Control concepts for image-based structure tracking with ultrafast electron beam X-ray tomography

Abstract

In this paper, a novel approach for tracking moving structures in multiphase flows over larger axial ranges is presented, which at the same time allows imaging the tracked structures and their environment. For this purpose, ultrafast electron beam X-ray computed tomography (UFXCT) is being extended by an image-based position control. Application is scanning and tracking of, for example, bubbles, particles, waves and other features of multiphase flows within vessels and pipes. Therefore, the scanner has to be automatically traversed with the moving structure basing on real-time scanning, image reconstruction and image data processing. In this paper, requirements and different strategies for reliable object tracking in dual image plane imaging mode are discussed. Promising tracking strategies have been numerically implemented and evaluated.

Full text

WCIPT 2018 Special Issue
Transactions of the Institute of
Measurement and Control
1–13
ÓThe Author(s) 2019
DOI: 10.1177/0142331219858048
journals.sagepub.com/home/tim
Control concepts for image-based
structure tracking with ultrafast
electron beam X-ray tomography
Dominic Windisch
1
, Martina Bieberle
2
,Andre
´Bieberle
2
and
Uwe Hampel
1,2
Abstract
In this paper, a novel approach for tracking moving structures in multiphase flows over larger axial ranges is presented, which at the same time allows
imaging the tracked structures and their environment. For this purpose, ultrafast electron beam X-ray computed tomography (UFXCT) is being
extended by an image-based position control. Application is scanning and tracking of, for example, bubbles, particles, waves and other features of multi-
phase flows within vessels and pipes. Therefore, the scanner has to be automatically traversed with the moving structure basing on real-time scanning,
image reconstruction and image data processing. In this paper, requirements and different strategies for reliable object tracking in dual image plane ima-
ging mode are discussed. Promising tracking strategies have been numerically implemented and evaluated.
Keywords
Ultrafast X-ray computed tomography, structure tracking, multiphase flow, model predictive control
Introduction
Fast imaging techniques are essential experimental tools in
fluid dynamics research, particularly for the investigation of
multiphase flows. Such flows are to be found in, for example,
chemical reactors, thermal power plants, oil and gas process-
ing, refrigeration systems, fluid transport systems and others.
Multiphase flows are inherently complex due to the co-
existence of multiple phases with different physical properties
and highly deformable interfaces; for example, in gas-liquid
and liquid-liquid flows. The modelling and numerical simula-
tion of multiphase flows with computational fluid dynamics
(Brennen, 2005: 20 ff.) require validation data from experi-
ments. For such measurement techniques with high temporal
and spatial resolution are needed. Particularly, non-invasive
imaging is of great attractiveness (Reinecke et al., 1998).
However, today there is no multiphase flow imaging tech-
nique available, which gives a full three-dimensional (3D)
view of opaque multiphase flows at high speed and resolu-
tion. As an example, we address a simple bubbly flow in a
pipe or vessel, that is, a coexistent flow of continuous liquid
and disperse bubble in a flow channel. As such, it would be
ideal to ‘‘see’’ all bubbles in a given volume, that is, pipe or
column section, at a spatial and temporal resolution that dis-
closes the dynamics of the bubbles themselves, the dynamics
of their interfaces and their geometric relations to other bub-
bles. Of course, it would also be of interest to know the local
continuous liquid velocities. As this is all not possible today,
an alternative would be to have a fast cross-sectional, that is,
two-dimensional (2D) imaging, with a capability to track a
moving structure, like a bubble. This would at least allow to
study a single bubble and its environment dynamically. In the
following, we will describe our approach to solve this task by
tracking structures in a flow with an ultrafast X-ray tomogra-
phy device. Before that, we will briefly review dynamic ima-
ging techniques for multiphase flows, to provide a good start
into the subject.
Today, there are a few fast flow measurement techniques
available for scientists and engineers. Most prominent are
high-speed cameras. However, they are seldom applicable for
multiphase flows as such are inherently opaque. The same
holds for ultrasound-based imaging techniques. Techniques,
which are in principle suitable for multiphase flows, are elec-
trical tomography, radiation-based imaging techniques and
magnetic resonance imaging. Hence, we will first briefly
review these techniques with a focus on their current capabil-
ity to deliver a full picture of, for example, a bubble flow in a
pipe or column.
Electrical tomography, with its variants electrical capaci-
tance tomography (ECT), electrical resistance tomography
(ERT) and electrical impedance tomography (EIT), is able to
recover structures with different electrical properties in
1
Chair of Imaging Techniques in Energy and Process Engineering,
Technische Universita
¨t Dresden, Germany
2
Helmholtz-Zentrum Dresden – Rossendorf, Institute of Fluid Dynamics,
Germany
Corresponding author:
Martina Bieberle, Helmholtz-Zentrum Dresden – Rossendorf, Institute of
Fluid Dynamics, Bautzner Landstr. 400, Dresden 01328, Germany.
Email: m.bieberle@hzdr.de

multiphase flows. The techniques can be made quite fast and
have a certain 3D imaging capability (Xie et al., 1995).
However, their spatial resolution is very limited, which ham-
pers tracking of dedicated structures.
Transmission imaging techniques based on radiation can
be classified into radiographic and tomographic imaging.
Fast radiography is known for X-rays (Boden et al., 2014)
and neutrons (Kaestner et al., 2011a, 2011b). X-ray radiogra-
phy may be used and has been implemented in the form of X-
ray stereoscopic particle tracking (see below). Conventional
X-ray tomography, that is being used in medicine and for
non-destructive testing, is generally too slow as it requires
mechanical movement of system components (Kak and
Slaney, 1988). An exception is ultrafast X-ray tomography,
which we address in this study (Fischer et al., 2008).
Magnetic resonance imaging (MRI) provides high spatial
resolution and 3D imaging capacity. However, the fastest
MRI scanners achieve up to 50 fps (frames per second)
(Mu
¨ller et al., 2007; Tayler et al., 2012b), which is still quite
slow compared with the time scales of multiphase flows.
Recent applications of ultrashort echo time MRI have
attempted to track moving structures in fluidized beds
(Fabich et al., 2017) and bubbly flows (Tayler et al., 2012a) at
40 fps. A main advantage of MRI is the simultaneous mea-
surement of liquid-phase velocities that cannot be achieved
by radiation-based tomography methods. However, the rela-
tively small volume of investigation limits the application to
snapshots of bubble swarms rather than visualizing their
paths and dynamics over a larger range.
Besides imaging techniques, there exist also pure structure
tracking techniques for multiphase flow. Such are CARPT
(Degaleesan et al., 2001), PEPT (Cole et al., 2010), and X-ray
stereoscopy (Nadeem and Heindel, 2018). In PEPT and
CARPT, radioactively marked tracer particles are tracked
over a longer period. As they are pure tracking techniques the
surroundings of the tracked structures (particles) are not
disclosed. X-ray stereoscopy obtains the position of high-
contrast particles from triangulation. To some degree sur-
rounding structures are disclosed in the associated X-ray
images. However, as these images provide no good depth
information, the 3D imaging capacity is rather low (Nadeem
and Heindel, 2018).
Ultrafast X-ray tomography is a relatively new fast ima-
ging technique that comes very close to the given require-
ments. It bases on X-rays, provides high frame rate of up to
8000 fps, 1 mm spatial resolution and dual plane imaging
(Bieberle et al., 2012). As this technique yet has only 2D ima-
ging capability, though in two planes simultaneously, struc-
ture tracking out of the imaging planes is not possible. To
qualify this technique for structure tracking, a fast positioning
system for the scanner has to be implemented and a fast data
analysis strategy for controlling the system has to be devel-
oped. The latter development has been started already in our
group with the transfer of the data processing onto graphic
processing units (GPU) (Bieberle et al., 2017; Frust et al.,
2017). This now gives short enough latency times for real-
time axial scanner position control.
In the scope of the control concept the two imaging planes
of the X-ray scanner act as a pair of binary structure sensors.
Many control schemes for binary sensors or binary sensor
networks (BSN) are known from the literature. However,
their application is limited to either unidirectional continuous
processes, for example, liquid level control (Wang et al.,
2003), or multi-dimensional positioning problems for zero-
dimensional objects, for example, tracking of persons across
various rooms, (Bai et al., 2015). Thus, Liu et al. (2013)
proposed a strategy for extraction of velocity and size of a cir-
cular object moving at constant speed using a set of
transmitter-receiver style binary sensors. However, the
extracted information is used neither to control the process
nor to track it actively by repositioning the sensors.
There are also various strategies for image-based control,
for example, based on high-speed camera footage
(Hutchinson et al., 1996). They are, however, only applicable
for controlling processes within the imaging region.
Combining the available concepts, we propose a control strat-
egy for image-based control of processes occurring normal to
the imaging plane(s). Here, instead of a BSN, only a pair of
controllably traversable binary sensors is used.
To track a moving structure, an effective position control
of the ultrafast X-ray CT scanner must be provided, employ-
ing a low-latency trajectory generation. For that a so-called
model predictive control approach is most suited in which the
target’s position changes are suitably modelled. Furthermore,
constraints regarding the maximal applicable velocity and
acceleration need to be included. This requires iterative com-
putation techniques that are critical in terms of real-time
operation (Kim et al., 2007; Neunert et al., 2016). Current
analytic approaches do not include such a movement model
(Haschke et al., 2008; Ruppel et al., 2011). However, for
tracking of a temporarily non-visible moving target, such as a
bubble moving between imaging planes, this is indispensable.
Thus, a time-optimal, analytic trajectory generation is pro-
posed that complies with maximum velocity and acceleration
constraints. A double-setpoint controller is employed based
on the periodic modelling of the structure’s movement with a
parabolic position profile. Similar to the receding horizon
approach, the model parameters are updated in every time-
step and only the optimal control output for the next time
step is used. Different from classic receding horizon control,
the analytic solution allows modelling the movement up to
the current control target instead of exploring only a fixed
prediction horizon.
Materials
The ultrafast electron beam X-ray CT scanner
As shown in Figure 1a, the ultrafast electron beam X-ray CT
scanners use an electron beam that is focussed and deflected
onto a circular tungsten target to generate a rapidly rotating
X-ray focal spot along two staggered paths without any
mechanical movement of components. Data acquisition is
performed by a radiation detector that comprises two distinct
rings of CdTe detector pixels arranged concentric to the X-ray
target. The CT scanner under consideration offers a circular
imaging area with a diameter of 190 mm and two distinct ima-
ging planes with a geometric distance Dhc=13 mm
(Figure 1b). The alternating scanning in two planes with a
small axial offset allows the determination of structure
2Transactions of the Institute of Measurement and Control 00(0)

velocities by time-of-flight methods (Barthel et al., 2015).
Currently, each detector ring comprises 432 seamlessly
arranged pixels, whose analogue signals are digitized with a
sampling frequency of fsamp =106samples/s. Cross-sectional
images are acquired alternately in both imaging planes (see
Figure 1c) with a maximal imaging rate of up to
fim =8000 fps.
Image reconstruction is currently performed offline. That
is, the digitized signals of the radiation detectors are tempo-
rarily stored in the random access memory of the detector
electronics before they are being transferred to the host com-
puter after completion of a scan (Bieberle et al., 2017). There,
image reconstruction and post-processing is done at a later
time.
For structure tracking, real-time image reconstruction as
well as control strategies to traverse the CT scanner are
needed. Data processing pipeline systems (Frust et al., 2017;
Kopmann et al., 2016) seem to be proper tools for that. For
that we evaluated three different traverse control concepts, as
explained in the following.
Tracking strategy
A moving structure, in this case represented by a rising gas
bubble, is fully described by the following set of one-
dimensional parameters (Figure 2a): the current position ssof
the structure ‘‘s’’, its velocity vs, its acceleration asand its
Figure 1. (a) Principle sketch of the ultrafast electron beam X-ray CT, (b) vertical view of the object area. Horizontal lines indicate the imaging
planes and (c) principal order of alternating cross-sectional images per plane over time. Latency is sketched for the real-time image reconstruction.
Figure 2. (a) Description of important system parameters. (b) Qualitative scanner movement for the different control strategies.
In Figure 2a, horizontal lines at h0and h1indicate the imaging planes, sthe structure’s path.
Windisch et al. 3

axial length ls. Furthermore, the CT scanner ‘‘c’’ is also fully
described by its current position of the upper imaging plane
(called scanning position) sc, velocity vcand acceleration ac.
As constraints we have a maximal absolute velocity vmax
c,a
maximal absolute acceleration amax
cand position limits smin
c
and smax
c. Moreover, we have the constant geometric distance
Dhcbetween both imaging planes h0and h1and the time
interval Dtcycle =2=fim for the acquisition of an image-pair.
The latter serves as a master clock for parameter extraction
and storage. With each newly acquired pair of images
n21,::,Nmax
½the system clock is updated to
tn=tn1+Dtcycle.
To track the moving structure, the scanning position sc
has to be adapted by controlling the scanner’s movement
based on these parameters. To determine this target scanning
position starget
c, three strategies have been considered. For this,
an additional offset parameter p\1is introduced which is
used to calculate starget
cbased on the current structure length
lsusing starget
c=ss+soff
ifor i21,2fgwith soff
1=plsand
soff
2=Dhc+1pðÞls
ðÞas described below. A value
0\p\1leads to a target scanning position within the tracked
structure at portion pof its length ls, that is, the structure
remains visible, whereas p\0leads to deliberate overshooting
by p
jj
ls, that is, temporary non-visibility of the structure.
The default values pfor each of the considered tracking stra-
tegies were determined empirically (see Table 1) and may be
adapted within the respective given ranges (see below) for
each of the following strategies.
Single image plane tracking (SIPT, 0\p\1): In the first
strategy, the CT scanner’s position is controlled such that the
structure remains visible in the lower image plane h0.
Therefore, the parameters ss,lsand vsare initially determined
while the structure passes both imaging planes first.
Afterwards, the CT scanner drives to its target scanning posi-
tion starget
cat a defined portion of the structure’s length ls
within the image plane h0with a final velocity of vc=vs,as
shown in Figure 2b (SIPT). The target position is therefore
defined to be starget
c=sspls. In case the velocity of the
structure vsdoes not change over the section to be investi-
gated, the scanner has not to be accelerated anymore.
Anyway, in the more likely case, where vs6¼ const:, the velo-
city of the scanner vchas to be iteratively adapted corre-
spondingly as described in chapter 2.3. With the structure
visible most of the time in one imaging plane, this strategy is
expected to provide detailed trajectory information.
However, size and shape changes of the structure cannot be
detected.
Dual image plane tracking (DIPT, 0\p\1): As in SIPT,
the structure is initially completely scanned in both imaging
planes to determine its current size and velocity. Then the CT
scanner moves upward, thereby overtaking the structure with
the upper imaging plane and partially with the lower imaging
plane until the lower image plane is a distance plsabove the
bottom of the structure (Figure 2b-DIPT). There, the CT
scanner accelerates with amax
csuch that the upper image
plane is positioned at distance plsbelow the top of the rising
structure. For very large or slowly rising structures, this leads
to intentional downwards movement of the scanner. Thereby,
the number of sampling points tkis maximized (see section
2.3). This procedure is then repeated. With DIPT the struc-
ture is always in the axial region between the upper and lower
image plane and visible for almost all the time. By letting the
structure frequently pass through both imaging planes, its
shape and size can be continuously measured. However, this
strategy is still somewhat sensitive to fast changes of the
structure’s geometry that may result from, for example, flow
disturbances.
Dual image plane re-tracking (DIPRT, p\0): In the third
strategy, the structure is repeatedly scanned completely by the
CT scanner in both image planes. As described for the DIPT
strategy, the target scanning position again alternates between
the two target offsets soff
1and soff
2but this time with the offset
parameter p\0. Thereby, the scanner drives above the struc-
ture and scans again the structure’s parameters. Afterwards,
the scanner accelerates with amax
cto let the structure pass
completely through both imaging planes once more and
repeats the cycle. Employing this strategy, the structure’s
shape and size changes can be characterised. However, infor-
mation about its trajectory is limited to the intermediate
scans. Further, the structure leaves the scanning planes multi-
ple times and needs to be rediscovered.
Parameter extraction of the moving structure
No matter which tracking strategy will be applied, parameters
of the investigated object have to be extracted initially from
the image pair data. However, as recognizable from Figure
1c, in a single image plane, a small and slowly rising structure
leads to the same image sequence as a tall and fast rising
Table 1. Parameter space for the numeric simulations of the behaviour
of the complete system, that is, CT scanner and control unit, as depicted
in Figure 9.
Parameter Symbol Values
Input delay Dtin 0,5,10½ms
Output
delay
Dtout 0,1,2½ms
CT scanner
position
uncertainty
Dsmeas
c0,0:1,0:5½mm=sample
Control
strategy
SIPT p=0:5ðÞ
DIPT p=0:25ðÞ
DIRPT p=0:25ðÞ
Movement
profiles
(1) vst0
ðÞ=50 mm s1,as=0
(2) vst0
ðÞ=300 mm s1,as=0
(3) vst0
ðÞ=50 mm s1,as=2mms2
(4) vst0
ðÞ=300 mm s1,as=10 mm s2
(5) vst0
ðÞ=50 mm s1,as=0:2mms2
(6) vst0
ðÞ=300 mm s1,as=5mms2
(7) up=down with vs
jj=200 mm s1
Length
profiles
(1) ls=8mm
(2) ls=18 mm
(3) ls=8mm+4mmss(2500 mm)1
(4) ls=18 mm +9mmss(2500 mm)1
(5) ls=8mm4mmss(2500 mm)1
(6) ls=18 mm 9mmss(2500 mm)1
(7) ls=8mm+2mmsin t2s12p

(8) ls=18mm +4:5mm sin t2s12p

4Transactions of the Institute of Measurement and Control 00(0)

structure. Thus, for the extraction of the structure velocity,
the images from the second imaging plane h1need to be
employed to track the boundaries of the structure whilst pass-
ing through both imaging planes (see Figure 3a).
The time interval Dt1=t2t1(see Figure 3a) is initially
determined as the time between the structure’s front entering
the lower plane h0and upper plane h1. Afterwards, the velo-
city of the structure’s boundary can be calculated by
vs=Dhc+sct2
ðÞsct1
ðÞ
Dt1
ð1Þ
Secondly, the time interval Dt2=t3t1between the entering
of the structure’s front at the lower image plane h0and the
structure’s back at the lower image plane h1is determined. As
can be seen in Figure 3b, the current axial length of the struc-
ture lscan then finally be calculated by
ls=vsDt2sct3
ðÞ
sct1
ðÞ½ð2Þ
using the latest previously estimated velocity vs. Similarly, the
structure’s lower boundary can also be used to determine
these parameters.
By following an axially moving structure, its boundaries
are tracked every time one crosses one of both image planes.
Between these crossing events at times tk, the structure’s
length is assumed to be constant. At each such event, an
updated structure velocity vsvalue can be calculated and,
thus, the structure’s acceleration as=vstk
ðÞvstk1
ðÞ½=
tktk1
ðÞ. Consequently, continuous updates of the esti-
mated structure parameters ss,vs,asand lsare realized by
evaluating the crossing events together with both their corre-
sponding time-stamp tkand their respective CT scanner posi-
tion sc(see Figure 7).
To distinguish between the structure’s upper and lower
boundary, six different CT scanner states Shave been defined,
as shown in Figure 4.
States 1,2band 3can be classified solely from visibility
information in the reconstructed cross-sections and are there-
fore defined as certain states. To differentiate between states
0,2aand 4, the state history of the CT scanner must be con-
sidered. These states are therefore classified as uncertain
states. Possible transitions between states are shown in
Figure 5.
Each transition is used to identify the tracked structure’s
upper or lower boundary, respectively. For example,
Figure 3. Determination of structure velocity and axial dimension using dual-image mode of the CT scanner.
Horizontal lines represent the imaging planes. (a) Velocity estimation for unknown structure length. (b) Subsequent structure length calculation using travelled distance
with the estimated velocity.
Figure 4. Defined CT scanner states with corresponding cross-sectional images to distinguish between upper and lower structure boundary.
Horizontal black lines represent the imaging planes of the CT scanner. Note, that states 2aand 2bare only valid for structures smaller than or greater than the distance
between the imaging planes, respectively.
Windisch et al. 5

transition 0!1indicates the structures upper boundary and
3!4the structures lower boundary at the time of scanning.
However, because uncertain states can only be determined
based on the latest estimated structure properties, like vsand
ls, false state estimations may occur due to disturbances like
turbulence or vibrations. This may lead to invalid transitions
as shown in Figure 6 (dotted line).
In case such an invalid transition is detected, the system
falls back to the latest certain state at time tmand retroactively
corrects all state estimates and structure property extractions
up to the current time-stamp tn. Thus, the CT scanner states
must additionally be acquired and saved at each state transi-
tion with their respective time-stamp. Each of these events is
considered as a sample point tkfor the parameter extraction.
Based on the continuously updated structure parameters the
CT scanner’s acceleration profile can be properly adapted (see
Figure 7).
Motion planning for the CT scanner
Depending on the above given tracking strategy and the latest
parameter estimation of the structure, a new target position
starget
cis calculated for each clock cycle (see Figure 2). To
reach the target height in the minimum positioning time inter-
val Dttrav, acceleration and deceleration phases have to be per-
formed with the systems maximal applicable acceleration
Figure 5. State transition graph with valid state transitions and their respective transition conditions.
Vector x1,x2,x3,x4
½represents visibility of the structure in the lower imaging plane (x1), in the upper imaging plane (x2), the velocity relation vsøvc(x3) and size
relation lsøDhc(x4), respectively, with ‘‘1’’ for true, ‘‘0’’ for false and ‘‘-’’ for no influence.
Figure 6. Exemplary retroactive correction for invalid state transitions.
The transition from state 4 at tnis invalid (dotted line). Therefore, the estimated system states are retroactively corrected from the last certain state and time stamp (S3
at tm) such that a valid sequence of state transitions is ensured (dashed line). Feature estimations from false state transitions are also corrected.
6Transactions of the Institute of Measurement and Control 00(0)

value amax
c. Thus, the generated trajectory for the CT scan-
ner’s movement needs to comply with these boundary
conditions
sct0+Dttrav
ðÞ=starget
ct0+Dttrav
ðÞ ð3Þ
vct0+Dttrav
ðÞ=v
st0+Dttrav
ðÞ ð4Þ
vctðÞ
jj
łvmax
cð5Þ
actðÞ2 0,amax
c,amax
c
ð6Þ
The structure’s movement profile is described by
sstðÞ=as
2t2+v
st0
ðÞt+s
st0
ðÞ,ð7Þ
vstðÞ=a
st+vst0
ðÞ,ð8Þ
astðÞ= const:ð9Þ
For better readability and without loss of generality, terms in
the form sst0
ðÞare shortened to ssand the initial time t0is set
to 0in the following. Based on the structure’s movement pro-
file, a similar profile for the target position starget
cof the CT
scanner can be calculated using starget
ctðÞ=s
stðÞ+soff
iwith
i21,2fgas explained in section 2.2. Because the three dis-
crete possible acceleration values acfor the CT scanner are
predefined (see equation (6)), only the time intervals for accel-
eration and deceleration phase need to be calculated to pro-
vide the time-optimal trajectory. This optimal acceleration
time Dtacc is calculated explicitly by solving the given para-
bolic position and linear velocity profiles (see Figure 8)
Dtacc =
dir vsvc
ðÞ+ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
diras
2amax
c+1
2

vcvs
ðÞ
2+2asdir amax
c

scstarget
c

hi
ramax
cdir as
:ð10Þ
Therein, the directional term dir 21,1
fg
is used to switch
the order of acceleration and deceleration depending on the
current situation at each master clock event. Using the wrong
dir-value leads to a transition time Dtacc\0. If this is the case,
the calculation for Dtacc is repeated with dir =dir.Ifthe
calculated acceleration interval Dtacc does not lead to a viola-
tion of the predefined maximum velocity vmax
c, the corre-
sponding deceleration time
Dtdec =2dir amax
cDtacc +vcvs
as+dir amax
s
Dtacc ð11Þ
can be calculated. Otherwise, an intermediate phase segment
with constant and maximum velocity of duration Dtlin must
be added between acceleration and deceleration interval
(Figure 8b). Therefore, the acceleration time interval Dtacc
must accordingly be updated at first by
Dtacc =vmax
c
amax
c
dir vc
amax
c
ð12Þ
considering the current velocity vcof the CT scanner.
Secondly, the corresponding deceleration interval is calcu-
lated by
Dtdec =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
vctacc
ðÞvstacc
ðÞ½
2+2assctacc
ðÞstarget
ctacc
ðÞ

dir asamax
c+amax
c

2
v
u
u
t:
ð13Þ
Lastly, the intermediate time interval Dtlin is calculated from
the given movement profiles by
Figure 7. Concept of evaluating structure’s front and back using image-pairs and the history of the CT scanner states using the example of the initial
investigation of structure parameters required at the beginning of each of the aforementioned structure tracking strategies.
Windisch et al. 7

Dtlin =
vctacc
ð Þvstacc
ð ÞDtdec as+dir amax
c

as
for as6¼ 0
starget
ctacc
ðÞsctacc
ðÞ
vctacc
ð Þvstacc
ðÞ
+vstacc
ð Þvctacc
ðÞ
2dir amax
c
for as=0
8
>
>
<
>
>
:ð14Þ
Finally, equation (15) compiles the minimum traverse time
ttravðÞ
Dttrav =Dtacc +Dtdec for vctacc
ðÞ
jj
\vmax
c
Dtacc +Dtlin +Dtdec for vctacc
ðÞ
jj
=vmax
c
ð15Þ
on which the scanner will hit its target scanning position. The
trajectory is updated every master clock cycle and passed as
input to the scanner’s positioning unit.
After presenting different tracking strategies and the para-
meter extraction procedure for the observation of dynamic
structures, the entire control concept (Figure 9) can be con-
cluded. As input parameters the continuously reconstructed
image-pair stream as well as the current position of its ima-
ging planes scare required.
Each time the CT scanner state Sis changed, the struc-
ture’s parameters are updated. Based on these extracted para-
meters as well as the limits of the positioning system, the CT
Figure 8. Velocity profile for the CT scanner (a) without and (b) with a constant velocity segment to be able to follow a moving structure.
Figure 9. Basic tracking sequence to determine a structure’s rising velocity and length using a dual-plane CT scanner.
8Transactions of the Institute of Measurement and Control 00(0)

scanner’s motion is planned using one of the three introduced
tracking strategies.
Results and discussion
To investigate the feasibility of the proposed control strate-
gies the behaviour of the entire system, that is, CT scanner
and control unit as depicted in Figure 9, has been simulated
for various flow scenarios. For this, an artificial 1D logical
phantom vector which resembles predefined structure motion
and length profiles (see Figure 10) was used.
To cover a wide range of technical applications different
movement and structure length profiles have been simulated
(see Figure 10). This set of parameters includes linear, acceler-
ated, decelerated and up/down movement as well as constant,
linearly increasing / decreasing and fluctuating structure
lengths. The used values for the study are compiled in Table 1
with their respective indices. Combining all parameter varia-
tions, a total number of 4536 different parameter sets have
been simulated.
During the simulation, the path and the velocity of the
structure phantom is calculated for each current time step tn
considering also the input delay Dtin , which accounts for data
transfer and data processing delays. According to Frust (2016),
the image reconstruction latency is expected to be 4:3ms at
maximum for the default imaging rate of fim =2000fps. Data
transfer times are estimated to be 0:2ms based on the available
bandwidth. For structural feature extraction an additional
latency of 0:5ms is assumed based on the usage of a threshold-
based binarization data processing stage. The total input latency
for the default image-pair rate is, therefore, estimated to be
Dtin =5:0ms (see Figure 9). A larger input delay Dtin is also
considered because the recognition and rediscovery of a struc-
ture may require multiple pairs of images. Furthermore, the
output delay Dtout , that is, the time interval between generating
the acceleration signal and realizing the corresponding move-
ment, is estimated to be 1ms based on commercially available
motor controllers (SEW-EURODRIVE, 2010).
In the real positioning system, the position scis determined
using a wire potentiometer with a measurement uncertainty
of Dsmeas
c=60:1mm. This offset was added as Gaussian noise
to the current system position scat each clock cycle in the
simulations. An additional larger position uncertainty
Dsmeas
c=60:5mm was simulated to account for mechanical
Figure 10. Simulated structure movements. a) Movement profiles with their respective indices (linear (1,2), accelerated (3,4), decelerated (5,6), up
and down (7)) and b) length profiles (constant (1,2), linear increase (3,4), linear decrease (5,6), fluctuating (7,8)) along the test section. Dotted lines
represent Dhc. Quantitative definitions are given in Table 1.
Windisch et al. 9

offsets, for example, vibrations or sagging of the wire, in the
real setup. Height information time delay is negligible. A time
step discretization, that is, cycle time of Dtcycle =1ms is used
to fit the typical acquisition rate of fim =2000fps. The CT
scanner’s position limits are
smin
c=500 mm and smax
c=2500mm:
The CT scanner starts at standstill, that is, vct0
ðÞ=0,atan
initial height sct0
ðÞ=500mm and comes to a complete stop at
its maximum height smax
c. Its maximum velocity and accelera-
tion were set to
vmax
c=500 mms1and amax
c=500 mm s2, respectively.
The structure’s initial height is sst0
ðÞ=0mm. All simulations
were carried out in Matlab. All parameter sets with Dsmeas
c.0
were simulated 100 times to get statistically significant infor-
mation about the influence of position noise Dsmeas
cwhilst
retaining manageable simulation times (about 5 seconds /
simulation).
Structure parameter extraction
To evaluate the tracking strategies regarding velocity infor-
mation extraction, the momentary velocity estimations vstk
ðÞ
at each sample point tk(see Figure 5) were compared with the
momentary nominal velocities vnominal
s, that is, the predefined
velocities of the phantom vector, for each set of parameters
being simulated. The median velocity estimation ~
vstk
ðÞof each
simulation was selected and averaged with the estimate of all
100 simulations of the same parameter set. The median value
was selected instead of the mean value because single estima-
tions may become implausibly large or small due to short
durations between sample points or numeric limitations, for
example, division by length scales close to floating point pre-
cision. Results are shown in a parity plot in Figure 11.
Results at all sample points show an agreement between
nominal velocity and median measured velocity ~
vstk
ðÞwith
deviations below 2%, which is acceptable for this application.
Furthermore, velocity estimates have been identified to be
insensitive to structure length ls, system delay Dtin=out and
position noise Dsmeas
cin the tested ranges.
To evaluate the length estimation quality the momentary
length estimations lstk
ðÞfor each simulation were compared
with the momentary nominal structure length lnominal
sas
explained previously for the velocity estimates. Median length
estimation results ~
lstk
ðÞshow good agreement with typical
deviations better than 10% (see Figure 12). Length estimation
deviations tend to increase for fluctuating structure lengths
which results from the limited number of sample points for
the length determination, that is, relatively low sample fre-
quency compared with the fluctuation frequency. Length esti-
mates are insensitive to system delays Dtin and Dtout as well as
position uncertainty Dsmeas
cin the tested ranges.
Comparison of control strategies
As depicted in Figure 13a, all control strategies deliver similar
velocity estimation results of about
~
vstk
ðÞ=vnominal
s=0:99960:019 averaged over all parameter
combinations. However, length estimates reveal larger relative
errors for the single image plane tracking (SIPT) strategy with
an average result of ~
lstk
ðÞ=lnominal
s=0:98560:084 (Figure
13b). This is due to false state estimates which cannot be cor-
rected with the limited data provided by SIPT, especially for
structure lengths shorter than the distance between the ima-
ging planes Dhcbecause a differentiation between states 0and
2ais impossible (see Figure 4). Dual image plane tracking
(DIPT) and dual image plane re-tracking (DIRPT) show
more narrow distributions of length estimates with respective
results of ~
lstk
ðÞ=lnominal
s=0:99260:060 and ~
lstk
ðÞ=lnominal
s=
0:99260:063.
Moreover, DIPRT’s length estimates show a bimodal dis-
tribution (see Figure 13b). Further investigations of length
estimations for DIPRT in different structure length profiles
reveal that this bimodal distribution occurs only for fluctuat-
ing structure length profiles (see Figure 14a).
Figure 11. Median momentary velocity estimates for different
movement profiles (standard deviation \5%).
Figure 12. Median momentary length estimates for different
movement profiles (standard deviations \10%).
10 Transactions of the Institute of Measurement and Control 00(0)

This bimodal distribution occurs for all simulated move-
ment profiles, delays Dtin and Dtout as well as position noise
levels Dsmeas
cin combination with fluctuating structure length
(see Figure 14b). It is especially apparent for initial structure
velocities vnominal
st0
ðÞ=50mm s1. The reason for this distri-
bution is a systematic underestimation of fluctuating struc-
tures with mean length ls\Dhccombined with an
overestimation of fluctuating structures with mean length
lsøDhc. This tendency is most apparent in DIPRT due to its
narrower distribution of length estimates. In SIPT and DIPT,
the wider distributions do overlap and thereby conceal this
tendency when averaging all test cases.
Increasing input latency Dtin leads to an overall increase in
the velocity estimate’s standard deviation in each control
strategy from s~
vstk
ðÞ=vnominal
s

=0:015 for Dtin 20,0:005s
fg
to s~
vstk
ðÞ=vnominal
s

=0:035 for Dtin =0:010s. Variation of
output delay Dtout and position noise Dscdo not show signifi-
cant deviations (s~
vstk
ðÞ=vnominal
s

ł0:03) in the simulated
range of values. An acceleration switching frequency of 10Hz
was sufficient for all simulated parameter sets, that is, the
electro-mechanical positioning system requires a correspond-
ing cut-off frequency. The influence of different time discreti-
zation Dtcycle was only briefly investigated and did not show
noteworthy differences.
Conclusion
Different tracking strategies for the application of ultrafast X-
ray tomography for studying moving structures in multiphase
Figure 13. Comparison of feature extraction quality for different control strategies "SIPT", "DIPT" and "DIPRT". (a) velocity determination,
(b) length determination.
Figure 14. Length estimation distribution for (a) different structure length profiles using DIPRT strategy and (b) fluctuating length profiles using
different control strategies.
Windisch et al. 11

flows have been evaluated. A control scheme was proposed
that provides a defined CT scanner positioning movement
based on currently acquired image-pair data. Therefore, three
different tracking strategies, namely Single-Image Plane
Tracking (SIPT), Dual-Image Plane Tracking (DIPT) and
Dual-Image Plane Re-Tracking (DIPRT), were discussed and
evaluated by numerical simulation. All strategies promise very
good velocity tracking results. However, SIPT is preferred for
cases with constant structure shapes and lengths, for example,
tracking of a tracer particle. To extract length and shape
information for time-variable structure length and shapes,
DIPT is more suitable for low disturbances. The DIPRT
approach is preferred for detailed shape determination at high
turbulence cases. Simulations have shown that DIPT and
DIPRT were more robust than SIPT concerning the influence
of time delays and position uncertainty.
Future work will focus on reliable structure recognition
from the image pair data. Moreover, further post-processing
steps to increase state estimation quality, and therefore fea-
ture extraction quality, using computationally complex tech-
niques like particle filtering are of high interest.
Declaration of conflicting interests
The author(s) declared no potential conflict of interests with
respect to the research, authorship and/or publication of this
article.
Funding
The author(s) disclosed receipt of the following financial sup-
port for the research, authorship, and/or publication of this arti-
cle: Financial support by Deutsche Forschungsgemeinschaft
(DFG) is gratefully acknowledged (BI 1770/2-1).
ORCID iDs
Dominic Windisch https://orcid.org/0000-0003-3558-5750
Martina Bieberle https://orcid.org/0000-0003-2195-6012
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