Surrogate-based cross-correlation for particle image velocimetry

TL;DR

This work tackles robustness in cross-correlation-based particle image velocimetry (PIV) by introducing surrogate-based cross-correlation (SBCC), which jointly optimizes forward and backward surrogate filters against multiple negative context images. SBCC derives a closed-form solution that yields a robust cross-correlation map, and it reveals that several generalized cross-correlation (GCC) methods are special cases of SBCC under specific settings. Empirical results on synthetic and real PIV data demonstrate improved accuracy and resilience to background noise and nonuniform illumination, with competitive computation costs and public code. The approach offers a unifying, principled perspective on GCC methods and opens avenues for applying negative-context surrogates to broader signal-tracking tasks.

Abstract

This paper presents a novel surrogate-based cross-correlation (SBCC) framework to improve the correlation performance for practical particle image velocimetry~(PIV). The basic idea is that an optimized surrogate filter/image, replacing one raw image, will produce a more accurate and robust correlation signal. Specifically, the surrogate image is encouraged to generate perfect Gaussian-shaped correlation map to tracking particles (PIV image pair) while producing zero responses to image noise (context images). And the problem is formularized with an objective function composed of surrogate loss and consistency loss. As a result, the closed-form solution provides an efficient multivariate operator that could consider other negative context images. Compared with the state-of-the-art baseline methods (background subtraction, robust phase correlation, etc.), our SBCC method exhibits significant performance improvement (accuracy and robustness) on the synthetic dataset and several challenging experimental PIV cases. Besides, our implementation with experimental details (\url{https://github.com/yongleex/SBCC}) is also available for interested researchers.

Figures (13)

• Figure 1: Different illustrative pipelines for noisy PIV images. Ⓔ: background/contexts extraction; $\ominus$: background subtraction; $\bigotimes$: cross-correlation. $\star$: surrogate-based cross-correlation.
• Figure 2: Different cross-correlation methods. The $\bigotimes$ denotes the standard cross-correlation in Fourier frequency domain (a). The generalized cross-correlation methods (b), the $\bigodot$ represents an element-wise multiplication.
• Figure 3: The bi-directional surrogate model, SBCC. The surrogate images $S_1, S_2$ and correlation response $R$ are jointly optimized with surrogate objective ${J}_{surr}$ and correlation consistency objective ${J}_{corr}$ (blue dash arrows). The $R_f$ and $R_b$ represent the correlation with forward surrogate ($S_1$) and backward surrogate ($S_2$) respectively.
• Figure 4: The motivation of surrogate objective is to find a surrogate $S_1$ that does not response to the negative context images $P_1, P_2, ..., P_m$.
• Figure 5: A correlation responses on synthetic particle images with background. Best viewed in color.