Shake The Box' - a 4D PTV algorithm: Accurate and ghostless reconstruction of Lagrangian tracks in densely seeded flows

 
Shake The Box' - a 4D PTV algorithm: Accurate and ghostless reconstruction of Lagrangian tracks in densely seeded flows
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                  17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
                                         Lisbon, Portugal, 07-10 July, 2014

        ‘Shake The Box’ - a 4D PTV algorithm: Accurate and ghostless
         reconstruction of Lagrangian tracks in densely seeded flows

                Daniel Schanz*, Andreas Schröder, Sebastian Gesemann
 German Aerospace Center (DLR), Inst. of Aerodynamics and Flow Techn., Dep. of Experimental Methods, Germany
                                 * correspondent author: daniel.schanz@dlr.de

Abstract The ‘Shake The Box’ (STB) PTV - method for the accurate reconstruction of particle tracks in densely
seeded flows was first introduced in the scope of the 10th International Symposium on Particle Image Velocimetry
(PIV13) in 2013 [Schanz 2013b]. At the time it was shown that the proposed method of incorporating the temporal
information into the process of particle position reconstruction is able to improve results in various aspects compared to
conventionally used techniques. However, only an experimental dataset was available to explore the abilities of the
technique [Schanz 2013b].
The aim of the current work is to quantify the key features of the STB-method - and to identify the benefits and
drawbacks. To this end, a scheme for the creation of synthetic tracks from input - vector volumes was created, allowing
the calculation of physically (sufficiently) correct track systems at arbitrary seeding densities and time separations.
Projections of such track systems on virtual cameras are used as input data for both STB, as well as an MLOS-SMART
[Atkinson 2009] tomographic reconstruction algorithm. The results are compared with respect to positional accuracy of
reconstructed particles, occurrence of ghost particles and reconstruction time.
It is shown that, after a sufficient number of snapshots to allow for convergence of the algorithm, the STB-method is
able to correctly identify nearly all particles in existence, even for high seeding density up to 0.125 particles per pixel
(ppp). On the same time, the average position error stays very low (0.023 px for 0.125 ppp) – a gain of more than an
order of magnitude compared to MLOS-SMART. The occurrence of ghost particles is almost completely suppressed
(ghost level below 0.2 percent for 0.125 ppp). The efficient utilization of the temporal information allows a significant
reduction in processing time, with STB being 4 to 6 times faster compared to MLOS-SMART.
The introduction of noise to the particle images reduces the achievable accuracy for both STB and SMART. For high
noise levels, STB shows positional errors up to 0.25 pixel (which can be improved to around 0.14 pixel using temporal
fitting of the reconstructed trajectory). Still, the vast majority of particles is found and ghost levels stay very low also
for these cases.
As the temporal information plays such a dominant role in the STB method – both in the gained results, as well as in the
reconstruction process itself – the method cannot be described as pure particle reconstruction, but rather as a method to
reconstruct the full temporal development of tracer particles within their residence in the measurement volume.
Therefore it is more appropriate to speak of a track reconstruction scheme - or 4D PTV.

1. Introduction

The evaluation of time-resolved particle-based experimental investigations of three-dimensional
flow fields typically falls into two different domains: on the one hand tomographic PIV (TOMO-
PIV) [Elsinga 2006] which relies on a tomographic reconstruction of the particle distribution and a
subsequent three-dimensional cross-correlation; on the other hand 3D PTV-methods (e.g. [Maas
1993]), which triangulate particle positions and try to find matching occurrences in successive time-
steps in order to form Lagrangian tracks. Both methods have advantages and disadvantages:
TOMO-PIV is very robust and allows the use of high seeding densities. The underlying Eulerian
grid enables easy computation of derived values, such as vorticity from the large number of tracer
particles. Yet, the occurrence of ghost particles tends to bias the velocity results (especially for high
seeding densities), the cross-correlation introduces a window-size dependent spatial smoothing and
the whole processing is computationally costly. 3D-PTV yields precise results at the location of the
tracer particles without any spatial smoothing, while a temporal smoothing allows for better
accuracy. Particle statistics of velocities and accelerations can give a different insight to flow

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              17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
                                     Lisbon, Portugal, 07-10 July, 2014

conditions, compared to a regular grid. On the downside, the methods are only applicable to seeding
densities that are around one order of magnitude lower, compared to TOMO-PIV, typically limiting
PTV to the evaluation of mean values (as too few tracer particles are present within each
instantaneous shot).
The ‘Shake The Box’ – method [Schanz 2013b] introduces a novel evaluation approach: it relies on
the principle that a particle whose trajectory is known for a certain number of time-steps should (a)
not disappear within the measurement volume and (b) its position should be quite accurately
predictable for the next time-step, based on a fit on the previous time-steps. Small errors introduced
in the prediction can be corrected using image matching schemes, as introduced in [Wieneke 2013].
Using this principle, it is possible to use information that was gathered from past time-steps to help
with the reconstruction of the current time-step, allowing greater accuracies, higher seeding
densities and faster reconstruction times.
It has been shown that the method is able to process densely seeded experimental data and to extract
high-quality tracks in great number and with high track-lengths [Schanz 2013b]. However, a precise
characterization of results is difficult using experimental data; therefore the current work focuses on
the application of the STB-method to synthetic data with known ground truth.
In the next chapter, the working principle of STB will be explained, followed by a description of the
process of creating synthetic tracks. Subsequently, the parameters and results of the application of
STB will be presented, a comparison to results gained by tomographic reconstruction and a study
on the effects of image noise conclude the work.

2. Scheme of the STB- method

Conventional methods of evaluating three-dimensional particle-based measurements rely on an
individual treatment of every single snapshot of the particle distribution and a subsequent treatment
of the results for consecutive images (volume correlation for TOMO-PIV, partner search for 3D
PTV). However, when sufficiently time-resolved data is present, the solutions to the reconstruction
problem differ only by the movement of the particles from step to step. It is therefore possible to
utilize results from previous time-steps in order to optimize the reconstruction of the current one.
Under the assumption that the trajectories of (nearly) all particles within the system are known for a
certain number of time-steps, the STB-method scheme for a single time-step is as follows:

   1. Fit a function (polynomial) to the last n positions of every tracked particle.
   2. Predict the position of the particle in the next time-step n+1 by evaluating the fitted
      polynomial.
   3. Shake the particles to their correct position and intensity, eliminating the error introduced by
      the prediction - this step is realized using an image matching technique discussed later.
   4. Find new particles entering the measurement zone using triangulation on the residual
      images.
   5. Shake all particles again to correct for residual errors.
   6. Iterate steps 4 and 5, if necessary.
   7. Add new tracks for all new particles that are identified within four consecutive time-steps.
   8. Remove particles from track system either if leaving the volume or if intensity falls below
      threshold.

The process of ‘shaking’ the particles was first described by Wieneke in the scope of the technique
of ‘Iterative reconstruction of Volumetric Particle Distribution’ (IPR) [Wieneke 2013]. This method
allows for the accurate reconstruction of particle positions in a single image with seeding densities
up to 0.05 ppp by using an iterative process of triangulation and particle position refinement.
Particles found by triangulation are moved (shaken) around the volume in small steps (0.1 px per

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direction of space), until a minimum of the local residual images (‘image matching’, including the
use of a calibrated optical transfer function, OTF [Schanz 2013a]) is found. After this process, new
particle candidates are triangulated from the (now sparser) residual images and again shaken into
the optimal position. The steps 4 - 6 of STB basically represent the IPR-method with reduced
number of iterations, as only few particles have to be considered. For more detailed information on
the IPR-process, see [Wieneke 2013].
Using the described scheme, the algorithm is capable of working through long time-series,
extending known tracks step-by-step and continually adding particles that enter the measurement
zone to the list of tracked particles. As the major part of the system is already solved after the
prediction, only small errors need to be corrected by shaking and by adding new particles.
Therefore, the method is computationally very effective.
However, the algorithm can only work efficiently if the majority of the present particles is known
and can be predicted. It is therefore very important to initialize the track system in a way that allows
STB to converge to the correct number of tracked particles. In the current study, this initialization is
done in a relatively simple way: For the first four time-steps, the particle distribution is determined
using the IPR-method with a high number of iterations. Within these four time-steps, particles that
follow a reasonable trajectory (with deviations from a linear fit below a certain threshold) are
identified. This initial track-finding is supported by a 3D vector field, gained by classical TOMO-
PIV evaluation of the first four time-steps, which is used as a predictor for the search of fitting
particles. For higher seeding-densities, the IPR-method produces significant numbers of ghost
particles per time-step – yet, these are greatly reduced by the temporal condition of connected
tracks within the four images.
The particles identified within the initialization process are added to the list of tracked particles and
their positions are extrapolated to the fifth time-step. From there on, the scheme depicted above is
applied with a reduced number of iterations and no assistance by correlation results.

3. Creation to synthetic tracks

In order to quantitatively capture and compare the accuracy of different methods, a process to
extract synthetic tracks from a known vector field was designed. For the first image, particles are
randomly distributed in the selected domain; the velocity of the particles is calculated as the
Gaussian weighted average of the eight neighboring velocity vectors of the source vector volume.
In the next step, the particles are moved according to the determined velocity and the chosen time
separation. Thus, smooth particle tracks following the source vectors can be created. To guarantee
constant densities, particles leaving the measurement domain are reinserted at a suitable location of
the volume border. To this end, all source velocity vectors located at the interfaces of the volume
are examined. A list of such vectors with a component directed to the inside of the volume is
created, weighted with the magnitude of this component. To determine the reinsertion point of a
particle, first the general region is chosen randomly from the weighted list of interface vectors.
Second, a position within a radius of 15 pixels around this point is determined randomly.
As source vector volume, a result from an experimental dataset of the flow behind a series of
periodic hills was chosen. This time-resolved TOMO-PIV dataset was already used to yield the first
STB-Results given in [Schanz 2013b]. The experimental setup is explained in detail in this
publication. Evaluations of the experiment are also presented on the 17th Lisbon conference by
Schröder et. al [Schröder 2014]. TOMO-PIV processing of the images gained by six PCO Dimax /
LaVision Imager Pro HS (4 MegaPixel each) yield vector data in a volume of 90x94x20 mm3. The
voxel spaces used for tomographic reconstruction are of dimension 1951x2035x405 voxel. Cross
correlation was performed using a final window size of 483 voxels with 75 % overlap, resulting in
163x170x34 vectors with a spacing of 12 voxels. From the vector results, a case offering high
dynamic range was chosen. A subvolume of 1000x1000x400 was cut from the middle of the

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                17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
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volume and the vector results originating from this volume were used as source vectors for the track
creation. For the placement of reinserted particles, a border of 30 non-imaged voxels was left at
each interface of the volume, so that an imaged volume of 940x940x340 voxel remained.
An important prerequirement is that the source vector field is divergence free, as otherwise particles
accumulate in sinks. To this purpose, a routine from LaVision Davis 8 was used to ensure
divergence free input vector volumes.

Fig. 1: (Top) Vector slices from the divergence-free source vector volume used to create synthetic tracks. (Bottom)
Tracks created for ppp = 0.01. Only 15 time-steps are shown. Flow in positive x-direction, color coded stream-wise
velocity.

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As time separation, the original sampling rate was chosen, resulting in a mean particle displacement
of around 6 px and a maximum displacement of around 11 px. Fig. 1 illustrates the vector volume
used as source and shows tracks created for a low seeding density case of 0.01 ppp. Only 15 time-
steps are shown in order to be able to discern single tracks.
The particle positions determined from the track creation scheme are projected using parallel
projection onto four virtual cameras (1200x1200 pixels each) in pyramidal configuration with a
square basis and an angle of +– 30° in x- and y- direction. As weighting function (OTF), a two-
dimensional Gaussian peak is used, which leads to particle diameters of 3-4 pixel. Seeding densities
ranging from 0.01 ppp to 0.125 ppp (calculated in respect to the imaged volume – in this case ppp =
Np/940/940, with Np: number of particles) were realized. Fig. 2 shows excerpts of a camera image
for three seeding densities.

Fig. 2: Details from camera image for ppp = 0.01, ppp = 0.05 and ppp = 0.125 (from left to right).

4. Application of STB to synthetic data

The Shake The Box – Scheme was applied to the particle images originating from synthetic tracks.
For initialization, the first four time-steps were treated with IPR as follows: the allowed
triangulation error was set to ε = 0.5 px for all iterations; each triangulation iteration was followed
by 8 shake-iterations; 6 triangulation iterations using all 4 available cameras were conducted,
followed by 4 triangulation iterations using a subset of 3 cameras (thus 4 triangulations in total for
every of these iterations, each with one camera missing; done to reduce the effects of overlapping
particles). In the resulting particle distributions, 4-step tracks are identified and those are chosen
that show a total deviation of less than 1.5 pixel in every direction of space from a linear fit. These
tracks are moved to the list of tracked particles and the position prediction is performed. For all
consecutive steps, the number of triangulations is reduced to 3 triangulations using all cameras and
2 triangulations using a subset of cameras. The number of shake-iterations remains unchanged. In
the prediction step, a second order polynomial was fitted to the four last time-steps and extrapolated
to the current one. New particles are added to the tracking system in a similar way as performed in
the initialization (4-step tracks with less than 1.5 px deviation from linear fit). Time-series of 50
images were processed for each seeding density.
Fig. 3 shows the temporal development of three parameters, describing the quality of the
reconstruction. The reconstructed tracks are compared to the original ones by searching for
reconstructed particles in a radius of 1 px around every real particle. The deviation of found real
particles to the original position is determined and averaged.

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                17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
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Fig. 3: Temporal development over 50 successive images of STB-runs for different seeding densities. The right side
always displays a zoom into time-steps 40-50, where the algorithm has converged for all cases. (First row) Number of
real particles not being detected (within 1px); (Second row) Development of the fraction of reconstructed ghost
particles; (Third row) mean positional error for all reconstructed real particles

For lower seeding densities (
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               17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
                                      Lisbon, Portugal, 07-10 July, 2014

errors (≈ 0.3 px for 0.125 ppp).
The higher the seeing density, the longer the STB-scheme needs to converge. For 0.075 ppp, the
system needs 3-4 time-steps to correct for the errors that were introduced during the initialization
(not all particles could be found, the ones found show a positional error, as they are shifted by
overlapping particle images and the occurrence of ghost particles). The 0.1 ppp case needs around
6-7 time-steps after initialization to converge to stable conditions, for 0.125 ppp this number rises to
around 20-22. Especially for this case it can be seen that the initialization is still very compromised
with less than 25 percent real particles identified and those with a high uncertainty of around 0.3 px.
Therefore, a percentage of the four-step tracks found by the initialization will either be completely
false or not predictable and are thrown out of the tracking process again – this explains the notable
rise in ghost particles during the first images after the initialization. The particles are not following
the correct track and are therefore seen as ghost particles. Step by step these are thrown out of the
tracking system, until after around 25 steps they are gone. At the same time, the correctly tracked
particles (though only a low fraction at first) help to reduce the complexity of the reconstruction
problem and allow the detection of new correctly tracked particles. This process can be seen by the
constant decline of the fraction of undetected particles. The accuracy of the detected particles is
improved with the identification of more and more real particles, as less ghost particles can shift the
particle and as more particle overlap conditions are resolved by correct positioning of the involved
particles.
Looking at the right column of plots, the converged results for the reconstructions of all seeding
densities can be examined. It can be seen that the system stays at a pretty constant state, with only
small variations, depending on instantaneous imaging conditions or small variations in particle
density. The fraction of undetected particles falls below 0.5 percent, even for the 0.125 ppp case;
the fraction of ghost particles is reduced even below 0.2 %. Particle peak accuracy is very high,
with Δ < 0.005 px for ppp
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                17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
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Fig. 4: Comparison of results gained by tomographic reconstruction and subsequent particle peak identification to
tracking results by STB. Values averaged over images 40-44 of the time series discussed in Fig. 3.

The accuracy determination and particle-/ghost-identification from the original track data was
conducted analogous to the STB data. For both MLOS-SMART and STB, the results from steps 40-
44 were averaged and are given in Fig. 4 and Table 1, respectively.
Looking at the MLOS-SMART tomographic reconstruction, most real particles are correctly
reconstructed (99 percent for low ppp, 92 percent for 0.125 ppp) with a positional error that rises
from 0.13 px for 0.01 ppp to 0.31 px for 0.125 ppp. The fraction of the summed ghost particle
intensity to the summed real particle intensity is low for ppp
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               17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
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produced over 280.000. For lower seeding densities ghost levels of less than 0.05 % can be reached.
The (nearly) absolute prevention of ghost particles, combined with the highly accurate image
matching (shaking) process leads to a significant increase in achievable accuracy: For low seeding
densities (
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                 17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
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6. Influence of image noise

As shown in the previous chapters, the concept of particle position prediction, followed by a
position refinement by image matching yields very good accuracy results for a wide range of
seeding densities when looking at perfect imaging conditions. However, image noise will have an
influence on several parts of the algorithm: The image matching process will not be able to find a
perfect match for the particle position, as the peak information is altered by the noise. Secondly, the
triangulation process for identifying new particles will be affected, as noise tends to shift 2D
particle position identification. This will directly influence the triangulation error - therefore the
allowed value ε has to be altered in order to find a sufficient number of particles. A higher value of
ε will lead to a higher probability of ghost particle formation.
In order to judge the effects of image noise, datasets have been created for three different noise
levels at two different seeding densities. The noise was introduced after imaging the synthetic
particle distribution on the four cameras by adding a randomized intensity to every pixel with a
value taken from a normal distribution with variance σ derived from the average maximum peak
intensity of a particle image Ip,avg. Images with noise levels corresponding to : σ = 0.03*Ip,avg, σ =
0.1*Ip,avg and σ = 0.2*Ip,avg were created for seeding densities of 0.01 ppp and 0.05 ppp. Fig. 5
shows exemplary excerpts of one camera image for the 0.01 ppp - case. The first two cases can be
seen as representative for good to very good experimental circumstances (considering noise levels),
while the σ = 0.2*Ip,avg – case is approaching experiments with poorly controlled conditions (sparse
illumination, small tracer particles). Application of any kind of image preprocessing was
intentionally omitted in order to not introduce further parameters.
Time-series of 50 time-steps were created and reconstructed both by STB and by MLOS-SMART.
Concerning STB, the allowed triangulation error was set ε = 0.85 for the two cases with lower noise
and ε = 1.1 for the high-noise case. Results of the STB-track-reconstruction can be examined in Fig.
6 (left side). It can be seen that the convergence-time of the algorithm rises with the noise level.
Especially the high-noise case with 0.05 ppp illustrates that the system has to work much harder in
order to identify real particles and to get rid of ghost particle tracks. For this case, convergence is
reached around 20 time-steps after the initialization, with a then constant ratio of undetected
particles of around 0.065. The cases with lower noise level converge faster (3 and 7 time-steps after
initialization, respectively). The 0.01 ppp case converges instantly for the lower noise levels, but
needs around 3 iterations for the high seeding density.
Looking at the mean displacement of the particles it is obvious that the very high accuracies seen in
the perfect imaging case cannot be reached. For σ = 0.03*Ip,avg displacement errors of around 0.03
pixels are found. The error rises to 0.1 pixel and 0.24 pixel for the higher noise cases.

Fig. 5: Detail view from camera image for ppp = 0.01 for different levels of artificially added noise: σ = 0.03*Ip,avg, σ =
0.1*Ip,avg, σ = 0.2 * Ip,avg (from left to right). σ is the variance of the normal distribution used for the random noise
generation, Ip,avg denotes the average maximum peak intensity of a particle image.

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           fraction of undetected particles                              fraction of undetected particles
   0.8
                               0.01 ppp, σ = 0.3                                STB, 0.01 ppp
                               0.01 ppp, σ = 0.1                   0.1
                                                                                STB, 0.05 ppp
   0.6                         0.01 ppp, σ = 0.2                  0.08          SMART, 0.01 ppp
                               0.05 ppp, σ = 0.03                               SMART, 0.05 ppp
                               0.05 ppp, σ = 0.1                  0.06
   0.4                         0.05 ppp, σ = 0.2
                                                                  0.04
   0.2
                                                                  0.02
      0                                                             0
       0       10        20    30         40        50                   0.03        0.1                    0.2
                         snapshot                                                     σ [I       ]
                                                                                             p,avg
     mean error of detected particles [px]                          mean error of detected particles [px]
   0.4                                                             0.4

   0.3                                                             0.3

   0.2                                                             0.2

   0.1                                                             0.1

      0                                                             0
       0       10        20    30          40       50                   0.03        0.1                    0.2
                         snapshot                                                     σ [I       ]
                                                                                             p,avg
              fraction of ghost particles                                 fraction of total ghost intensity
                                                                   2.5
   0.1                                                              2
  0.08
                                                                   1.5
  0.06
                                                                    1
  0.04
  0.02                                                             0.5

      0                                                             0
       0       10        20    30          40       50                   0.03        0.1                    0.2
                         snapshot                                                     σ [I       ]
                                                                                             p,avg
Fig. 6: (Left): Temporal development over 50 successive images of STB-runs for seeding densities 0.01 ppp and 0.05
ppp for varied amounts of image noise. (Right): Comparison of results gained by tomographic reconstruction and
subsequent particle peak identification to tracking results by STB for varied amounts of image noise. Values averaged
over images 40-44 of the time series from the left hand side.

As soon as the system is converged, the error is largely dependent on the noise level and less on the
seeding density – clearly indicating the compromised accuracy of the image matching process as
source for the position error. The ghost particle level stays very low for the two low-noise cases.
For the high-noise case the ghost level rises. In this case, single noise peaks can be of
approximately the same intensity as the particle images. These false particle peaks can lead to

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random ghost particle tracks if they match by chance in four consecutive images. The fraction of
ghost particles is indeed higher for the lower seeding density, as less real particles are present to
counterweigh the ghost particles. However, also for these cases the ghost level is low with a
fraction of 0.025 and 0.06, respectively.
Fig 6 (right side) compares the converged STB-results to reconstructions using MLOS-SMART and
a subsequent particle peak identification. The fraction of undetected particles is largely similar
between the two techniques. The mean positional error rises for both STB and SMART at
approximately the same rate. As already discussed, STB does not reach the very high accuracy seen
in the previous chapters, but always hold an accuracy advantage compared to tomographic
reconstruction. SMART exhibits an error of around 0.39 pixel for the high-noise case, while STB
shows around 0.24 pixel. The comparison of the total ghost particle intensity shows – as before –
distinct advantages for the STB technique. Maximum values of a fraction of 0.025 for STB are
opposed by values of around 2.2 for SMART. The SMART case shows the same pattern as
recognized for STB: For high noise levels the ghost ratio is higher for lower seeding densities.
It should be noted that no temporal fitting of the particle tracks gained by STB was conducted for
the data shown in Fig. 6. A fit of a moving polynomial of length 15 to the track system enhances the
accuracy for the two cases with higher noise (average errors of around 0.07 pixel for σ = 0.1*Ip,avg
and 0.14 pixel for σ = 0.2*Ip,avg are found).

7. Conclusion

The 4D-PTV scheme, casually termed ‘Shake The Box’ (STB), was introduced in 2013 and at the
time applied to an experimental dataset, showing profound advantages over conventionally used
techniques to evaluate time-resolved three-dimensional data (tomographic PIV, 3D PTV) [Schanz
2013b]. For the work presented here, the method is characterized in terms of accuracy,
completeness of the reconstruction, occurrence of ghost particles and computation time by means of
synthetic data.
Systems of synthetic tracks were derived from divergence-free source vector fields taken from a
tomographic PIV experiment. Time-series of 50 snapshots each were created for different seeding
densities ranging from 0.01 ppp to 0.125 ppp and projected onto four virtual cameras using parallel
projection.
Application of the STB-method to the gained image-series showed that for low to moderate seeding
densities (
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              17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
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accuracy; however it is doubtful that results resembling those gained by STB can be realized. High
quality tomographic reconstructions and velocity information have been shown to be achievable
using advanced reconstruction methods that incorporate temporal information, like Motion
tracking-enhanced MART (MTE) [Novara 2010] or Fluid trajectory correlation (FTC) [Lynch
2013] or combinations of both. Nevertheless the application of these techniques is computationally
very costly.
When introducing noise to the particle images, the realized accuracy is reduced. However, at noise
levels of a well-conditioned experiment, positional error of under 0.1 pixels should be achievable if
using a temporal fit on the particle trajectory. The ghost level remains very low also for images with
high noise levels. For images with even worse conditions it is expected that the STB-method starts
to break down at some point and that TOMO-PIV will be more suited to extract velocity
information due to the robust character of the tomographic reconstruction and the correlation.
The STB-method allows for the first time to extract highly accurate Lagrangian information from
densely seeded flows. Such information is especially valuable for the validation and development of
CFD-code and turbulence models, demanding precise measurements of derivation tensors.
Turbulence research benefits greatly from the availability of accurate acceleration pdfs.

8. Outlook

While the ghost level is remarkably low, it is desirable to remove these last residues, as such
particles might carry plainly wrong velocity data - potentially biasing velocity- and acceleration
statistics. To this end, the algorithm will be modified to allow walking backwards in time. Ghost
particles in STB are often particles that were not predicted correctly and have wandered off their
position during the shake-iterations. Their place was taken by a new particle that starts a new track
at the location the original particle should have been moved to. When walking backwards in time
the two tracks - representing the same real particle - can be connected and the remaining ghost
particle will be deleted. This method also enables a second processing of the first images that show
reduced particle number and accuracies due to the initialization. After the second pass these will
show the same accuracy as the ones in the converged state.
Concerning the generated synthetic track data it is still to be determined to what extent the origin of
the source vector field (3D cross correlation) has smoothed out the most extreme particle
accelerations present in real data. This smoothing could potentially give an advantage to the STB-
method compared to experimental data, as highly accelerated particles are the most difficult to
predict. Variations of the velocity dynamic range of the synthetic data will be processed by STB in
order to characterize maximum accelerations that still can be processed by the algorithm.
First attempts have been made to apply the STB-idea to short time-series (even down to 2 pulses).
For these cases of few measurement points per particle track, the focus is less on the prediction of
particle positions (which at the moment is only possible if at least 5 time-steps are present, as the
minimum track length is 4). Instead, IPR is applied to all time-steps, yielding particle distributions
for every time-step. Within these, matching particles are identified using a predictor vector field
gained from TOMO-PIV. Afterwards, only those particles found to be within a track are kept, a
residual image is calculated and the process is iterated on this image. This method has shown good
results on a four-pulse TOMO-system [Schröder 2013], opening a path to an accurate track-based
evaluation of high-speed flows.

Acknowledgements
The work has been conducted in the scope of the DFG-project “Analyse turbulenter Grenzschichten
mit Druckgradient bei großen Reynoldszahlen mit hochauflösenden Vielkameramessverfahren”.
The experiment providing the data for the first experimental application of STB, as well as the
source velocity field for the synthetic tracks, was funded by the European Research Council through

                                                    - 13 -
th
              17 International Symposium on Applications of Laser Techniques to Fluid Mechanics
                                     Lisbon, Portugal, 07-10 July, 2014

the AFDAR project (grant no. 265695). The authors thank Bernhard Wieneke from LaVision for
fruitful discussions and providing software to eliminate divergence from a given vector volume.

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