# FTGM: Fast Transformer-Based Global Matching for Particle Image Velocimetry
## 6 Conclusions  
The focus of this study is to redefine PIV estimation as a pixel-matching problem using a global matching approach, with the aim of improving the inefficiency caused by sequential iteration in learning-based flow regression methods. While enhancing efficiency, we also take into account the accuracy and the number of model parameters. Considering the differences in data between PIV and optical flow tasks, we have successfully applied global matching-based optical flow estimation methods to PIV estimation by customizing a Transformer for PIV image feature enhancement, combined with a global matching layer composed of correlation matching and softmax. Utilizing the similarity between particle images and optical flow field, we optimize the estimation structure of optical flow through feature self-similarity.  
The performance of the proposed method is demonstrated through numerical evaluation and visualization analysis on both synthetic datasets and experimental data in comparison with the state-of-the-art PIV estimation method, RAFT256-PIV. We first conducted error estimation on the public PIV benchmark set PIV Dataset I and the results showed that our method has elevated the estimation accuracy to a new level. Subsequently, we performed error estimation on PIV Datasets II and III, which feature richer scenarios and are closer to real experimental data, and our method surpassed the best baseline model in multiple outcomes. Additionally, we assessed our method on datasets with large displacements (greater than \(\pm 16\) pixels). Compared to RAFT256-PIV, FTGM-PIV and FTGM-PIV-Ref reduced the error by 2.88% and 45.4%, respectively. Finally, we tested the spatial resolution and conducted visualization analysis of experimental PIV images to demonstrate our model's capability in capturing small-scale structures. The experimental results indicate that the FTGM model has raised the estimation accuracy to a new standard. Importantly, while maintaining high accuracy, our method has reduced computational time by 54.5% and 78.8% compared to RAFT256-PIV.  
This paper strongly demonstrates the great potential and research value of global matching methods in PIV estimation. Firstly, further investigation into fluid characteristics can lead to targeted improvements in estimation methods, thereby enhancing their effectiveness. Moreover, with the development of optical flow models, components or frameworks more suitable for PIV tasks will emerge, and it is only a matter of time before integrating more excellent frameworks for PIV estimation.  
Conceptualization, J.Y. and D.Z.; funding acquisition, D.Z.; methodology, S.D.; project administration, J.Y. and D.Z.; validation, S.D. and T.Z.; visualization, S.D. and T.Z.; writing--original draft, S.D.; writing--review and editing, T.Z. and J.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Laboratory of Intense Pulsed Radiation Situation and Effect, Northwest Institute of Nuclear Technology of China, Grant No. D55061902.  
Not applicable.  
The authors declare no conflicts of interest.