Objective Pressure sensitive paint (PSP) technology is a non-contact optical pressure measurement method utilized extensively for surface pressure measurement of parts in wind tunnel environments. The surface of a part coated with PSP fluoresces under excited light conditions, and the pressure results can be inverted using the Stern-Volmer formula. This formula requires the ratio of the windy image to the windless image, but the displacement and non-rigid deformation of the part in the wind tunnel environment will result in computational errors in the division of non-corresponding points. Consequently, the accurate registration of windy and windless images is fundamental to processing PSP experimental data. Typical PSP images comprise only two distinct components: a bright light-emitting region and a black background region, leading to sparse image features and a relatively limited number of feature points, which makes it difficult to apply typical registration methods directly. Moreover, as the number of images in a single experiment exceeds tens of thousands, conventional non-rigid registration methods are often slow and insufficient for fast registration requirements. Consequently, there is an urgent demand to develop a new method that can register images accurately and swiftly without relying on marker points. Methods To achieve the demand for accurate and fast registration of PSP images, we propose a registration method based on unsupervised learning. The method does not require a priori information and directly learns an end-to-end from image pairs to deformation fields. The registration network structure incorporates multiple scales of structures, through a multi-cascade approach, facilitating a coarse-to-fine registration of PSP images. Furthermore, we have designed a new loss function based on the structural similarity of images, which maximizes the similarity between the registration image and the input fixed image. In our study, two sets of PSP experimental images of typical parts, each comprising 20000 image pairs, are introduced for the training and testing of the registration network. The image sizes are 640x272, and the format is a 16 bit greyscale image. The registration process utilizes only image pair information, without the assistance of external supervisory information. To assess the efficacy of this method, we compare and analyze it with conventional algorithms currently used for PSP image alignment. These conventional algorithms include feature-based matching algorithms, MIBspline algorithms that combine greyscale and B-spline, and deep learning-based alignment models such as Voxelmorph, CycleMorph, BIRGU-Net, and LRN. The image registration methods are also evaluated based on registration accuracy and time. Registration accuracy is measured by three common quantitative metrics: root mean square error (RMSE), normalized correlation (NCC), and target alignment error (TRE). Results and Discussions Evaluating and analyzing our method with the conventional methods, it is evident from the registration results of shell parts and thin plate parts in Figs. 6 and 7 that the five regions of the two sets of experimental data in the PIR-Net registration results have essentially completed the registration. This suggests that the method possesses a stronger robustness in handling complex scenes and large deformation alignments in PSP images and enhancing accuracy. To further quantify the accuracy of the registration, we utilize the RMSE and NCC indices to evaluate the results (Tables 1 and 2). The tables indicate that the PIR-Net significantly outperforms the comparison methods in both the RMSE and NCC metrics. Compared to the conventional methods, the RMSE index is improved by 51.6% and the NCC index is improved by 181.7%. This improvement is primarily attributed to the non-rigid deformation and feature sparsity in the PSP image. Neither the feature matching nor the iterative optimization-based methods can effectively address these issues, leading to sub-optimal overall registration. Compared to other deep learning-based registration methods, PIR-Net demonstrates superior adaptability in large deformation regions due to its multi-scale network structure and attention mechanism. This results in a 16.4% improvement in the NCC and a 19.1% improvement in the RMSE. To further illustrate the advantages of the algorithm in registration error control, we compare and demonstrate the maximum error position and the average error in the experiments. Due to the combination of the smoothing term constraint and the attention mechanism, it exhibits a more consistent distribution of error, with a relatively smooth error limit constraint (Figs. 10 and 11). The average time for each method's registration is experimentally demonstrated in Table 5. Our method outperforms other conventional methods. Compared to other deep learning methods, the registration time of PIR-Net is slightly longer. This is primarily due to the use of multi-scale registration. However, using a very small difference in registration time for a higher accuracy of registration is a good compromise between time performance and accuracy of registration, which is more practical. Conclusions We introduce an unsupervised learning-based registration method for the PSP image registration. This method directly learns the end-to-end mapping from image pairs to deformation fields. It designs a multiscale network structure and a coarse-to-fine registration strategy to address the issue of large offsets and non-rigid deformations in wind tunnel environments. Additionally, it incorporates a novel loss function paradigm based on image similarity, which enhances image registration in feature-sparse scenarios. Comparing with typical alignment methods such as MI-Spline and Voxelmorph on two sets of PSP images, the experimental results prove that our method achieves a far better registration performance than the existing methods in visual evaluation and RMSE, NCC, and TRE metrics, under the premise of ensuring the performance of the algorithm. This method provides a reliable solution to the PSP image registration problem.
