16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

Rapid 3D velocity reconstruction from volumetric particle fields via
re-slicing and recombination
Christoph Brücker1,*, Thomas Nonn2
1: Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Freiberg, Germany
2: Dantec Dynamics, Skovlunde, Denmark* correspondent author: bruecker@imfd.tu-freiberg.de

Abstract 3D processing of volumetrically reconstructed particle fields is still a very time-consuming partin 3D-3C velocity field reconstruction. The iterative procedures of multi-pass processing with interrogation
volume adaptation and deformation in 3D cross-correlation (3D CC) or 3D Least-Squares Matching (3DLSM) again increase the computational cost extensively. The number of iterations can be largely reduced
when an initial guess of the translational particle displacement field is determined with 1st order accuracy.
Under the typical assumption of constant velocity gradient tensor VGT in the interrogation volume IV andlow shear and rotation such that the individual correlation functions of each individual particle add in aconstructive manner, the initial guess can be determined in a robust way from the 2D processing of theplanar projections of the interrogation volume when sparsity in the 3D reconstruction process is achieved.
Re-slicing of the voxel volumes in parallel sheets, processing the planar projections of the sheets with 2D CC
or 2D LSM and recombination of the planar velocity field information from orthogonal re-slicing yields thetranslational 3D-3C initial guess field. Total processing time can be speed up about a factor of 20 incomparison to standard processing.

1. Introduction
Processing of voxel-based volumetric particle field reconstructions in volumetric PIV applications
such as Tomo-PIV, 3D Scanning-PIV or Digital Holographic PIV is still a critical bottleneck inprocessing of time-resolved data when longer recording periods are taken. Usually, 3D crosscorrelation or 3D Least-Squares Matching requires huge computational time when interrogating thevoxel volume in 3D interrogation volumes. Typical box sizes of the interrogation volume are oforder of 323 voxel and the corresponding search cuboids are twice as large to ensure that noparticles are lost. In general, discrete 3D cross-correlation (3D CC) is performed using three Fast
Fourier Transforms (FFT) and a complex multiplication. As discussed by Atkinson & Soria (2009)
3D cross-correlation can typically extend to times on the order of 1 hour on a single core machine
for a single pass of 323 interrogation regions IV over an order of 105 vectors. Multi-pass processing
for more accurate estimation of the average particle displacement in the IV requires considerablylarger computational costs with a typical number of 5-10 iterations leading to a full processing timeof 5-10 hours.
On the other hand, 3D LSM is an iterative procedure per se which estimates the averagetranslational displacement of the particles simultaneous to the rotation and shear in the IV. The
number of iterations is dependent on seeding density, the time between successive frames and theaffine parameters enabled in the analysis. A typical number of 30-50 iterations is required for small
box sizes to achieve the residual limit in case of larger contributions of shear and rotation in thefluid. However, regions of unidirectional or smooth flow converged rapidly after a few iterations (5<). The bulk of the processing time for 3D LSM takes place in the iterative deformation of the
cuboids which require efficient three-dimensional interpolation schemes. Typical processing time
for a 313 voxel interrogation volume over an order of 105 vectors on a single core machine amounts-1-

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

to 35h and to 9 hours on a 8core CPU. A mean value of 10 iterations is reported. Thus, both 3D CC
and 3D-LSM are comparable in processing time when rotation and shear is present in the fluid anditerative techniques are required to resolve the velocity gradients and mean translational
components with high accuracy.
However, 3D LSM can largely take profit of GPU-processing as shown in Nonn (2010). As clearlyseen in his results GPU implementation of 3D-LSM clearly reduces the overall time required toprocess a large volumetric dataset. It is also clear that in flows that experience reasonably large
rotation and shear that a GPU solution would clearly reduce the workload experienced by the PC.
The lack of double-precision performance in the GPU did not affect the overall performance. The
processing of interpolations alone were an impressive two orders of magnitude faster than on a
typical workstation CPU. GPU implementations of volumetric applications in general experience a
30-50-fold improvement over CPU implementations. Similar, good performance of GPU processing
in 2D-LSM is reported in the study of Champagnat et al (2011). The showed that iterative gradientbased cross-correlation optimization is an accurate and efficient alternative to multi-pass processing
with FFT-based cross-correlation. Indeed, their FOLKI algorithm is actually a Least Squares
Matching of IW, thus it can be compared to the study of Nonn (2010) as a 2D counter-part. The
processing of 5 image pairs (1376 × 1040 each) is achieved in less than a second on a NVIDIA
Tesla C1060 GPU. Various tests on synthetic and experimental images, including a dataset of the
2nd PIVChallenge, show that the accuracy of their GPU processing is found comparable to that ofstate-of-the-art FFT-based commercial softwares, while beeing 50 times faster. Furthermore, initial
guess methods of the mean translational velocity in the IV may further reduce the 3D-LSM
processing cost by reducing the number of iterative steps in the affine transformation. This isaddressed herein to optimize the existing code even further as processing of many time-steps is of
growing interest.

2. Interrogating sparse reconstructions
Volumetric particle fields are usually reconstructed from limited number of angular displaced
camera orientations with a typical camera number of 4. Voxel-based reconstruction schemes areeither of algebraic nature (e.g. MART) or analytical nature (e.g. back-projection techniques). The
reconstruction of a relatively dense particle distribution in a volume from few projections can bemodeled as finding the sparsest solution of an underdetermined linear system of equations, because
the original particle distribution can be well approximated with only a very small number of active
basis functions relative to the number of possible particle positions in a 3D domain (Petra et al.
2009). Maximizing the sparsity via regularization is an optimization approach and typical values ofreconstructed voxels occupied by particles should be or order of 1% of the total voxel volume when
the reconstruction with 4 cameras is aimed to reconstruct the original (volumetric fill ratio 0.01). In
practice, maximum values of 4% are typical for a 4 camera set-up and MART reconstruction due tonoise and non-spherical particle reconstructions. More sophisticated reconstruction methods such as
the sequential linearization algorithm (SLA) are especially designed to find the sparsest solution(Petra et al 2009) to achieve finally the optimum sparsity with volumetric fill ratio of 1%. When the3D volume reconstructed from 4 projections is discretized in voxels in view of one particle diameterof 3 voxels the resulting particle image density in the projections is roughly N=0.01ppp (particle per
pixel) for exact reconstruction. Imperfect reconstructions may have a larger fill factor at the same
number of true particles. Indeed, the empirical approach of Petra et al (2009) has shown, that typicalparticle densities for ideal reconstruction performance with 4 cameras and sufficient sparsity in thereconstruction is only achieved when the particle image density is of order of 0.01ppp or less.
Higher densities may increase the spatial resolution, however, higher densities also aggravate ill-2-

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

posedness of the reconstruction problem (Petra et al. 2009). As a consequence, particle “smearing”
and Ghost particles appear which considerably reduce the accuracy of the velocity estimation.
Lower densities on the other hand reduce the spatial resolution and limit the application ofcorrelation-based processing. Therefore, we assume in the following a typical particle image density
in the projections of roughly N=0.01ppp which fulfills the sparsity condition of exact
reconstruction.
When interrogating the reconstructed volume with small interrogation volumes (IV) of typical sizeof 323 voxels and using 3D CC procedure, the average velocity within the IV is represented by theconstructive add up of the individual correlation functions of each individual particle (Soria 2008).
A typical value of 12 individual particles is considered in the 323 voxel IV when a particle image
density of N=0.01ppp is given. Due to the effect of velocity gradients represented by the velocity
gradient tensor (VGT), the individual correlation function of particle Pi may not add constructively
but may be distributed around the 3D location in the cross-correlation volume with a radius of ρi.
Thus, 3D peak searching may fail to determine the average velocity. It is generally accepted as apractical rule in PIV to assume a constant VGT in the IV so that the minimum spatial resolution andthe maximum size of the IV in PIV must be such that in the worst measurement case the VGT isconstant within the IV. The resulting requirement then means that the add up will work when thefollowing condition is fulfilled (Soria 2008)

ρi ≈ Δt ri −Qs + Qω ≤ (0.5 particle radius)eq. (1)

where the position ri means the radial distance of the particle from the center of the IV, Qs thesecond invariant of the rate of strain tensor and Qω the second invariant of the rate of rotation
tensor. Therefore, for particles with a diameter of 3 voxels the maximum slip relative to the average
displacement is of order of 1 voxel within the period of t to achieve a constructive add-up of theindividual cross-correlations.
From this condition and the sparsity of N=0.01ppp at 4 cameras it becomes obvious, that 2D CC
processing of the 2D planar projection images of the particle field in the IV may be useful tocircumvent the processing costs of full 3D CC while it may achieve the same quality of the velocity
estimation in the different components of the velocity vector. A similar approach has been proposedby Bilsky et al. (2011). First, such values of sparsity of occupied voxels in the complete
reconstructed volume equate to a typical signal source density on a single projection image well
below the speckle limit. This is when 30% of the particle images overlap and interference effects
start to become significant, which contribute to the degradation of the 2D CC quality. The source
density is defined as the number density of particle images per unit area multiplied by the area of asingle particle image. Thus, at typical particle images densities of N=0.01ppp and projected particle
diameters of 3 pixel the source density is less than 0.1 which means that less than 10% of theparticle images overlap. Secondly, the problem of constructive add-up of individual correlations in
3D reduces in 2D since the radial distance of the particle to the center is always smaller in the 2Dprojection image of the IV than in the IV itself. As a consequence, peak location in the 2D
projection images of the IV is easier to be detected while the 10% overlapping of the particles may
reduce the signal to noise ratio slightly. Consequently, orthogonal planar projections of the IV canbe used to determine all 3 velocity components via 2D CC along the projections. As shown by Soria(2006) in order to keep the 2D CC peak above a normalised value of 0.9 the velocity gradient fieldmust not result in relative displacements across the IW that are larger than 7.8% of the IW size.
Therefore, the condition in eq. (1) always satisfies the conditions in the 2D projections of the IV fora typical IV size of 323 voxel and typical particle diameter of 3 voxels in the reconstructed volume.
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

In conclusion, the method of choice to speed up any iterative procedure in 3D CC or 3D LSM is theinitial guess of the translational field from 2D CC processing of planar projection images of parts of
the reconstructed volume which are obtained by re-slicing the volume in sheets with the thicknessof the IV. These projection images of the sheets are comparable to light-sheet images in standard
PIV taken at arbitrary positions and orientations in the volume. Herein one can profit from the large
bulk of pre- and post-processing tools developed so far for 2D DPIV. In addition, spatial derivativesof the velocity field may help to adapt also an initial guess of the affine parameters in 3D LSM or in
iterative IV deformation. Furthermore, time series analysis may also profit from planar preprocessing.

3. Re-Slicing and 2D processing
Under the discussed conditions of particle image density, reconstruction sparsity maximization andconstant VGT in the IV the velocity vector in the IV itself can be represented to first order accuracy
as the 3 components obtained from planar projections of the small interrogation volume. For
maximum use of the methods developed in traditional planar image processing in 2D DPIV,
processing of the voxel reconstructions is best adapted by successive processing of planar image
projections of sheets taken out of the volume via re-slicing. Typical thickness of the sheet is thedesired thickness of the IV and successive sheets are sliced with an overlap of 50%. For ease of recombination of the planar vector fields into a full 3D cartesian data grid with isotropic grid spacing,
successive runs of re-slicing the volume in orthogonal sheets is applied.
Note that the same procedure can be applied to voxel-based reconstructions from Scanning lightsheet methods (Brücker et al 2012) or holographic recordings with stepwise digital reconstructionsof planes in different depth-positions. Therein, voxel reconstructions are obtained by stacking theplanar images and planar projection images of sheets within the volume can be extracted by reslicing. Such an application of the re-slicing is shown in figure 1 for the data set obtained by highresolution Scanning of the measurement volume with N=100 light-sheets with an overlap of 75% at
a sweep repetition-rate of 90 sweeps/s. The high-speed camera is running in slave mode
synchronized by the sync-pulse of the sheet generating timer of the electronics and reaches a frame
rate of 10kHz for a pixel format of the sensor adjusted to 752×752 px. The flow of interest is avortex ring as seen by the particle distribution in the images. For details the reader is referred to
Brücker et al. (2012). Isotropic re-structuring of the particles in the voxel-based reconstruction of
the scanned measurement volume is achieved by using the intensity variation of a particle image inthe overlapping sheets due to the change of the position of the particle relative to the maximum
intensity in the sheet. For a Gaussian intensity profile of the light-sheet in z-direction, the intensity
variation of the particle image with varying z-position of the particle in the light-sheet follows aGaussian profile, too. Therefore a Gaussian regression can be used to relocate the maximum
position from intensity information of the particle image in overlapping light-sheets.
Herein, only the processing of the top-view planes is discussed further while the processing of theside-view planes is analogue. Within the top-view planes, a 1D Gaussian fit is applied to columns
with constant x-position, which represent light intensity profiles along lines normal to the sensor
plane. The light intensity values at the zn, zn-1 and zn+1 positions along the super-voxels are used
to determine a 1D Gaussian regression curve from which the maximum position and the 2-left and
2-right neighborhood is determined in the smaller set of sub-voxels. The characteristic width of theGaussian regression is re-scaled down to the scale of 3 voxel units irrespective of the value of thecurve fit. Thus, the intensity information along the super-voxels with the maximum at zn is re-4-

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

structured into a set of isotropic sub-voxel with the maximum located at zv-max. The new intensity
distribution is written into a copy of the top-view image, which has been set initially to zero values
and after processing of all collumns a new top-view image is formed. This image is finallysmoothed with a 2D Gaussian in a 3x3 kernel. The same procedure is applied to all re-sliced planes
parallel to the top-view plane in the voxel space. Analogue, the procedure is run thereafter over theside-view planes. Finally both voxel volumes with identical size are combined in an averaging
procedure to obtain the final reconstructed voxel space. This leads to a particle representation in the3D voxel space approaching an isotropic Gaussian blob of a 33 voxel size.

Figure 1: Reconstruction of particle image patterns in orthogonal sheets through the center of thevoxel space. The volume is reconstructed from high-resolution Scanning PIV after voxel fill-up via
stacking and isotropic re-structuring of the particle using a Gaussian regression procedure (Brücker
et al 2012). The planar particle images are gained from re-slicing the voxel space with a sheet
thickness equivalent to the thickness of the light-sheet in the original recordings (thickness w=21)
and planar projection of the sheet into a planar image. Note, that the front view information iscomparable to the image quality of the original recordings in the scan. The particle patterns
indicate the flow in a vortex ring.
Along these planar images gained from re-slicing, classical 2D CC is applied on a regular grid with
322 IW size and 50% overlap resulting in an equidistant grid of 50x50 vectors in the front viewplane. Further sets of parallel planes are generated by re-slicing the volume in the other Cartesian
directions which are orthogonal to each other. 2D CC is repeated on these planar projections of the
sheets and finally, the 3D velocity information along the intersecting grid lines is obtained byrecombination of the vector components. A field of 50x50x30 vectors (in total 75.000 vectors) isachieved in less than 1 minute processing time on a standard quad-core PC. In comparison, thesame volumetric data set needs a processing time of roughly 6 hours in 3D LSM with 30 iterations
for a single time-step. Figure 2 shows the velocity field information in the mid-planes of the voxel
volume corresponding to the image planes shown in figure 1 and figure 3 demonstrates the resultsof the 3D velocity field recombination. As the results demonstrate, the velocity field information is
captured well with the stacking and re-slicing method in all planes.
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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

Figure 2: 2D CC processing results (raw data) of the planar flow in the orthogonal mid-planes of
the reconstructed volume, compare the image planes in figure 1.

Figure 3: Recombination of the velocity data into a 3D velocity grid with equidistant spacing after
re-slicing and 2D CC processing in the orthogonal planes. Left: 3D streamlines, isosurface ofvorticity (green) and isosurface of streamwise velocity (red). The vortex core shows the TsaiWidnall instability as azimuthal waviness and pockets of high-speed axial fluid near the bends ofthe core which indicate the generation of streamwise striations.

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Lisbon, Portugal, 09-12 July, 20124.

Influence of Reconstruction imperfections

As discussed above, imperfections in the reconstruction mainly appear as a consequence of noise
plus a smearing of the particle images in direction of the projections such that the particles appear
as non-spherical reconstructions. This is a typical problem of MART algorithm at larger seeding
densities with N>0.01ppp. On the other hand, voxel stacking from parallel planes in Scanning PIV
or holographic reconstructions suffer from the same problem where the particles are reconstructed
as ellipsoids in direction of depth. It is known from 2D CC analysis that these elongated particle
images distort the correlation peak in direction of the long axis of the particle images and therefore
increase the uncertainty in this component of the velocity vector. While in holographic PIV this“smearing” can only be avoided by a second viewing direction, in Scanning PIV it can be
circumvented by the method proposed in Brücker et al (2012) and describe herein using the methodof isotropic voxel restructuring using the intensity information in overlapping planes and a Gaussian
regression. The resulting improvement of the particle image in the projection is shown in theexample in figure 4. Therefore, sparsity is maximized without addition of extra noise.

Figure 4: Comparison of a re-sliced voxel sheet (thickness w=12) in the top-view plane before andafter isotropic voxel-restructuring using the Gaussian regression procedure. The variation ofbrightness along the elongated ellipsoids in the upper right image corresponds to the variation of
the particle image intensity in the overlapping light-sheets. The isotropic re-structuring in the lower
right image shows the re-shaping of the elongated intensity distributions into smaller Gaussian
blobs representing the particles within the sheet. These blobs are re-located at the maximum
intensity positions of their original individual regression fits.
Application of 2D CC on the upper right-hand image would result in a large stretch of thecorrelation peak in vertical direction, which is restored to a circular shape when the isotropic voxel
restructuring is applied within the reconstruction process. As a matter of fact, orientation of theelongated particle images is always in direction of the voxel stacking and is therefore coherent over
the whole reconstruction volume. In comparison, non-spherical particle reconstructions in MART
appear also as ellipsoids, however the long axis of the ellipsoids may locally vary in the volume
while the typical orientations coincide with either of the viewing directions of the cameras.
Therefore it is expected that the smearing of the particle images may not add in a constructive
manner and thus the uncertainty in 2D CC processing of the re-sliced images is not as large as incomparison to the voxel stacking reconstruction. The effect of MART reconstruction on the planar-7-

16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

projection and CC process is demonstrated in figure 5. It shows the difference of perfectreconstruction in comparison to MART reconstruction on a planar 2D volume and the resulting 1D
CC profiles of the orthogonal projections of the particle images. The images are taken from Petra etal. (2007). The MART reconstruction clearly demonstrates the smearing in direction of the
projections which are at an angle of -45°, -15°, 15° and 45° in a 4-camera set-up. From thesereconstructions we have built the orthogonal projections and applied a 1D CC shown as the plots on
the right-hand side and at the bottom in figure 5. In addition, the 2D CC distribution is shown for alinear displacement of 5 pixels. As expected, the 2D CC distribution shows a deformation of thepeak in case of MART reconstruction in one direction of the projections and some local secondary
peaks near the center peak. As a consequence in the 1D CC of the 1D projections, the peak location
is mismatched with the original peak position in horizontal direction as shown by the green line andthe relative shift of the maximum between the green and red profile at the bottom of figure 5. In
addition, the secondary peak in the green profile representing the true location in the 2D CC inhorizontal direction is shifted about one pixel from the maximum of the red profile. Therefore, theparticle smearing has a distinct effect not only in the 2D CC distribution but more critical in the 1D
CC of the 1D projections in a possible misdetection of the true peak location. As a consequence,
imperfect 3D reconstructions need to be analyzed after re-slicing and application of 2D CC on theplanar images more carefully for possible match of primary or secondary peaks in the correlation
distribution. The result is a higher probability to determine erroneous vectors in comparison to thefull 3D evaluation. On the other hand, the higher uncertainty of the smearing effect leads in any
way to less precision on subvoxel scales as shown by the deformation of the correlation field.

Figure 5: Influence of reconstruction sparsity in a 2D particle field reconstruction on 2D CC
distribution and 1D correlation profiles of the planar projections in orthogonal directions. The
image is reconstructed from a 4 camera set-up measuring the 2D plane from angles -45°, -15°, 15°
and 45°. Top left: exact reconstruction; bottom left: MART reconstruction; bottom plot: 1D CC
profile from vertical projection; right plot: 1D CC profile from horizontal projection (red line:
perfect reconstruction, green line: MART reconstruction). Reconstructions are taken form Petra etal. (2007).

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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

Contrary to the destructive effect of the VGT on the CC procedure, for MART reconstruction thevelocity gradients may reduce the probability that the same particle in successive time steps appears
in the non-spherical reconstruction with the same orientation of the long axis of the ellipsoids. Thismay counteract the reduction of the signal-to-noise ratio of the correlation peak in the projection
images.

5.

Discussion and conclusion

Under the discussed conditions of particle image density, reconstruction sparsity maximization andconstant VGT in the IV the velocity vector in the IV itself can be represented to first order accuracy
as the 3 components obtained from planar projections of the small IV. For maximum use of themethods developed in traditional planar image processing in 2D DPIV, processing of the voxel
reconstructions is best adapted by successive processing of planar image projections of sheets takenout of the volume via re-slicing and thereafter a recombination of the 2D planar velocity fields into
a 3D velocity grid. Under good reconstruction qualities, this 3D velocity field is a perfect initial
guess of the velocity distribution which may help to reduce largely the iterative costs of multi-path
3D CC processing or iteration in 3D LSM.
When comparing the 2D CC case of projected images with the 3D CC case of interrogating thereconstructed volume in small IV, the number of multiplication operations requires = (Nlog2N)
operations, where N is the product of the dimension of the IV such that for a 3D IV N=Nx×Ny×Nz.
A further O(2N) operations are then required for the complex conjugate, bring the total number ofoperations of FFT based cross-correlation to O(3Nlog2N + 2N). In addition, one has to take into
account the 3D peak search algorithm to determine the maximum position in the IV, which takes
again a number of time for quick-sorting. In comparison, the 2D CC may reduce the processing
costs about the maximum number of the size of the IV in comparison to the full 3D CC procedure.
More significant, GPU processing may drastically improve the computational 2D CC performance
as shown by Champagnat et al (2011). They demonstrated that iterative gradient-based crosscorrelation optimization is an accurate and efficient alternative to multi-pass processing with FFTbased cross-correlation. The accuracy of their GPU processing is found comparable to that of stateof-the-art FFT-based commercial softwares, while beeing 50 times faster. Thus, initial guess
processing may not only profit from re-slicing the volume but also from the extraordinary
performance of GPU processing in planar images. They reported processing times of less than asecond for 5 image pairs (1376 × 1040 each) on a NVIDIA Tesla C1060 GPU. Extrapolating thetimes to the processing estimations above in our application of the vortex ring with a voxel volumeof 750×750×500 voxel and a total number of roughly 75.000 vectors leads to a total processing timeof 0.08s per image pair of size (750×750 px) and for the total number of 50xy + 50yz planes to a
total processing time of 8 seconds for 75.000 vectors. Note that the re-slicing can be performed in
the RAM and the planar projected images can be kept during this time in the RAM, too. In
conclusion, application of state of the art 2D processing of planar image reconstruction may largely
reduce the total processing costs for volumetric velocimetry based on voxel reconstruction. This
may either be as an initial guess of the 3D velocity field distribution including the VGT or
immediately as the final 3D velocity field result when the voxel reconstruction has maximum
sparsity at a given particle density.

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16th Int Symp on Applications of Laser Techniques to Fluid Mechanics
Lisbon, Portugal, 09-12 July, 2012

List of References
Bilsky AV, Dulin VM, Lozhkin VA, Markovich DM, Tokarev MP (2011) Two-dimensionalcorrelation algorithms for Tomographic PIV. In: Proc. 9th Int. Symp. Particle Image Velocimetry(PIV 2011), Kobe, Japan, July 21-23, 2011.
Brücker Ch, Hess D, Kitzhofer J (2012) Single-View Volumetric PIV via High-Resolution
Scanning, isotropic voxel restructuring and 3D Least-Squares Matching (3D-LSM). Accepted for
publication in special issue of Measurement Sci. Techn. on Volumetric Velocimety.
Champagnat F, A. Plyer1 A, Le Besnerais G, Leclaire B, Davoust S, Le Sant Y (2011) Fast andaccurate PIV computation using highly parallel iterative correlation maximization. To appear inExp. Fluids.
Hess D, Brücker C, Kitzhofer J, Nonn T (2011) Single-View Volumetric PIV using High-resolution
Scanning and Least Squares Matching. In: Proc. 9th Int. Symp. Particle Image Velocimetry (PIV2011), Kobe, Japan, July 21-23, 2011.
Nonn T (2010) Application of High Performance Computing on Volumetric Velocimetry
Processing. In: Proc. 15th Int. Symp. Laser Techn. Fluid Flows, Lisbon, Portugal, 2010.
Petra S, Schnörr C, Schröder A, Wieneke B (2007) Tomographic image reconstruction inexperimental fluid dynamics: synopsis and problems. In Proc. 6th Workshop on Modelling ofEnvironmental and Life Sciences Problems (WMM 07), Constanta, Romania, Sept. 5-Sept. 9 2007.
Petra S, Schnörr C, Schröder A (2009) 3D Tomography from Few Projections in Experimental
Fluid Dynamics. In: Notes on Numerical Fluid Dynamics. Springer, 2007.
Soria J (2008) Effect of velocity gradients on 3D cross-correlation PIV analysis. In: Proc. 14th Int.
Symp. Laser Techn. Fluid Flows, Lisbon, Portugal, 2008.

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