## 3 Results and Discussion
### Comparative Experiment Results and Analysis  
To evaluate the effectiveness of the proposed method, it will be compared with traditional homography estimation methods and deep-learning-based homography estimation methods. The average L2 distance between the true corner coordinates and the predicted coordinates will be calculated for all four corners of all images in the test set. Specifically, ORB + RANSAC and SIFT + RANSAC will be chosen as traditional feature-based homography estimation methods due to their superior performance over most traditional methods. HomographyNet and PFNet [28] will be selected as supervised learning-based homography estimation methods, where HomographyNet is the first model to estimate homography using deep learning, and PFNet is an excellent supervised homography estimation model that performs well on various datasets. The homography estimation model from [PERSON] et al. [15] will be chosen as the unsupervised learning-based homography estimation method, as it is the first to apply unsupervised learning to the homography estimation task and has been used as a basis in subsequent studies. To demonstrate the novelty of the method proposed in this paper, the content-aware unsupervised homography estimation network (C-AHomE) from [PERSON] et al. [16] and the bidirectional implicit loss-based unsupervised homography estimation network (biHomE) from [PERSON] et al. [17] are selected as the latest research methods for comparison. The comparison results of the mean corner error between the proposed method and other homography estimation methods are shown in Figure 7. It can be seen that the two traditional methods based on image features have significantly higher errors. This is because they overly rely on the quality of feature points during the feature extraction stage and the content of the image itself. Due to the fact that the feature points on the surface of the metal sheet are concentrated on the edges, punching holes, etc., and are not sufficiently abundant or well-distributed, they are prone to errors from lighting changes and perspective changes, resulting in poor homography estimation accuracy. Deep-learning methods, due to their strong feature representation capabilities, extract features of higher quality than traditional algorithms, resulting in lower errors. Among them, PFNet performs better. Unsupervised homography estimation networks do not rely on real labeled data during training and improve robustness to lighting changes by minimizing pixel-level photometric errors, resulting in better accuracy than supervised learning methods. However, this method uses a single-stage network structure. The proposed method achieves the lowest error estimation, reducing the MACE error by 2.66 compared to the previous unsupervised homography estimation network, with a 61.4% improvement in performance. When compared to the latest unsupervised homography estimation networks, C-AHomE and biHomE, the performance is improved by 13.9% and 8.2%, respectively. Figure 7: Comparison results of MACE between the proposed method and other methods. Figure 8 presents the visualized results of homography estimation using the aforementioned eight methods across eight different test images, including five sets of stamping monitoring images and three sets of images from the MSCOCO2014 dataset. This selection aims to demonstrate the effectiveness of the proposed method in the specific industrial context of stamping monitoring while also highlighting its general applicability to various types of images. The leftmost column shows the template images of the eight test images, with blue frames representing the initial image patches and corner points. The green frames indicate the predicted positions of the corner points, with different levels of precision based on the homography matrices estimated by each method. The higher the overlap between the blue and green frames, the higher the accuracy of the homography estimation and the lower the error.