Globally optimized cross-correlation for particle image velocimetry
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RESEARCH ARTICLE
Globally optimized cross‑correlation for particle image velocimetry Hongping Wang1 · Guowei He1,2 · Shizhao Wang1,2 Received: 5 May 2020 / Revised: 25 July 2020 / Accepted: 19 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We propose a global optimization method to automatically search for the correlation peak instead of computing the entire cross-correlation map throughout an interrogation window (IW) using a fast Fourier transform (FFT)-based method. The proposed method, named globally optimized cross-correlation for particle image velocimetry (GOCCPIV), minimizes an objective function consisting of a residual term for cross-correlation and a penalty term for smoothness to solve the optimal velocity field. A very small IW is adopted in GOCCPIV to obtain a dense velocity field with a high spatial resolution. The proposed method is quantitatively validated on synthetic particle image pairs with different flow patterns and is compared with the mainstream FFT-based cross-correlation method (FFTCCPIV) and physical-based optical flow (OpticalFlow). We consider the influences of the IW size, particle concentration, particle image diameter, large displacements and image noise on the velocity measurements. Error analysis indicates that GOCCPIV outperforms FFTCCPIV in resolving small-scale vortices and reducing the measurement error. Finally, the proposed method is applied to a real PIV experiment with an impinging jet. The results indicate that GOCCPIV is more suitable than FFTCCPIV for resolving high-velocity-gradient regions. Graphic abstract
1 Introduction The particle image velocimetry (PIV) technique (Adrian 1991; Willert and Gharib 1991) is widely used to estimate flow motions in the field of experimental fluid mechanics. The greatest advantage of PIV is that it can simultaneously measure many points in a planar or volumetric domain. In * Shizhao Wang [email protected] 1
The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
School of Engineering Sciences, University of the Chinese Academy of Sciences, Beijing 100049, China
2
a planar PIV experiment, the tracer particles seeded in the flow field are illuminated by a sheet of laser light. Particle images are then recorded at two consecutive instants using a CCD or CMOS camera. Image analysis methods, such as region-based cross-correlation (Huang and Fiedler 1993; Scarano 2002), particle tracking (Adamczyk and Rimai 1988; Maas et al. 1993) or optical flow (Horn and Schunck 1981; Barron et al. 1994; Corpetti et al. 2002), are adopted to estimate the velocity field from the image sequence. Recently, neural networks have also been used to estimate flow motions by learning from acquired datasets (Lee et al. 2017; Cai et al. 2019). Correlation-based methods are a simple and robust means of assessing displacement by finding the maximum
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of the cross-correlation map within a given interro
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