POD-based Background Removal for Particle Image Velocimetry

TLDR: The results show that, unlike existing techniques, the proposed method is robust in the presence of significant background noise intensity, gradients, and temporal oscillations and the computational cost is one to two orders of magnitude lower than conventional image normalization methods.

About: This article is published in Experimental Thermal and Fluid Science.The article was published on 2017-01-01 and is currently open access. It has received 103 citations till now. The article focuses on the topics: Image quality & Background noise.

Figures

Figure 6: Error plots in the average velocity magnitude within the 256 256 example window W in Fig.2a for the original video sequence in (6a, c.f. 5a), historical minimum removal (6b, c.f. 5b), high pass filter (6c, c.f. 5c), CLAHE recontrasting (6d, c.f. 5d), min/max adjusting (6e, c.f. 5e), and the proposed POD filtering (6f, c.f. 5f). The velocity error is defined in eq.(29) and the title reports the percentage of vectors, within the window, fow which ErrV % 0.01 (nvv).

Figure 1: Analysis of statistical convergence on synthetic PIV images with source density NS 0.02 (example in Fig.1a) and NS 0.9 (example in Fig.1c). Fig.s 1b and 1d compare the corresponding error maps, defined in term of Frobenious norm in eq.(24), as a function of image size and number of images.

Figure 5: Examples 256 256 image crop in the window W in Fig.2a, showing the result of image preprocessing using historical minimum removal (5a), high pass filtering (5b), CLAHE recontrasting (5c), min/max adjusting (5d) and the proposed POD filtering method (5d). While levelization methods such as b) and c) performs poorly for time varying and sharp reflections, normalization methods encounter difficulties for background noise brighter than the particle images. The proposed POD filter is insensitive to both issues.

Figure 11: Singular value spectra of the experimental video sequence for the flapping wing experiment (Fig.11a:); Fig.11b: scalar product of the corresponding temporal eigenvectors ψk with the first temporal eigenvector of the ideal PIV images, computed as ψp1 1©Ónp " Rnt 1 as derived in Sec.2.1. For r % 40, the singular values become constant and the eigenvectors orthonormal to ψp1, indicating that no significant background contribution remains.

Figure 10: Image crops from Fig.9 for the original sequence (10a) and the results of the ensemble minimum removal (10b) and POD filter (10b). Figures 10d-10f plots the corresponding cross-correlation maps. Contrary to the ensemble minima removal, the proposed POD filter is insensitive to the reflection motion produced by the wing vibration and the cross-correlation map recovers the particle displacement.

Figure 9: Example PIV snapshot for of the PIV investigation of the flow over a flapping wing. In a 96 96 window W located close to the wing trailing edge, the image difference between two exposures is shown. Particles and wind motion are evident, with the yellow referring to the first exposure, the blue referring to the second.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Pod-based background removal for particle image velocimetry" ?

In this work, a novel image preprocessing method is proposed. The method is based on the Proper Orthogonal Decomposition ( POD ) of the image recording sequence and exploits the different spatial and temporal coherence of background and particles. 

Q2. What is the threshold for the validation of vectors?

Vector validation is carried out with a universal median test [55] on a 3x3 vectors kernel and threshold equal to 2 is used to identify invalid vectors. 

Q3. What is the way to approximate the ideal PIV video sequence Xp?

Since r 8 nt and σpk σpk 1 (assumption 1), it is possible to approximate the ideal PIV video sequence Xp underlying the video sequence X (eq.6) filtering out its first r POD modes:Xp nt= k 1 φpkσpkψ T pk X̃pnt= k r 1 φpkσpkψ T pk . 

Q4. What is the effect of the high pass filter on the noise sources?

The high pass filtered completely removes the blurred noise source g2, and the random noise source pedestal g4, but it encounters problems on the high gradient regions of the noise sources g1 and g4. 

Q5. What is the effect of the spatial cut-off frequency on the background removal?

increasing the spatial cut-off frequency improves the background removal, but at the cost of chopping the particle images in the smooth areas, and thus increasing the risk of peak locking ([51]). 

Q6. What is the effect of the vector validation on the velocity fields?

the sharp and time varying edges of the noise sources g1 and g3 (c.f Fig.2a) result in a significant error in the flow field evaluation, only partially reduced by the vector validation. 

Q7. What is the criterion for removing the light reflection without disturbing the particle images?

In this test, the proposed POD filter was capable to remove the light reflection without disturbing the particle images, and therefore allowing for recovering the particle displacements in an otherwise corrupted cross-correlation map. 

Q8. What is the criterion for identifying the POD modes related to the background noise?

In particular, it is shown that correlated background noise can be well approximatedby a few of the first POD modes of the video, while the PIV particle pattern is equally distributed along the entire POD spectra. 

Q9. How many counts of the noise source are there?

the fourth noise source Xb4 g4 f4 mimics the thermal camera noise, modeled as a random distribution in both time and space with a mean value of 20 counts and standard deviation of 8 counts. 

Q10. What is the impact of the particle image on the background noise?

While all the background noise is completely removed, the impact on the particle image is very limited, with several particles overyling the non saturating background noise areas being entirely recovered. 

Q11. What is the scope of low dimensional modeling of matrix X?

The scope of low dimensional modeling (or low rank approximation) of matrix X is to find the approximation X̃ " Rnp nt of rank r $ min np, nt minimizing the L2 norm (¶¶ ¶¶) of the error matrix Er:min Er min ¶¶X X̃¶¶2 . 

Q12. What is the background removal efficiency of the proposed method?

To confirm this derivation, the background removal efficiency or the proposed method is compared to that of four popular image preprocessing techniques: the minimum intensity background subtraction [12], high pass filtering [9], contrast-limited adaptive histogram equalization (CLAHE) [19, 49] and min/max recontrasting [20]. 

Q13. What is the value of the vectors in the contour plot?

The contour plots compare the corresponding velocity fields with those evaluated from the ideal PIV sequence Xp, considered as reference flow field ure f , vre f , in terms of velocity magnitude error:ErrV u ure f 2 v vre f 2 ure f 2 vre f 2 (29)The figures title reports the number of invalid vectors (nnv) computed in the postprocessing of the win-dow considered as those vectors for which ErrV % 0.01.