## 3 Results and Discussion
### Ablation Experiment Results and Analysis  
To validate the effectiveness of the proposed improvements on homography estimation performance, experimental analysis was conducted on the module selection of the improved HomographyNet, the construction of the scale pyramid, and the number of stages in the overall network. Firstly, ablation studies were conducted on the special deformation convolution layer and GN normalization layer introduced in the improved HomographyNet, as shown in Table 2. The results indicate that the original HomographyNet, even with a three-stage network structure, had the highest error in homography estimation. Introducing either the special deformation convolution layer or the GN normalization layer independently improved network performance to different extents, with the deformation layer having a greater impact. This is because this module expands the receptive field and enhances the learning ability for feature rotational invariance during the feature extraction process, which reduces the error in homography estimation. Meanwhile, the GN normalization layer provides stable training capabilities when dealing with small batches of large sizes, but it does not directly affect the error in homography estimation. The improved HomographyNet model proposed in this paper, which incorporates both the special deformation convolution module and the GN normalization module, shows the smallest error in homography estimation. Subsequently, the method proposed in this paper was tested by using images of different scales at various stages and images of the same scale at all stages to verify the effectiveness of constructing an image pyramid for multi-scale input in homography estimation. As shown in Table 3, the method with same-scale input exhibited higher \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **ORB +** & **SIFT +** & **Homography** & **PFNet** & **Unsupervised** & **C-AHomE** & **biHomE** & **Ours** \\  & **RANSAC** & **RANSAC** & **Net** & **HomographyNet** & **C-AHomE** & **biHomE** & **Ours** \\ \hline \(\rho=10\) & 8.34 & 6.82 & 3.19 & 2.72 & 2.26 & 0.97 & 0.89 & 0.72 \\ \(\rho=20\) & 10.82 & 8.57 & 6.56 & 4.85 & 3.49 & 1.40 & 1.31 & 1.19 \\ \(\rho=30\) & 12.10 & 10.73 & 9.41 & 6.36 & 4.33 & 1.94 & 1.82 & 1.67 \\ \(\rho=40\) & 15.79 & 13.32 & 15.13 & 8.91 & 5.27 & 3.82 & 3.51 & 2.23 \\ \(\rho=50\) & 18.35 & 17.91 & 19.78 & 11.28 & 6.12 & 5.11 & 4.67 & 2.81 \\ \(\rho=60\) & 21.27 & 20.45 & 24.30 & 13.14 & 7.91 & 6.39 & 5.75 & 3.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Error results of different methods under different offset values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Special Deformation** & **Group Normalization** & **Stage 1** & **Stage 2** & **Stage 3** \\
**Convolution Layer** & **Layer** & & & \\ \hline \(\times\) & \(\times\) & 10.15 & 6.21 & 4.32 \\ \(\surd\) & \(\times\) & 4.28 & 3.16 & 1.91 \\ \(\times\) & \(\surd\) & 9.93 & 5.38 & 3.23 \\ \(\surd\) & \(\surd\) & 3.91 & 2.85 & 1.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ablation study results of on module selection in the improved HomographyNet. homography estimation errors at each stage compared to the method proposed in this article. To demonstrate the effectiveness of the improvements, the same test images from the previous experiment were used for homography estimation at three stages, with both same-scale and different-scale inputs. The visualization results, as shown in Figure 9, include the following: (a) the template image with the initial positions of the four corners marked by red boxes; (b), (c), (d) the estimation results at three stages with same-size image inputs; and (e), (f), (g) the estimation results at three stages with different-scale image inputs, where the yellow boxes indicate the predicted positions of the four corners. The higher the overlap between the two boxes, the smaller the error in the estimated homography matrix.