1 Introduction
Case | Description | Provider | Image type | Number of sets |
---|---|---|---|---|
A | Microscopic PIV | Kähler/Cierpka | Real | 600 Single exposed double-frame images |
B | Time-resolved PIV | Kähler/Hain | Real | 1044 Single exposure images |
C | Resolution/accuracy of tomo-PIV | Astarita/Discetti | Synthetic | 1 Single exposed double-frame imagea (4 views) |
D | Time-resolved tomo-PIV of complex flow | Astarita/Discetti | Synthetic | 50 Single exposure images (4 views) |
E | Stereoscopic PIV | Vlachos/La Foy | Real | 1800 Single exposure images (2 views) |
F | Standard PIV (interactive) | Sakakibara | Real | 1 Single exposed double-frame image |
2 Organization
Name | Country | Institution |
---|---|---|
Christian J. Kähler | Germany | Bundeswehr University Munich |
Tommaso Astarita | Italy | University of Naples Federico II |
Pavlos P. Vlachos | USA | Purdue University |
Jun Sakakibara | Japan | Meiji University |
Name | Country | Institution |
---|---|---|
Michel Stanislas | France | Ecole Centrale de Lille |
Koji Okamoto | Japan | University of Tokyo |
Ronald J. Adrian | USA | Arizona State University |
3 Review
4 List of Challenge Participants
Acronym | Company/university | Country | Contact person | A | B | C | D | E |
---|---|---|---|---|---|---|---|---|
ASU | Arizona State University | USA | John Charonko |
\(\times\)
|
\(\times\)
| |||
BUAA | Beijing University of Aeronautics and Astronautics | China | Qi Gao |
\(\times\)
|
\(\times\)
| |||
Dantec | Dantec Dynamics A/S | Denmark | Vincent Jaunet |
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
| |
DLR | German Aerospace Center (DLR) | Germany | Christian Willert |
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
|
INSEAN | CNR-INSEAN | Italy | Massimo Miozzi |
\(\times\)
|
\(\times\)
| |||
IOT | Institute of Thermophysics SB RAS | Russia | Mikhail Tokarev |
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
|
IPP | Institut Pprime | France | Laurent David |
\(\times\)
|
\(\times\)
|
\(\times\)
| ||
LANL | Los Alamos National Lab | USA | John Charonko |
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
|
LaVision | LaVision GmbH | Germany | Dirk Michaelis |
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
|
MicroVec | MicroVec Inc. | China | Wei Runjie |
\(\times\)
|
\(\times\)
| |||
MPI | Max Planck Institute for Dynamics and Self-Organization | Germany | Holger Nobach |
\(\times\)
| ||||
ONERA | ONERA | France | Benjamin Leclaire |
\(\times\)
| ||||
TCD | Trinity College Dublin | Ireland | Tim Persoons |
\(\times\)
|
\(\times\)
| |||
TSI | TSI Incorporated | USA | Dan Troolin |
\(\times\)
|
\(\times\)
| |||
TsU | Tsinghua University | China | Qiang Zhong |
\(\times\)
| ||||
TUD | Technical University Delft | Netherlands | Kyle Lynch |
\(\times\)
|
\(\times\)
|
\(\times\)
|
\(\times\)
| |
UniG | University of Göttingen | Germany | Martin Schewe |
\(\times\)
| ||||
UniMe | University of Melbourne | Australia | Dougal Squire |
\(\times\)
|
\(\times\)
| |||
UniNa | University of Naples Federico II | Italy | Gennaro Cardone |
\(\times\)
| ||||
URS | University of Rome La Sapienza | Italy | Monica Moroni |
\(\times\)
|
5 Case A
5.1 Case description and measurements
-
High dynamic velocity range (Adrian 1997)
-
Depth of correlation
-
Optical aberrations due to the thick window
-
Low signal-to-noise ratio (SNR) and cross-talk
-
Cavitation
5.2 Image quality for \(\upmu \hbox {PIV}\)
5.3 Participants and methods
Team | Type of evaluation | Code description | Final IW size [px] | Window weighting | Final VS [px] | Fit | Preprocessing | Mask generation | Postprocessing |
---|---|---|---|---|---|---|---|---|---|
Dantec | PIV eval1 mean/rms | Adaptive multi-pass, window deformation, universal outlier detection between passes, predictor from ensemble average | 32 × 32 | Wall windowing (only near the walls) | 4 | 2D Gauss | Harmonic mean subtraction, reduction of cross-talk, min/max contrast enhancement | Algorithmic | Temporal N-Sigma validation (Sigma = 5.0) |
DLR | PIV eval1/2, mean/rms | Multi-pass algorithm, coarse-to-fine resolution pyramid, starting at 256 × 256, using images deformed a priori with predictor field for eval2 | 32 × 32 (eval1), 24 × 24 (eval2) | None | 4 | 3 × 3 2D Gauss | Median filtering, mean intensity subtraction, mild smoothing | Manual, from rms image | Normalized median filter (Scarano and Westerweel 2005), 3 × 3 neighborhood difference filter |
INSEAN | optical flow, eval1/2, mean/rms | Multi-pass pyramidal algorithm, minimization of sum of squared differences, tracking | 32 × 32 (eval1), 24 × 24 (eval2) | Gauss |
\(<\)2 | Subtract mean img., subtract local mean, histogram stretching | Algorithmic | Multivariate filter in u’v’ space, 2 px std. dev. Gauss filter | |
IOT | PIV eval1/2 mean/rms | Multi-pass algorithm, ensemble correlation (eval1), single–pixel correlation (eval2) (Karchevskiy et al. 2016) | 32 × 32 (eval1), 2 × 2 (eval2) | None | 2 | Elliptic 2D Gauss | Subtract mean image, local median 3 × 3, subtract local median 7 × 7, low-pass Gaussian 5 × 5 | Manual | Velocity range validation (eval1), moving average filter 10 × 10, kriging interpolation |
LANL | PIV eval1 mean, PTV eval2 mean/rms | Multi-pass deform algorithm, ensemble correlation, robust phase correlation for eval1 (Eckstein et al. 2008), particle ID by dynamic thresholding, multi-parametric particle matching (size, intensity, position) for eval2 | 32 × 32 | Gauss (Eckstein et al. 2009) | 2 (eval1), varied (eval2) | 1D 3 pt Gauss (eval1), 2D Gauss (eval2) | Subtract mean image separately on A/B, subtract attenuated B-A/A-B, threshold background level | Algorithmic (max intensity then morphological operations) | None |
LaVision | PIV eval1/2 mean/rms | Single-pass cross-correlation with predictor by ensemble correlation | 32 × 32 (eval1), 16 × 16 (eval2) | 8 (eval1), 4 (eval2) | Minimum subtraction, hot pixel correction, offset subtraction | Vector averaging for \(\pm 10\) pixel | |||
MicroVec | PIV eval1 mean/rms | Multi-pass algorithm | 32 × 32 | none | 2 | 1D Gauss | 3 × 3 Gauss filter | manual | Normalized median filter |
TCD | PIV eval1/2 mean/rms | Multi-pass FFT algorithm (Persoons and O’Donovan 2010), continuous window deformation, non-square interrogation windows | 32 × 32 (eval1), 128 × 32 (eval2) | None | 2 (eval1), 32 × 16 (eval2) | 2D Gauss (special ranking) | None | Manual | 3 × 3 Gauss filter |
TSI | PIV eval1 mean/rms, eval2 mean | 32 × 32 | Gauss | 8 | 2D Gauss | Mean subtraction, noise removal | Manual | Rohaly-Hart (Rohaly et al. 2002), 3 × 3 universal median filter, 3 × 3 Gauss filter | |
TUD | PIV eval1/2 mean/rms | Iterative image deformation initialized using ensemble correlation predictor | 32 × 32 | Gauss, \(\alpha = 2.5\)
| 4 | 1D Gauss | Historical minimum subtraction, average normalization, spatial bandpass filtering, thresholding | Manual | |
UniG | PIV eval1 mean/rms | Direct cross-correlation, multi-grid/pass, mod. Whittaker deform., multi-pass peak finder (Schewe 2014), ensemble correlation | 32 × 32 | Triangular and bell-shaped window weighting | 2 | 2 × 1D Gauss | Only gray value clipping | Manual and algorithmic | 3 × 3 median-based peak prediction within the multi-peak finder, but no direct vector postprocessing |
UniMe | PIV eval1/2 mean/rms | Multi-grid algorithm, multiple pass spurious correction, iterative mean offset with adaptive thresholding, multiple correlation spurious correction | 32 × 32 (eval1), 16 × 16 (eval2) | None | 2 | 1D Gauss | Background subtraction, Gaussian smoothing, median filtering | Manual | 3 × 3 median criterion validation with cubic interpolation (Scarano and Westerweel 2005), second-order Savitzky–Golay filter |
UniNa | PIV eval1/2 mean | Multi-pass algorithm(Astarita and Cardone 2005), ensemble correlation | 33 × 33 (eval1), 11 × 11 (eval2) | Blackman window weighting | 1 | 3 Points | Local minimum subtraction, band-pass median filter, threshold | None |
5.4 Mask generation
Team | Mask generation | Small channel width in px |
---|---|---|
Dantec | Algorithmic, temporal maximum, spatial smoothing, thresholding | 176 |
DLR | Manual from rms image | 182 |
INSEAN | Algorithmic | 174 |
IOT | Manual | 180 |
LANL | Algorithmic, maximum image and morphological operations | 190 |
LaVision | (Manual) | 162 |
MicroVec | Manual | 178 |
TCD | Manual | 184 |
TSI | Manual | 194 |
TUD | Manual | 178 |
UniG | Manual and algorithmic | 178 |
UniMe | Manual | 190 |
UniNa | None | 160 |
5.5 Results
5.5.1 Evaluation 1
5.5.2 Evaluation 2
5.6 Conclusion
-
In \(\upmu \hbox {PIV}\) usually fluorescent tracer particles are used to separate the signal from the background using optical filters. Thus one may assume that preprocessing is not needed to enhance the signal-to-noise ratio. However, the analysis of case A shows that image preprocessing is important to avoid incorrect displacement estimations caused by typical camera artefacts such as cold and hot pixel or cross-talk between camera frames. The latter appears if the laser pulse separation is comparable to the interframing time of the digital cameras. The influence of gain variations for different pixels is usually lowered using image intensity correction implemented in most camera software. If it can not fully be balanced, the analysis shows that the different background removal methods applied by the teams work similarly well. However, it is evident from the results provided by MicroVec and TCD that smoothing does not work effectively to eliminate fixed pattern noise.
-
It is well known that the precise masking of solid boundaries before evaluating the measurements is a very important task. The masking affects the size of the evaluation domain and thus the region where flow information can be measured. Thus a precise masking is desirable to maximize the flow information. However, the present case shows that this is associated with large uncertainties. The estimated width of the small straight channel varied by more than 20 % among all submissions. This unexpected result illustrates the strong influence of the user. To avoid this user-dependent uncertainty, universal digital masking techniques are desirable to address this serious problem in future measurements.
-
Another interesting effect could be observed by comparing the strongly varying velocity profiles across the small channel. Due to the spatial correlation analysis, the flow velocity close to solid boundaries is usually overestimated. However, as the spatial resolution effect was almost identical for all teams in the case of evaluation 1 the variation can be attributed to the special treatment of near-wall flow. While most teams did not use special techniques, variations are mainly caused by the masking procedure. In contrast, UniMe seems to resolve the boundary layer effect much better than the other teams. This was achieved by implementing the no-slip condition in the evaluation approach. Although this model-based approach shows the expected trend of the velocity close to the wall, it is evident that the results are strongly biased by defining the location of the boundaries. Unfortunately, the definition of the boundary location is associated with large uncertainties, as already discussed, and therefore, this model-based approach is associated with large uncertainties. Therefore, it would be more reliable to make use of evaluation techniques which enhance the spatial resolution without making any model assumption such as single-pixel PIV or PTV evaluation techniques (Kähler et al. 2012b). However, as the uncertainty of these evaluation techniques is not always better than spatial correlation approaches, it is recommended to evaluate the measurements in a zonal-like fashion as done in numerical flow simulations, where RANS simulations are coupled with LES or even DNS simulations to resolve the flow unsteadiness at relevant locations. The zonal-like evaluation approach minimizes the global uncertainty of the flow field if the near-wall region is evaluated using PTV (to avoid uncertainties due to spatial filtering or zero velocity assumptions at the wall) while at larger wall distances spatial correlation approaches are used (because the noise can be effectively suppressed using statistical methods).
-
Furthermore, the precise estimation of the mean velocity is very important for the calculation of higher-order moments. The strong variation of the rms values illustrates that the uncertainty quantification is very important because the differences, visible in the results, deviate much more than expected from general PIV uncertainty assumptions. Here future work is required to quantify the reliability of a PIV measurement.
-
Since in microscopic devices the flow fields show large in-plane and out-of-plane gradients and are inherently three-dimensional, it is beneficial to use techniques that allow a reconstruction of all three components of the velocity vector in a volume (Cierpka and Kähler 2012). Of special interest are techniques that allow a depth coding in 2D images as confocal scanning microscopy (Park et al. 2004; Lima et al. 2013), holographic (Choi et al. 2012; Seo and Lee 2014) or light-field techniques (Levoy et al. 2006), defocusing methods (Tien et al. 2014; Barnkob et al. 2015) or the introduction of astigmatic aberrations (Cierpka et al. 2011; Liu et al. 2014).
6 Case B
6.1 Case description
-
Low signal strength and signal-to-noise ratio
-
Small particle image size due to the large pixel size of the camera
-
Large dynamic velocity range (DVR)
-
Large turbulent intensities
-
Strong out-of-plane motion due to 3D effects (turbulence, separation)
-
Laser light reflections at the walls.
6.2 Evaluation of case B
6.2.1 Evaluation 1
6.2.2 Evaluation 2
6.3 Participants and methods
Team | Type of evaluation | Code description | Final IW size [px] | Window weighting | Final vector spacing before interpolation [px] | Fit | Preprocessing | Mask generation | Postprocessing |
---|---|---|---|---|---|---|---|---|---|
Dantec | PIV | Multi-pass algorithm |
\(32 \times 32\)
| No | 2 | 2D Gauss | Background subtraction + intensity normalization | Algorithmic | Temporal N-Sigma validation (Sigma = 5.0) |
DLR | PIV | dual frame, coarse-to-fine pyramid correlation (\(96 \times 94\) start) |
\(32 \times 32\)
| No | 2 |
\(5 \times 5\) 2D Gauss | Subtract mean image (combined subtract and divide), intensity capping of 2.5 % pixels, pixel mirroring on mask edge | Manual, from maximum image | Normalized median filter, Z-score validation (4 sigma) |
INSEAN | OF | Multi-pass pyramidal algorithm, minimization of sum of squared differences, tracking |
\(32 \times 32\)
| Gaussian window weighting | <2 | N/A | Subtract mean img + subtract local mean + histogram stretch | Algorithmic | Natural neighborg interpolation with Bezier–Berenstain patches |
IOT | PIV | Multi-pass multi-grid algorithm |
\(32 \times 32\)
| Gaussian window weighting | 2 | 3-Point least square | Fourier high pass with the cutoff frequency 56 Hz | Manual | spatial \(7 \times 7\) and temporal adaptive median filters, Gaussian weighted interpolation, Fourier low-pass with the cutoff frequency 300 Hz |
IPP | PIV | Multi-pass algorithm |
\(32 \times 32\)
| Gaussian window weighting | 2 | 3-Point 1D Gauss | Subtract mean image, subtract local mean (normalized FFT) | Manual |
\(5 \times 5\) Median outlier correction |
LANL | PIV | Multi-pass deform algorithm, robust phase correlation |
\(32 \times 32\)
| Gaussian window weighting, \(16 \times 16\) resolution | 2 | 3-Point 1D Gauss | Median subtraction, multiplied by mask | Mean intensity, threshold, morphological operations, with manual edits | Universal outlier detection, \(16 \times 16\) px (\(8 \times 8\) vec) Gaussian filter |
MicroVec | PIV | Multi-pass algorithm |
\(32 \times 32\)
| No | 2 | 3-Point 1D Gauss |
\(3 \times 3\) Gauss filter | Manual | Normalized median filter |
MPI | PIV | Multi-pass algorithm, window sub-pixel shift and first-order deformation, Whittaker image interpolation (2 frames distance) |
\(32 \times 32\)
| 2D-triangular window | 2 | 2D Gauss, correction of particle image intensity variations | No | No | Universal outlier detection, second peak validation |
TCD | PIV | Multi-pass algorithm, continuous window deformation |
\(32 \times 32\)
| No | 2 | 1D Gauss | High-pass spatial filter (5 pixel sliding background) | Manual |
\(3 \times 3\) Gauss filter |
TSI | PIV | Multi-pass, cascading window deformation, Rohaly–Hart, spot offset |
\(32 \times 32\)
| Gaussian window weighting | 8 | 2D Gauss | Subtract mean image, noise removal | Manual | Rohaly–Hart, \(3 \times 3\) universal median filter, \(3 \times 3\) Gauss filter |
TsU | PIV | Multi-pass, multi-grid, image deformation algorithm |
\(32 \times 32\)
| No | 2 | 3-Point 1D Gauss | Replace no-fluid regions with pre-generated particle image, median filter, local contrast-stretching transformation | Manual |
\(3 \times 3\) Gauss filter |
TUD | PIV | Multi-pass algorithm with window deformation |
\(32 \times 32\)
| Gaussian window weighting | 2 | 3-Point 1D Gauss | intensity normalization with respect to time-averaged temporal minimum subtraction and \(3 \times 3\) Gaussian smoothing | Manual | No |
UniMe | PIV | Multi-grid algorithm with iterative window deformation, multiplication of correlation plane |
\(32 \times 32\)
| No | 2 | 2D Gauss, 1D Gauss | Subtract mean image, histogram clipping, Gaussian smoothing, local image normalization | Manual | Validation median criterion, cubic interpolation |
Team | Type of evaluation | Code description | Final IW size [px] | Window weighting | Final vector spacing before interpolation [px] | Fit | Preprocessing | Mask generation | Postprocessing |
---|---|---|---|---|---|---|---|---|---|
Dantec | FTC (fluid trajectory correlation) | Second-order polynomial fit to trajectory across 5 temporal neighbor images |
\(32 \times 32\)
| No | 8 | 2D Gauss | Background subtraction + intensity normalization + \(3 \times 3\) Gaussian blur | Algorithmic | Bilinear interpolation to 2 pixel vector spacing |
DLR | PIV | Triple-frame, coarse-to-fine pyramid correlation (96x94 start), image separation \(\pm 2\)
|
\(32 \times 16\)
| No | 2 | 5x5 2D Gauss | Subtract mean image (combined subtract and divide), intensity capping of 2.5 % pixels, pixel mirroring on mask edge | Manual, from maximum image | Normalized median filter, Z-score validation (4 sigma), Gaussian smoothing (sigma=node spacing), Gaussian smoothing in time (\(\pm 2\) fields) |
INSEAN | OF | Multi-pass pyramidal algorithm, minimization of sum of squared differences, tracking |
\(28 \times 28\)
| Gaussian window weighting | 2< at first step. Free to evolve (<2) with trajectory sway | N/A | Subtract mean image. Subtract local mean. Histogram stretch | Algorithmic | Temporal Savitzky and Golay filter on trajectories. Natural neighborg interpolation with Bezier–Berenstain patches |
IOT | PIV | Adaptive sampling Multi-pass algorithm with pyramid correlation over 5 image frames | Adaptive, square IW’s from 16 to 48 px | Gaussian window weighting | 2 | 3-Point least square | Fourier high pass with the cutoff frequency 56 Hz | Manual | Spatial \(7 \times 7\) and temporal adaptive median filters, Gaussian weighted interpolation, Fourier low-pass with the cutoff frequency 300 Hz |
IOT-PTV | PTV | Relaxation PTV algorithm | 3-Point least square | Subtract mean image | Manual | Spatial \(7 \times 7\) and temporal adaptive median filters, gaussian weighted interpolation, fourier low-pass with the cutoff frequency 300 Hz | |||
IPP | PIV | Multi-pass algorithm, FTEE (fluid trajectory evaluation based on an ensemble-averaged cross-correlation) |
\(32 \times 32\)
| Gaussian window weighting | 2 | 3-Point 1D Gauss | Subtract mean image, subtract local mean (normalized FFT) | Manual |
\(5 \times 5\) Median outlier correction |
LANL | PIV | Multi-pass algorithm, fluid trajectory correlation |
\(32 \times 32\)
| Gaussian window weighting, \(16 \times 16\) resolution | 2 | 3-Point 1D Gauss | Median subtraction, multiplied by mask | Mean intensity, thresholded, morphological operations, with manual edits | Universal outlier detection in space and time |
LaVision | PIV | Multi-pass algorithm, pyramid correlation |
\(24 \times 24\)
| Gaussian window weighting | 6 | 3-Point 1D Gauss | Subtraction of average of each pixel over time | Manual | None |
MPI | PIV | Multi-pass algorithm, window sub-pixel shift and first-order deformation, Whittaker image interpolation (4 frames distance) |
\(32 \times 32\)
| 2D-triangular window |
\(2 \times 2\)
| 2D Gauss, correction of particle image intensity variations | No | No | Universal outlier detection, second peak validation |
TCD | PIV with HDR | Multi-pass algorithm, continuous window deformation |
\(32 \times 32\)
| No | 4 | 1D Gauss | High-pass spatial filter (5 pixel sliding background) | Manual |
\(3 \times 3\) Gauss filter |
TSI | PIV | Multi-pass, cascading window deformation, Rohaly–Hart, spot offset |
\(32 \times 32\)
| Gaussian window weighting | 8 | 2D Gauss | Subtract mean image, noise removal | Manual | Rohaly–Hart, \(3 \times 3\) universal median filter, \(3 \times 3\) Gauss filter |
TsU | PIV | Multi-pass, multi-grid, image deformation algorithm |
\(32 \times 32\)
| No | 4 | 3-Point 1D Gauss | Replace no-fluid regions with pre-generated particle image, median filter, local contrast-stretching transformation | Manual |
\(3 \times 3\) Gauss filter |
TUD | PIV | Multi-pass algorithm with window deformation, multi-frame pyramid correlation |
\(16 \times 16\)
| Gaussian window weighting | 4 | 3-Point 1D Gauss | Intensity normalization with respect to time-averaged temporal minimum subtraction and \(3 \times 3\) Gaussian smoothing | Manual | Second-order polynomial regression in space-time (\(5 \times 5\) spatial kernel, 9 samples in time) |
UniMe | PIV | Multi-grid algorithm with window deformation, multiplication of correlation plane, multi-frame correlation multiplication |
\(16 \times 16\)
| No | 2 | 2D Gauss, 1D Gauss | Subtract mean image, histogram clipping, gaussian smoothing, local image normalization | Manual | Validation median criterion, cubic interpolation |
URS | PTV-OF | Hybrid lagrangian particle tracking |
\(11 \times 11\)
| No | 2 | N/A | No | No | Adaptive Gaussian arithmetic average |
6.4 Results
6.5 Conclusions
-
The discussion shows that results from evaluation 1 are quite consistent, but the results from evaluation 2 show significant differences, in particular when the rms fields are considered. This implies that the results depend significantly on the user and his/her experience and intention. This holds in particular true for the parameters of the preprocessing, the evaluation as well as the postprocessing. Thus it is dangerous to use PIV as black box because the application of the technique still requires substantial expert knowledge and experience.
-
The analysis also shows that the uncertainty of the technique can be greatly reduced by making use of multi-frame evaluation techniques because they evaluate the temporal history of particle image trajectories. However, in order to benefit from the temporal analysis of the particle pattern, different aspects in an sophisticated evaluation method have to be considered. In the case of strongly oversampled image sequences, as provided here, a damping of the amplitudes at higher frequencies is acceptable from the physical point of view. However, caution is advised not to suppress physically relevant frequencies. A smooth field in space and time does not necessarily mean a high evaluation accuracy.
-
Another strong advantage of multi-frame evaluation techniques is the reduction in bias errors due to the peak-locking effect. How a displacement at a certain location is obtained by a sophisticated evaluation method determines the level of the peak-locking reduction. Choosing an optimal temporal separation between correlated images at a certain location may lead to an increased relative measurement accuracy and will reduce peak locking. However, if a displacement at a certain location is determined not only from a single correlation but from a kind of (weighted) average from many correlations with different temporal separations, the peak-locking effect can be averaged out in principle. Finally, the multi-frame analysis makes it possible to compensate also acceleration and curvature effects, which is important for highly accurate measurements in strongly unsteady flows.
7 Case C
7.1 Abbreviations
7.2 Case description
7.3 Algorithms
Team | Image density (ppp) | Calibration | Reconstruction | PIV processing | Postprocessing |
---|---|---|---|---|---|
ASU | 0.050 | Image segmentation (Ding and Adrian 2014) at 20 vox/mm. Intensity value on images interpolated with cubic spline. Intensity distributions smoothed with Gaussian filter (\(3 \times 3 \times 3\), std 0.6) | Planar 2D multi-pass image deformation method on xz and xy planes (summing 20 planes in the y and z direction respectively). Interrogation volume side 1.0 mm | Gaussian smoothing (\(9 \times 9 \times 9\), std 2.4) | |
BUAA | 0.075 | Third-order polynomial mapping, in x and y and 1st in z
| 10 Intensity-enhanced MART (inverse diffusion equation) iterations at 20 vox/mm. Gaussian smoothing of the original images (\(3 \times 3\), std 0.5). Gaussian smoothing between the iterations (Discetti et al. 2013) | Iterative discrete windows offset. Interrogation volume side 1.6 mm | Gaussian smoothing (\(5 \times 5 \times 5\), std 0.8). POD-based postprocessing to reduce noise |
Dantec | 0.075 | Direct linear transformation | 10 MART iterations after initialization with MinLOS (Maas et al. 2009) at 20 vox/mm. Gaussian blurring on \(3 \times 3 \times 3\) voxels, iterated 5 times | 3D Least squares matching algorithms Westfeld et al. (2010). Interrogation volume side 1.65 mm | Median filter (\(3 \times 3 \times 3\)) |
DLR | 0.075 | Artificial volume with 6 voxels diameter Gaussian blobs, generated at reconstructed particle positions. 3D cross-correlation with volume deformation. Interrogation volume side 1.6 mm | Moving average smoothing (\(2 \times 2 \times 2\)) | ||
Hacker | 0.075 | Perfect | Perfect at 20 vox/mm | Iterative volume deformation with a top hat moving average approach (Astarita 2006). Interrogation volume side 1.6 mm | None |
IoT | 0.100 | Pinhole camera model Tsai (1987). | 20 SMART iterations after initialization with MLOS followed by 5 MTE iterations each composed of 20 SMART (Novara et al. 2010) at 20 vox/mm. Volume extended by 4 mm on each side to minimize edge effects | Iterative volume deformation method. Interrogation volume side 1.4 mm | None |
IPP | 0.050 | Pinhole camera model Tsai (1987) | 8 BIMART (Byrne 2009) iterations, block size 4, relaxation parameter 0.38 at 20 vox/mm. Volume extended by 2.4 mm on each side to minimize edge effects | Iterative volume deformation with Gaussian window \((\alpha = 2)\). Interrogation volume side 2.35 mm | None |
LANL | 0.075 | Direct linear transformation | Optimized MLOS with exponent 1 (La Foy and Vlachos 2011) at 20 vox/mm. Particles suppression in order to get ppp matching with the images. Background suppression (1 % of maximum) | Iterative volume deformation with Motion Tracking Blanking and Robust Phase Correlation (Eckstein et al. 2008). Interrogation volume side 1.0 mm. Gaussian windowing (effective size 0.8 mm) | Gaussian smoothing (std 2 voxels) |
LaVision | 0.075 | Pinhole camera model Tsai (1987) | Iterative volume deformation with fast direct cc (Discetti and Astarita 2012). Interrogation volume side 2.4 mm. Gaussian windowing (effective size 1.2 mm) | None | |
ONERA | 0.075 | Pinhole camera model Tsai (1987). | 25 PVR+SMART iterations after initialization with MLOS (Champagnat et al. 2014) at 45 vox/mm. Decimation to reach 23 vox/mm. | FOLKI3D algorithm (Cheminet et al. 2014) based on least square optimization. Interrogation volume side 1.8 mm. Gaussian windowing (effective size 1.2 mm) | None |
ONERA_PTV | 0.030 | Pinhole camera model Tsai (1987) | Local maxima detection after initialization with MLOS, refinement with 15 PVR-CoSaMP iterations (Cornic et al. 2013) | 3D Particle tracking embedded within the reconstruction step | Natural neighbor interpolation on structured grid |
TUD | 0.075 | Iterative volume deformation with fast direct cc (Discetti and Astarita 2012) and Gaussian windowing. Interrogation volume side 1.6 mm | None |
7.4 Reconstruction
-
Number of true and ghost particles \((N_T, N_G)\);
-
Quality factor, as defined in Elsinga et al. (2006b), i.e., the correlation factor between the true and the reconstructed intensity distributions, as defined in Eq. 5:where \(I_{ijk}\) and \(I_{ijk}^{e}\) are the intensity values of the reconstructed and the exact distributions, respectively. Since each participant used its own grid (different voxel origin, resolution, etc.), in order to evaluate Q all the reconstructed volumes are interpolated on a common grid by using third-order spline interpolation;$$\begin{aligned} Q = \frac{\sum I_{ijk}I_{ijk}^{e}}{\sqrt{\sum ( I_{ijk} )^2 \sum ( I_{ijk}^{e} )^2}} \end{aligned}$$(5)
-
Mean intensity of true and ghost particles \(\left( \left\langle I_T \right\rangle , \, \left\langle I_G \right\rangle \right)\);
-
Weighted levels WL and power ratio PR, as defined in Eqs. 6 and 7:$$\begin{aligned} \hbox {WL}= & {} \frac{N_T \left\langle I_T \right\rangle }{N_G \left\langle I_G \right\rangle } \end{aligned}$$(6)$$\begin{aligned} \hbox {PR}= & {} \frac{N_T}{N_G} \left( \frac{\left\langle I_T \right\rangle }{\left\langle I_G \right\rangle }\right) ^2 \end{aligned}$$(7)
7.5 Displacement field
-
3D modulation transfer function (MTF) as a function of discrete wavelengths \(\lambda _{vort}\) in the regions of the 3D vortices;
-
2D MTF as a function of the wavelength \(\lambda _\mathrm{jet}\) in the region of the sinusoidal jet;
-
Cutoff wavelengths where the MTFs drop below 0.8;
-
Total, random and systematic errors (respectively indicated with \(\delta\), \(\sigma\), \(\beta\))
-
Wavelengths at which the total error becomes larger than 0.25 voxels at 20 vox/mm;
-
Profile of the response to the step function: step amplitude and equivalent wavelength corresponding to the slope of the detected step variation.
7.5.1 3D vortices
Team |
W (vox) |
---|---|
ASU | 20 |
BUAA | 24 |
Dantec | 33 |
DLR | 32 |
Hacker | 32 |
IoT | 28 |
IPP | 47 |
LANL | 16 |
LaVision | 24 |
ONERA-PTV | – |
ONERA | 24.4 |
TUD | 32 |
7.5.2 Jet
7.5.3 Step function
7.6 Conclusions of test case C
-
Artificial additional operations (apart from triangulation/algebraic reconstruction) are beneficial when using both the exposures, as in the MTE-based reconstruction algorithms or in the shake-the-box method. Methods based on removing particles via thresholding appear less effective due to the superposition between the intensity statistical distribution of true and ghost particles.
-
As a general guideline, since the quality of the reconstruction might have dramatic effects on the final outcome of the process, it is recommended to avoid pushing toward high particle image densities. Reducing slightly the particle image density below the typically used value of \(0.05\,{\mathrm {ppp}}\), at the present state, might be very rewarding in terms of reconstruction quality while turning down only weakly the spatial resolution. Nevertheless, careful analysis of the reconstructed distributions can still provide some edge, since some participants were able to perform better than Hacker even if not working on the same exact volumes.
8 Case D
8.1 Case description
DNS domain | Physical space (mm) | Voxels space | |
---|---|---|---|
Taylor-scale Reynolds number | 433 | ||
Integral length scale | 1.376 | 44.85 | 897 vox (20 vox/mm) |
Taylor length scale | 0.118 | 3.85 | 77 vox (20 vox/mm) |
Kolmogorov length scale | 0.00287 | 0.09 | 1.9 vox (20 vox/mm) |
8.2 Algorithms
Team | Calibration | Reconstruction | PIV processing | Postprocessing |
---|---|---|---|---|
ASU | Pinhole camera model Tsai (1987) | Image Segmentation (Ding and Adrian 2014) at 20 vox/mm. Intensity distributions smoothed with Gaussian filter (\(3 \times 3 \times 3\), std 0.6) | Planar 2D multi-pass image deformation method on xz and xy planes. Interrogation volume side 1.0 mm | |
BUAA | Third-order polynomial mapping, in x and y and 1st in z
| 10 Intensity-enhanced MART (inverse diffusion equation) iterations at 20 vox/mm. Gaussian smoothing of the original images (\(3 \times 3\), std 0.5).Gaussian smoothing between the iterations (Discetti et al. 2013) | Volume deformation algorithm, 4 iterations (predictor with windows shift) Interrogation volume side 1.6 mm | Gaussian smoothing (\(5 \times 5 \times 5\), std 0.6), second-order central difference scheme for vorticity |
DLR | Particle tracking over the entire set | Second-order spline curve to fit data on regular grid. Penalization on divergence and high spatial frequencies | ||
Hacker | Perfect | Perfect | Iterative volume deformation with a top hat moving average approach (Astarita 2006). Interrogation volume side 1.6 mm | None |
IoT | Direct Linear Transformation | 15 SMART iterations after initialization with MLOS followed by 5 MTE iterations, performed on 2 objects, each composed of 15 SMART (Novara et al. 2010) at 20 vox/mm. Volume extended by 6.4 mm on z to minimize edge effects | Iterative volume deformation. Interrogation volume side 1.6 mm | Fields averaged on 3 consecutive couples (pyramid scheme). Moving average filter \(3 \times 3 \times 3\) to identify and replace outliers on edges. Gradient correction technique to reduce the divergence |
IPP | Pinhole camera model Tsai (1987) | 8 BIMART Byrne (2009) iterations, block size 4, relaxation parameter 0.38 at 20 vox/mm | FTEE Jeon et al. (2014). Interrogation volume side 2.0 mm Gaussian windowing \((\alpha = 2)\), second-order polynomial trajectory using 9 images | None |
LANL | Direct Linear Transformation | Optimized MLOS with exponent 1 (La Foy and Vlachos 2011) at 20 vox/mm. Particles suppression in order to get ppp matching with the images Background suppression (1 % of maximum) and Gaussian smooth | Iterative volume deformation with Motion Tracking Blanking and Robust Phase Correlation (Eckstein et al. 2008). Interrogation volume side 2.0 mm (effective side 1.0 mm), Gaussian windowing | Gaussian smoothing (std 1.25) and Multi-frame analysis with FTC 4th-order Noise Optimized Compact Richardson scheme for vorticity |
LaVision | Pinhole camera model Tsai (1987) | Polynomial fit of second order to \(3 \times 3 \times 3\) vectors for the vorticity | ||
TUD | Vorticity with second-order central differences |
8.3 Reconstruction
8.4 Displacement field
8.4.1 Turbulent flow features
8.4.2 Temporal history
8.4.3 Turbulent spectra and spatial resolution
8.4.4 Measurement accuracy assessment
8.5 Conclusions
-
In general, it is difficult to find a correlation between power ratio, quality factor and the different metrics introduced for the error (spectral energy fraction, factor of correlation of the second invariant of the velocity gradient tensor, error, etc.). However, it can be stated that there is a broad correlation according to how refined the full algorithm analysis is.
-
The divergence test is interesting, unless it is not “tricked” with algorithms that artificially reduce the divergence in the measured fields. The relationship between measurement error and standard deviation of divergence is approximately linear within a range of relatively small total error (up to about 0.5 voxels). However, optimizing the measured velocity fields using physical criteria seems beneficial in some cases.
-
The poor reconstruction performance of direct methods affects the resolution at the medium–large frequencies, but the main flow field features are still captured even if the provided images were characterized by a relatively large particle image density. This is due to the limited velocity gradients along the depth direction. However, in such situations direct methods can be very appealing for providing a predictor or a very fast preview of the reconstructed flow field due to their intrinsic simplicity.
-
The exploitation of the time coherence both in the reconstruction and in the displacement estimation considerably improves the spatial resolution. As predicted, enforcing the time coherence in both reconstruction and displacement estimation provides the best results. Additionally, an intense cross-talk between the two steps of the process is very beneficial (e.g., in the shake-the-box method). Furthermore, PTV-based methods with oriented particle search and refinement seem to overcome classical algebraic reconstruction + cross-correlation-based methods, at least on synthetic images, without noise.
9 Case E
9.1 Case description and measurements
Pass | Grid spacing | Window resolution | Window dimension | Correlation | Multi-frame method | Validation | Smoothing |
---|---|---|---|---|---|---|---|
1 | 32 × 32 × 16 | 64 × 64 × 32 | 128 × 128 × 64 | RPC | Pyramid | UOD, threshhold | Gaussian |
2 | 24 × 24 × 16 | 48 × 48 × 32 | 96 × 96 × 64 | RPC | Pyramid | UOD, threshhold | Gaussian |
3 | 12 × 12 × 8 | 48 × 48 × 32 | 96 × 96 × 64 | RPC | Pyramid | UOD, threshhold | Gaussian |
9.2 Evaluation of case E
9.3 Results
Institution | Acronym |
---|---|
Dantec Dynamics A/S | Dantec |
German Aerospace Center | DLR |
Institute of Thermophysics SB RAS | IOT |
LaVision GmbH | LaVision |
Los Alamos National Lab | LANL |
Stereo method | Cameras | Acronym |
---|---|---|
Generalized (calibration) | 1 and 3 | HC13 |
Generalized (calibration) | 2 and 4 | HC24 |
Geometric | 1 and 3 | HG13 |
Geometric | 2 and 4 | HG24 |
Institution | Dantec | DLR |
---|---|---|
Calibration model | Third-order polynomial | First-order pinhole |
Image preprocessing | Normalized by local maximum | Sequence minimum subtraction, maximum intensity clipping |
Stereo method | Geometric | Geometric |
Multi-frame method | None | Weighted sum of triple correlation displacements |
First pass window size | 48 × 48 | 96 × 96 |
Final pass window size | 24 × 24 | 32 × 32 |
Final pass mesh size | 5 × 5 | 8 × 8 |
Vorticity calculation | Fit second-order polynomial | Circulation method with 3 × 3 Kernal |
Circulation calculation | Weighted sum of vorticity | Line integral |
Institution | IOT | LaVision |
---|---|---|
Calibration model | Third-order polynomial | First-order pinhole |
Image preprocessing | Sequence minimum subtraction | Sliding background subtraction |
Stereo method | Generalized | Geometric |
Multi-frame method | Weighted pyramid correlations | Weighted sum of correlations |
First pass window size | Camera 1: 40 × 40, Camera 3: 64 × 64 | 96 × 96 |
Final pass window size | Camera 1: 20 × 20, Camera 3: 40 × 40 | 48 × 48 |
Final pass mesh size | Camera 1: 5 × 5, Camera 3: 8 × 8 | 6 × 6 |
Vorticity calculation | Least squares fit | Central difference |
Circulation calculation | Integration of vorticity | N/A |
Institution | LANL | Hacker |
---|---|---|
Calibration model | Third-order polynomial | Third-order polynomial |
Image preprocessing | Subtraction of camera artifacts | Sequence minimum subtraction, intensity normalization |
Stereo method | Geometric | Geometric and generalized |
Multi-frame method | Fluid trajectory correlation | Pyramid correlations |
First pass window size | 32 × 32 | 64 × 64 |
Final pass window size | 16 × 16 | 32 × 32 |
Final pass mesh size | 4 × 4 | 4 × 4 |
Vorticity calculation | 4th-order compact noise optimized Richardson | 4th-order explicit noise optimized Richardson |
Circulation calculation | Integration of vorticity | Integration of vorticity |
9.4 Conclusions
10 Case F
10.1 Introduction
10.2 Method
10.3 Evaluation of the image
Contributor | Image preprocessing | Interrogation scheme | Final interrogation window size | Iteration | Image interpolation scheme | Window shift direction | Correlation peak fitting | Image postprocessing |
---|---|---|---|---|---|---|---|---|
F01 | High-pass filter | FFT |
\(32 \times 32\)
| Multiple | B-spline 6th | Symmetric | Gaussian | None |
F02 | None | FFT,DCC |
\(24 \times 24\)
| Multiple | Sinc \(8 \times 8\)
| Symmetric | Gaussian | None |
F03 | None | FFT | – | Multiple | Sinc \(8 \times 8\)
| Symmetric | Gaussian | None |
F04 | – | Robust phase correlation |
\(48 \times 48\)
| Multiple | Sinc \(8 \times 8\)
| – | Gaussian | – |
F05 | None | FFT | – | Multiple | B-spline | Symmetric | Gaussian | – |
F06 | Histogram threshold: 10 % highest values are removed—zero mean and std normalization | DCC |
\(17 \times 17\)
| Multiple | B-spline 3rd | Symmetric | Gradient | None |
F07 | None | FFT |
\(24 \times 24\)
| Multiple | B-spline 3rd | Symmetric | Gaussian | – |
F08 | None | DCC | – | Single | None | Asymmetric | Gaussian | None |
F09 | None | DCC |
\(32 \times 32\)
| Multiple | Whittaker | Symmetric | Gaussian | – |
F10 | None | Minimization of sum of squared errors |
\(15 \times 15\)
| Multiple | B-spline 5th | Symmetric | – | Interpolation by natural neighbors using Bezier–Berenstain patches |
F11 | – | – |
\(32 \times 32\)
| – | – | – | – | – |
F12 | – | FFT | – | Multiple | Biquadratic | Symmetric | Gaussian | – |
F13 | – | – |
\(16 \times 16\)
| – | – | – | – | |
F14 | – | FFT | – | Multiple | Bicubic | Symmetric | Gaussian | – |
F15 | None | Adaptive PIV |
\(24 \times 24\)
| Multiple | Bicubic | Symmetric | Gaussian | None |
F16 | – | FFT |
\(16 \times 16\)
| Multiple | Bicubic | Symmetric | Gaussian | – |
F17 | None | FFT | – | Multiple | Bilinear | – | Gaussian | Gaussian filter |
F18 | None | FFT |
\(16 \times 16\)
| Multiple | Bicubic | Symmetric | Gaussian | None |
F19 | – | FFT |
\(16 \times 16\)
| Multiple | None | Symmetric | Gaussian | – |
F20 | – | DCC | – | Multiple | Modified Whittaker and splines | Asymmetric | Gaussian | None |
F21 | Gaussian filter | FFT |
\(16 \times 16\)
| Multiple | – | Symmetric | Gaussian | None |
F22 | Image has been enlarged to \(2048 \times 2048\)
| DCC |
\(8 \times 8\)
| Multiple | Bilinear | Symmetric | Gaussian | Data has been reduced to half scale to fit the original images |
F23 | High-pass filter | LSM |
\(17 \times 17\)
| Multiple | – | – | – | – |
F24 | – | DCC |
\(32 \times 32\)
| Single | None | – | Parabolic | None |
F25 | None | Multi-pass cross-correlation |
\(64 \times 64\)
| – | – | – | – | Linear least square filter |
F26 | Particle intensity normalization filter | FFT |
\(32 \times 32\)
| Multiple | – | – | Gaussian | Smoothing |
F27 | Histogram equalization | FFT |
\(32 \times 32\)
| Multiple | B-spline 5th | Symmetric | Gaussian | Low-pass filtering |
F28 | None | FFT |
\(32 \times 32\)
| Multiple | B-cpline 6th | Symmetric | Gaussian | Smoothing |
F29 | “High-pass filter background subtraction Gaussian filter to recover particles” | FFT |
\(32 \times 32\)
| Multiple | – | – | Gaussian | Gaussian smoothing |