# FTGM: Fast Transformer-Based Global Matching for Particle Image Velocimetry
## 4 Experiments
### Quantitative Evaluations  
RAFT256-PIV [26] currently represents the state of the art in performance within benchmark evaluations. In the tests, this method serves as the baseline. We adhere to the benchmark evaluation procedures detailed in [26] for all subsequent assessment tests. Initially, our model FTGM is trained on the public benchmark dataset PIV Dataset I. Table 1 presents the test results for FTGM alongside a series of existing methods, specifically the average AEE for each test case in the test set. Without any refinements, our method's performance matches or exceeds that of the RAFT256-PIV method with iterative optimization (iteration = 16). After incorporating a single refinement, namely the addition of 1/4 resolution features, our method achieves state-of-the-art performance on the benchmark set. Our method achieved an average endpoint error of 0.8 px on backstep, 3.0 px on DNS turbulence, 4.2 px on JHTDB, and 7.2 px on SQG, with the error unit is set to pixels per 100 pixels. These results represent reductions of 11%, 70%, 73%, and 14% in AEE compared to RAFT256-PIV, respectively. The FTGM model thus exhibits superior estimation accuracy. This significant improvement validates our approach of formulating PIV estimation as a global matching problem and demonstrates that substantial enhancements can be achieved after a single refinement. To further validate the performance of FTGM across a spectrum of flow conditions, ranging from simple to complex flows, we trained and tested the FTGM model alongside the state-of-the-art model RAFT256-PIV on the PIV Dataset II, with the results presented in Table 2. Given that PIV Dataset II introduces random noise and random light intensity distribution in the particle images, it is anticipated that there would be an increase in error compared to the results in Table 1. It can be observed that all models perform best in simple flows, such as sink and source, and as the irregularity of the flow and the fine structures increase, the AEE tends to rise, as seen in DNS turbulence. Overall, the FTGM series of methods demonstrates excellent performance. We trained our model and conducted tests on the challenging PIV Dataset III, which resembles real experimental data. Table 3 summarizes the evaluation results. Consistent with expectations, the average endpoint error for all methods increased relative to the ideal PIV Dataset I. Nevertheless, our method still outperformed the RAFT256-PIV. To assess the capability of our method and baseline to estimate large displacements, we tested on a high-displacement dataset, which consists of particle image pairs with maximum displacements greater than \(\pm 16\) pixels. The results demonstrated that the Transformer-based global matching method is superior to RAFT256-PIV, which maintains a sequential iteration strategy. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **Backstep** & **Cylinder** & **DNS Turbulence** & **JHTDB** & **SQG** \\ \hline WIDIM [4] & 3.4 & 8.3 & 30.4 & 8.4 & 45.7 \\ Horn-Schunck optical flow [5] & 4.5 & 7.0 & 52.5 & 6.9 & 15.6 \\ \hline PIV-NetS-noRef [22] & 13.9 & 19.4 & 52.5 & 24.7 & 52.5 \\ PIV-NetS [22] & 7.2 & 11.5 & 28.2 & 15.5 & 29.4 \\ \hline PIV-LiteFlowNet [24] & 5.6 & 8.3 & 19.6 & 10.4 & 20.0 \\ PIV-LiteFlowNet-en [24] & 3.3 & 4.9 & 12.2 & 7.5 & 12.6 \\ \hline UnLiteFlowNet-PIV [30] & 10.1 & 7.8 & 13.5 & 9.6 & 19.7 \\ RAFT256-PIV [26] & 0.9 & **1.6** & 10.0 & 15.7 & 8.4 \\ \hline FTGM-PIV & 1.0 & 2.3 & 4.3 & 6.2 & 11.8 \\ FTGM-PIV-Ref & **0.8*** & 2.6 & **3.0** & **4.2** & **7.2*** \\ \hline \hline \end{tabular}  
* All methods listed are trained and tested based on PIV Dataset I. The error unit is set to pixels per 100 pixels for easier comparison. The best and runner-up results are highlighted in bold and underlined, respectively. For these metrics, lower is better.  
\end{table} 
Table 1: Average endpoint error for all test cases of PIV Dataset I.