# Self-Supervised Keypoint Learning for the Geometric Analysis of Road-Marking Templates
## 4 Results
### Keypoint-Matching Comparison vs. SIFT/ORB
#### 4.2.2 Evaluation of the ARE  
The ARE, measured as the Mean-Square Error (MSE), quantifies the accuracy of the estimated geometric transformation by comparing a warped-source template image to the target-transformed template image within the object's masked area, as defined in Section 3.7.3. A lower ARE value indicates a more accurate alignment. Table 5 presents \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Backbone** & **K** & **Class 0 (\%)** & **Class 1 (\%)** & **Class 2 (\%)** & **Class 3 (\%)** & **Class 4 (\%)** \\ \hline ResNet-50 & 3 & 50.33 & 35.60 & 7.14 & 23.19 & 30.67 \\ \hline ResNet-50 & 4 & 28.17 & 52.50 & 12.49 & 32.62 & 39.77 \\ \hline ResNet-50 & 5 & 33.27 & 32.93 & 14.02 & 42.50 & 41.93 \\ \hline VGG-16 & 3 & 53.40 & 33.07 & 8.90 & 22.94 & 29.40 \\ \hline VGG-16 & 4 & 41.73 & 50.27 & 28.22 & 31.90 & 29.14 \\ \hline VGG-16 & 5 & 52.80 & 43.07 & 14.81 & 46.27 & 33.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Per-class IMRs in the synthetic test set for different GeoTemplateKPNet configurations. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Backbone** & **K** & **Average IMR (\%)** \\ \hline ResNet-50 & 3 & 35.49 \\ \hline ResNet-50 & 4 & 29.99 \\ \hline ResNet-50 & 5 & 30.98 \\ \hline VGG-16 & 3 & 30.38 \\ \hline VGG-16 & 4 & 28.55 \\ \hline VGG-16 & 5 & 36.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Overall average IMRs in the synthetic test set for different GeoTemplateKPNet configurations. the overall average AREs and their standard deviations across all the template classes for different GeoTemplateKPNet configurations, as well as for traditional SIFT+RANSAC and ORB+RANSAC methods, focusing on cases where at least \(N_{min}=3\) matches were found. Table 5 presents the overall average AREs and standard deviations for different methods and configurations. Comparing GeoTemplateKPNet with traditional methods in cases where at least \(N_{min}=3\) matches were available for SIFT/ORB, we observe that GeoTemplateKPNet with VGG-16 and K = 3 achieves the lowest average ARE (0.0889), indicating the most accurate overall alignment among tested configurations and traditional methods. GeoTemplateKPNet with ResNet-50 and K = 3 (0.1392) is also competitive with or better than SIFT+RANSAC (0.207) and significantly better than ORB+RANSAC (0.387) at \(N_{min}=3\). For K = 4 and K = 5, the overall average AREs for GeoTemplateKPNet generally increase compared to those for K = 3, with ResNet-50 with K = 4 showing a particularly high ARE of 0.5300. This supports the observation that K = 3 provides the most suitable balance for the overall alignment accuracy. ResNet-50 generally achieves a lower overall average ARE compared to that for VGG-16 with K = 3 but is worse for K = 4 and similar for K = 5. The overall ARE for VGG-16 with K = 5 is 0.501. These overall results suggest that our self-supervised approach can achieve more accurate geometric alignment on template data compared to traditional feature-based methods, particularly with certain configurations, when sufficient matches are available. Beyond merely establishing correspondences, the ARE serves as a critical indicator of the geometric precision achieved using each method. The consistently lower ARE values exhibited by GeoTemplateKPNet across various backbone and K configurations, particularly the optimal VGG-16 with K = 3, underscore a key strength: Its self-supervised training successfully guides the model to learn keypoints that are not only localizable but also inherently stable and geometrically reliable for estimating accurate transformations. This contrasts sharply with traditional feature-based methods, where even a high count of matches, as observed with ORB+RANSAC, does not consistently translate to accurate geometric alignments, often leading to visually unreliable reconstructions due to imprecise or inconsistent feature localization.