# A Registration Method for Historical Maps Based on Self-Supervised Feature Matching
## 3 Materials and Methods
### Self-Supervised Map Feature Extraction  
Traditional supervised learning methods [22; 23] rely on manually annotated datasets. However, human annotations typically provide approximate localization of feature points  
Figure 3: Map image segmentation result. rather than subpixel-level precision. Moreover, expert-guided annotation of cartographic features requires substantial resources, including domain expertise and dedicated infrastructure. Finally, the scarcity of annotated historical maps hinders the training of supervised models on limited datasets, which constrains their ability to learn robust feature representations. Inspired by [PERSON]'s self-supervised geometric reasoning framework [26], we pre-train our model on a synthetic dataset of geometric primitives (e.g., lines, polygons, and curves). Through self-supervised pretraining [27], the model autonomously learns structural patterns from automatically generated labels, thereby eliminating manual annotation and enabling scalability for large-scale historical map analysis. The decoder generates a 65-channel probability map through a \(1\times 1\) convolution, where each spatial position corresponds to an \(8\times 8\) grid in the input image. Each channel encodes activation probabilities for discrete positions within the \(8\times 8\) grid, with the 65 th channel representing the absence of features. The use of non-overlapping \(8\times 8\) grids ensures exact spatial correspondence between decoder outputs and input regions. A channel-wise softmax operation computes pixel-level probabilities. During training, the spatial position with the highest probability within each \(8\times 8\) grid is selected as the feature point. During inference, a confidence threshold rejects low-probability candidates, and the 65 th channel is excluded to suppress non-feature regions. The structure of our map feature extraction is shown in Figure 4.  
To mitigate upsampling artifacts, we replace transposed convolution with Pixel Shuffle [28], which preserves structural integrity through sub-pixel convolution. We further augment the dataset using geometric transformations (such as rotation and scaling) and photometric distortions, then fine-tune the model to jointly predict pixel-accurate feature locations and rotation-invariant feature descriptors. In order to achieve self-supervised training of the model, we pretrained the model on synthetic geometric primitives (e.g., intersecting lines, rectangles, squares) with programmatically generated feature points (e.g., intersections, endpoints). This pretraining phase enhances the model's sensitivity to structural features such as intersection points, endpoints, and corners. In this study, semantic segmentation is applied to map data to extract road networks containing dense structural features. Direct application of the model for feature extraction would yield excessively dense correspondence sets between the images to be registered. Overly dense correspondence sets adversely affect downstream  
Figure 4: Structure of map feature extraction. processing--they increase computational costs, demand higher hardware resources, and complicate graph-based matching architectures. Therefore, we propose a customized Non-Maximum Suppression (NMS) [29] algorithm to appropriately adjust the quantity and distribution of output feature points, mitigating computational complexity in downstream tasks. The customized NMS algorithm, integrated into the feature extraction pipeline, is formalized in Algorithm 1. Non-Maximum Suppression is a computational technique that iteratively selects local maxima while suppressing neighboring non-maximal responses within a defined neighborhood. The search neighborhood is parameterized by its spatial extent (e.g., kernel size), with both scale and geometry configurable to meet empirical requirements. In Algorithm 1, the local search radius r means the size of the neighborhood, and by setting the value of r, the local search range can be restricted.