, Dieter-G

orlitz-Platz 2, 94469 Deggendorf, Germany

Deggendorf Institute of Technology, Dieter-G

orlitz-Platz 1, 94469 Deggendorf, Germany

Keywords:

X-ray Computed Tomography, X-ray Simulation, Robotics, Robot-based Imaging, Scanning Trajectory.

Abstract:

In this work the application of six-axis robots for robot-based industrial X-ray computed tomography (CT)

imaging is investigated. In contrast to classical Cartesian manipulators with a turntable used in industrial

cone-beam CT, robots offer increased ﬂexibility regarding scanning trajectories. The increased ﬂexibility

with respect to scanning trajectories helps to gather highly informative content from alternative ray paths for

a high-quality 3D reconstruction of the object to be scanned. Using numerical simulations we show that

this additional informations increase the image quality of a CT scan of a multi-material measuring object,

consisting of tantalum spheres and a carbon structure.

1 INTRODUCTION

Industrial X-ray computed tomography (CT) nowa-

days is an important non-destructive testing method

and is well established in production industry as a

ﬂexible tool for quality assurance and process opti-

mization (De Chiffre et al., 2014). Since time-to-

market constantly decreases in industry, sensing and

automation technology is seen as a key technology

to develop the autonomous production of the future.

For imaging technologies like CT it is therefore con-

sequent, to work on CT systems based on ﬂexible

robotic manipulators. Medical CT systems are al-

ready equipped with robotic manipulator (Fieselmann

et al., 2016), (Ouadah et al., 2017), (Zhao et al.,

2019), industrial robot-based CT systems are arising

as well, for example, used for quality control in the

automotive industry. The robot’s advantage compared

to classical Cartesian manipulators in CT is its ﬂexi-

bility to reach a wider range of positions in space. Ac-

quisition trajectories beyond a single circular one can

be advantageous with respect to the resulting image

quality in industrial as well in medical applications

(Herl et al., 2019), (Noo et al., 1998), (Katsevich,

2005), (Ouadah et al., 2017). The increased ﬂexibility

with respect to scanning trajectories helps to gather

highly informative content from alternative ray paths

(X-ray projections), resulting in high-quality 3D re-

constructions of the object to be scanned. Particu-

larly, when scanning multi-material specimens, con-

sisting of low and high absorbing materials, addi-

tional ray paths prevent the formation of metal arti-

facts to a certain extent. In this paper, the advantages

of non-circluar trajectories using a virtual Kuka KR

15-2 robot are shown by means of numerical simu-

lations, whereas positioning errors of the (real) robot

are neglected in the simulation.

2 X-RAY COMPUTED

TOMOGRAPHY

X-ray based inspection is widely used in industrial

manufacturing (De Chiffre et al., 2014). The dif-

ference between X-ray inspection systems based on

radiographs and X-ray CT is the fact that CT uses

plenty of X-ray projection images to reconstruct the

inner structure of a specimen in terms of a 3D voxel

volume. Each voxel represents the local attenuation

coefﬁcient of a workpiece (material) to be scanned.

Typically, those voxel datasets are displayed as gray-

value slice images or a 3D rendering image as shown

exemplary in Figure 2. Usually, projection images are

generated in a circular trajectory on a machine bed us-

ing a Cartesian manipulator system with a turntable as

shown in Figure 1. In such a setup, X-ray source and

detector remain ﬁxed and the specimen, placed on the

turntable, turns around in, e.g., 1000 angle steps. In

each angle step, the X-ray detector acquires one pro-

518

Landstorfer, P., Herl, G. and Hiller, J.

Investigation of Non-circular Scanning Trajectories in Robot-based Industrial X-ray Computed Tomography of Multi-material Objects.

DOI: 10.5220/0007966405180522

In Proceedings of the 16th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2019), pages 518-522

ISBN: 978-989-758-380-3

Detector

Specimen

X-ray Source

Turntable

Figure 1: Schematic illustration of a standard cone-beam

CT scanner using a circular trajectory.

Figure 2: Projection image (top) and 3D rendering image

(below) of a casting.

jection image. This set of projection images is then

reconstructed to a 3D voxel volume (De Chiffre et al.,

2014).

3 BENEFITS OF NON-CIRCULAR

TRAJECTORY

In this work, we focus on two advantages for the ap-

plication of non-circular scanning trajectories. A pos-

sible system conﬁguration is shown in Figure 3.

In industrial CT there are several mathematical

and physical conditions and limitations that restrict

the obtained image quality of a CT image. First of all,

in circular cone-beam CT there is a data-sufﬁciency

problem: In order to reconstruct a 3D volume mathe-

matically correct, projection data from certain direc-

tions are needed that fulﬁll the so-called Tuy-Kirillov

conditions (Tuy, 1983). The most important one of

these conditions states that every plane that intersects

the volume has to intersect the trajectory of the X-ray

source. Using a circular trajectory, this condition can

be fulﬁlled for all volume points in the middle plane,

but not in other planes of the volume. Therefore, the

further the point is away from the source plane and

the higher the aperture angle, the stronger the form-

ing of image artifacts (so called cone-beam or Feld-

kamp artifacts) in the resulting dataset will be. By

using robots and adapting the scanning trajectory, the

Tuy-Kirillov conditions can be fulﬁlled, resulting in a

high-quality CT image.

Figure 3: Schematic illustration of a possible CT scanner

setup using a robot as manipulator.

Secondly, most reconstruction methods assume a

linear model of penetration length and attenuation

based on Lambert-Beer’s law in order to calculate

the local attenuation coefﬁcient of a material. But as

the spectrum of X-ray sources is polychromatic, this

model is not true. As a consequence, one is faced

with beam-hardening and metal artifacts, especially

when scanning objects consisting of low and high ab-

sorbing materials, for example multi-material objects

made from metal and plastic. Some of the measured

and attenuated X-rays contain information that cannot

be interpreted correctly by the used models, result-

ing in beam-hardening and metal artifacts. Therefore,

these strongly attenuated X-rays should be ignored by

the reconstruction algorithm.

In order to fulﬁll the mentioned Tuy-Kirillov con-

ditions, projections from different directions are nec-

essary. For example, using projections from several

tilted circular trajectories and using only attenuation

values of speciﬁc X-rays can increase the image qual-

Investigation of Non-circular Scanning Trajectories in Robot-based Industrial X-ray Computed Tomography of Multi-material Objects

519

ity and the dimensional accuracy of reconstructed ob-

jects signiﬁcantly (Herl et al., 2019). In this work,

we show that image artifacts due to almost total ab-

sorption can be decreased by using a robot and a non-

circular scanning trajectory.

4 ROBOTS AS MANIPULATORS

In this work, we investigated a robot-based CT as

shown in Figure 3. Using such a setup, source

and detector are mounted in ﬁxed positions and the

robot handles (manipulates) the specimen. Besides

this setup, other conﬁgurations are possible. Med-

ical CT scanners for example use a C-bow to han-

dle source and detector using one robot (Fieselmann

et al., 2016). Other conﬁgurations are based on one

robot for source and one to handle the detector while

the specimen remains ﬁxed. It is further possible to

use robots on linear rails to further enhance the work-

ing volume or to additionally use a turntable.

Generally speaking, it can be said from a theoret-

ical point of view that, the more directions a voxel

is scanned from, the higher the image quality of the

resulting reconstructed volume will be. Thus, a scan-

ner fully performing a sphere-like trajectory would be

ideal to penetrate each voxel out of every possible di-

rection. However, this can not even be achieved by

a six-axis robot. The reasons are: The specimen in

mounted on a ﬁxture and source and detector can not

move into that ﬁxture. For some positions, the robot’s

hand would mask the cone-beam. Those projections

also have to be omitted. Further, even a six-axes in-

dustrial robot can not reach any position and orienta-

tion in its working volume due to its joint angle limits.

Figure 4 shows possible projection positions

(green area) the robot can approach based on the

conditions mentioned before using numerical calcula-

tions based on geometric assumptions. Using homo-

geneous coordinates and Denavit-Hartenberg param-

eters, the possible positions the robot can approach

were determined.

5 EXPERIMENT: SIMULATION

STUDY

As mentioned earlier, the robot can not reach all

spatial positions on the virtual sphere. We deter-

mined the feasible positions using geometric assump-

tions. Using homogeneous coordinates and Denavit-

Hartenberg parameters of the Kuka KR 15-2 robot,

the possible positions of the robot can be estimated.

Figure 4: Calculated projection positions in space for the

non-circular case: The robot main axes are visualized as

blue lines, reachable projection positions as green area,

unreachable ones as red area. The robot base ﬂange is

mounted on the x/y plane and reaches the projection po-

sitions with its tool ﬂange (TCP), pointing to the center of

the object. The X-ray source is visualized as a circle and

the X-ray detector as a square.

Figure 5: Projection positions for a standard circular CT

scan using a turntable. The X-ray source is visualized as a

circle and the X-ray detector as a square.

In this simulation experiment, the center of the ob-

ject was located x = 650 mm and z = 1300 mm from

the base ﬂange of the robot. Further, a distance from

the center of the object to the tool ﬂange of the robot

of 200 mm was modeled as specimen ﬁxture. In a

real approach, one would build up this ﬁxture of low

density foam material in order not to compromise the

imaging process. Ideally, the robot could turn the

specimen around in a full sphere so that the X-ray sys-

tem can gather information from all directions. Due to

certain technical limitations, this is not possible. We

cannot reach some positions on top of the sphere be-

cause of the robots wrist angular range limit of ±135

degrees. Further we omitted those positions where

the hand of the robot moves into the relevant X-ray

beams. All positions inside a cylinder of 200 mm in

diameter with the central X-ray as center line were

omitted. Using a 5 degree pattern for azimuth angle

from 0 to 355 degree and elevation from 0 to 175 de-

ICINCO 2019 - 16th International Conference on Informatics in Control, Automation and Robotics

520

gree, in total 1859 spatial coordinates deliver the po-

sition data for the following simulations.

The output of our calculation is a set of spatial

coordinates (see Figure 4) we passed over to our

X-ray simulation tool XLab from Fraunhofer EZRT

(Reisinger et al., 2011). We computed noise-free vir-

tual projections of the virtual specimen out of carbon

as shown in Figure 6 using the X-ray simulation pa-

rameters, summarized in Table 1.

Figure 6: The simulated specimen is 3 cm tall and made out

of carbon.

In order to clearly show the beneﬁts of non-

circular CT scanning trajectories, we additionally

modeled four tantalum spheres of 6.5 millimeter di-

ameter and one sphere of 4 millimeter in diameter

and added it to the virtual specimen, so that it can

be treated as a multi-material object with low and

high density material contributions. For 3D recon-

struction to a voxel volume, we used a modiﬁed alge-

braic reconstruction technique (ART) (see (Herl et al.,

2019)).

In total, we simulated one non-circular (see Fig-

ure 4) and one circular (see Figure 5) trajectory. The

results of the simulations are summarized in the fol-

lowing section.

Table 1: Simulation parameters.

Specimen materials Tantalum and carbon

Tube voltage 225 kV

Tube current 0.02 mA

Focus detector distance 2000 mm

Magniﬁcation factor 2

Detector pixel size 0.469 mm

Detector pixel grid 512 × 512 pixels

Detector noise off

6 RESULTS

The results of the simulations in term of slice im-

ages using the two different scanning trajectories are

shown in Figure 7 and Figure 8.

When comparing Figure 7 and 8 we can clearly

see that the non-circular CT trajectory results in a

much higher image quality (no streak artifacts) due

to the fact that the additional information from the

non-circular trajectory compensates the impact of al-

most fully absorbed rays (due to the high dense tanta-

lum spheres) in the reconstructed volume and, as con-

sequence, reduces image artifacts signiﬁcantly. The

circular trajectory mainly suffers from partial total

absorption due to the high density tantalum, where

the non-circular trajectory, performed by the (virtual)

robot, suffers much less from those physical restric-

tions.

Figure 7: Reconstruction using circular scanning.

Figure 8: Reconstruction using non-circular scanning.

Investigation of Non-circular Scanning Trajectories in Robot-based Industrial X-ray Computed Tomography of Multi-material Objects

521

7 CONCLUSIONS AND

OUTLOOK

We investigated a non-circular trajectory for robot-

based X-ray CT and its application for the reconsti-

tution of a multi-material object using numerical sim-

ulations. Within the study we calculated a set of fea-

sible robot positions to obtain a set of X-ray projec-

tion images to reconstruct a voxel dataset. Further, we

simulated a standard circular CT and visually com-

pared the results of the two reconstructions qualita-

tively. We have shown that when using additional

information from different non-circular directions, a

much higher image quality can be expected in contrast

to a standard circular scan. Future work will focus

on optimization methods for robot CT path planning,

taking trajectory and accuracy limitations of robots,

material and geometrical properties of various speci-

mens as well as object and scan-speciﬁc X-ray inter-

action effects into account. Furthermore, experiments

using a real robot-based CT system will be performed

in the near future.

REFERENCES

De Chiffre, L., Carmignato, S., Kruth, J.-P., Schmitt, R., and

Weckenmann, A. (2014). Industrial applications of

computed tomography. CIRP Annals - Manufacturing

Technology, 63(2):655–677.

Fieselmann, A., Steinbrener, J., Jerebko, A. K., Voigt, J. M.,

Scholz, R., Ritschl, L., and Mertelmeier, T. (2016).

Twin robotic x-ray system for 2d radiographic and 3d

cone-beam ct imaging. In Kontos, D., Flohr, T. G.,

and Lo, J. Y., editors, Medical Imaging 2016: Physics

of Medical Imaging, SPIE Proceedings, page 97830G.

SPIE.

Herl, G., Hiller, J., and Sauer, T. (2019). Artifact reduc-

tion in x-ray computed tomography by multipositional

data fusion using local image quality measures. In

9th Conference on Industrial Computed Tomography,

(iCT 2019) Padua-Italy.

Katsevich, A. (2005). Image reconstruction for the circle-

and-arc trajectory. Physics in medicine and biology,

50(10):2249–2265.

Noo, F., Clack, R., White, T. A., and Roney, T. J. (1998).

The dual-ellipse cross vertex path for exact recon-

struction of long objects in cone-beam tomography.

Physics in medicine and biology, 43(4):797–810.

Ouadah, S., Jacobson, M., Stayman, J. W., Ehtiati, T.,

Weiss, C., and Siewerdsen, J. H. (2017). Task-driven

orbit design and implementation on a robotic c-arm

system for cone-beam ct. Proceedings of SPIE–the

International Society for Optical Engineering, 10132.

Reisinger, S., Kasperl, S., Franz, M., Hiller, J., and Schmid,

U. (2011). Simulation-based planning of optimal con-

ditions for industrial computed tomography. In Inter-

national Symposium on Digital Industrial Radiology

and Computed Tomography, Berlin, Germany, vol-

ume 3.

Tuy, H. K. (1983). An inversion formula for cone-beam

reconstruction. In SIAM Journal on Applied Mathe-

matics 43.3 p. 456-552.

Zhao, C., Herbst, M., Vogt, S., Ritschl, L., Kappler, S.,

Siewerdsen, J. H., and Zbijewski, W. (2019). A

robotic x-ray cone-beam ct system: trajectory opti-

mization for 3d imaging of the weight-bearing spine.

In Bosmans, H., Chen, G.-H., and Gilat Schmidt, T.,

editors, Medical Imaging 2019: Physics of Medical

Imaging, page 56. SPIE.

ICINCO 2019 - 16th International Conference on Informatics in Control, Automation and Robotics

522