## 4 Experiments
### Essential Matrix Estimation  
In essential matrix estimation, we decompose \(\mathbf{E}\) into its rotation and translation matrix, and subsequently calculate their respective errors. The area under the curve (AUC) is then computed with thresholds at 5\({}^{\circ}\), 10\({}^{\circ}\), and 20\({}^{\circ}\). As presented in Table 2, RootSIFT features and the SNN ratio [36] are utilized to derive matching information and confidence, which serve as inputs to the model for estimating the essential matrix. Our approach outperforms both traditional and deep learning-based methods, achieving the highest accuracy. However, we fall behind some methods in terms of inference time.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Scene/Method** & **RANSAC** & **MAGSAC++** & **OANet** & **CLNet** & **NG-RANSAC** & **RLSAC** & **D-RANSAC** & **SA-Net** \\ \hline Taj Mahal & 42.21 & 58.63 & 54.13 & 56.22 & 57.65 & 54.98 & 59.66 & **60.51** \\ Saxe Coeur & 45.83 & 52.11 & 47.28 & 48.10 & 51.03 & 53.71 & 53.09 & **55.08** \\ Trevi Fountain & 31.77 & 35.93 & 29.32 & 30.07 & 36.25 & 34.89 & 35.97 & **39.45** \\ Pantheon Exterior & 58.20 & 63.44 & 51.39 & 55.79 & 59.81 & 61.49 & 65.38 & **66.97** \\ Brandenburg Gate & 36.95 & 39.32 & 37.03 & 38.48 & 39.20 & 41.94 & 41.43 & **44.91** \\ Colosseum Exterior & 46.80 & 51.34 & 43.58 & 47.87 & 53.21 & **56.86** & 55.43 & 56.08 \\ Buckingham Palace & 25.65 & 29.76 & 25.93 & 27.81 & 29.88 & 29.13 & 30.71 & **33.79** \\ Grand Place Brussels & 29.75 & 33.84 & 29.56 & 33.52 & 35.39 & 34.35 & 35.56 & **37.52** \\ Palace of Westminster & 31.73 & 33.85 & 31.65 & 32.72 & 35.12 & 34.27 & 34.92 & **39.88** \\ Prague Old Town Square & 35.56 & 38.73 & 34.32 & 37.34 & 39.43 & 38.31 & 39.72 & **41.23** \\ Notre-Dame Front Facade & 37.93 & 39.84 & 34.58 & 36.85 & 39.74 & 39.47 & 43.51 & **45.63** \\ Westminster Abbey & 52.06 & **52.99** & 43.38 & 49.03 & 51.27 & 50.41 & 52.04 & 52.57 \\ Avg & 39.54 & 44.14 & 38.51 & 41.15 & 44.00 & 44.15 & 45.61 & **47.80** \\ \hline \hline \end{tabular}
\end{table}
Table 1: The F1 scores (each, average in last row) for F matrix estimation on 6K image pairs from the PhotoTourism dataset [35]. Best results are in **bold**, and the second best are underlined.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Method** & **AUC@5\({}^{\circ}\)** & **AUC@10\({}^{\circ}\)** & **AUC@20\({}^{\circ}\)** & **Run-Time (ms)** \\ \hline LMEDS & 0.237 & 0.292 & 0.345 & **21** \\ RANSAC & 0.251 & 0.334 & 0.394 & 42 \\ GC-RANSAC & 0.315 & 0.375 & 0.413 & 81 \\ MAGSAC & 0.355 & 0.405 & 0.457 & 102 \\ MAGSAC++ & 0.354 & 0.411 & 0.459 & 68 \\ OANet & 0.259 & 0.323 & 0.374 & 25 \\ CLNet & 0.334 & 0.395 & 0.449 & 31 \\ NG-RANSAC & 0.369 & 0.413 & 0.464 & 52 \\ D-RANSAC & 0.394 & 0.426 & 0.501 & 61 \\ SA-Net & **0.436** & **0.442** & **0.524** & 78 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The average AUC scores and run-time of SA-Net and comparison methods over 12 scenes on RootSIFT [34] matches. Best results are in **bold**, and the second best are underlined.  
Figure 9: The comparison of RANSAC, GC-RANSAC, MAGSAC, MAGSAC++, OANet, CLNet, NG-RANSAC, D-RANSAC and ours; we show the cumulative distribution functions of the epipolar errors.