## 3 Methods
### Integrated Matching Model Framework
The proposed method increases the number of matched point pairs by applying multi-scale transformations, including image scaling and rotation, during feature matching. However, these transformations can introduce errors that result in a high number of incorrect matches in the initial matching stage. To address this issue, we apply the DBSCAN algorithm for preliminary outlier removal. Despite its effectiveness, DBSCAN is highly sensitive to parameter selection, and its clustering performance largely depends on these parameters. In complex feature matching scenarios--characterized by noise, transformation model complexity, and feature similarity--manually selecting appropriate parameters is challenging and often impractical. To address these challenges, the improved DBSCAN algorithm known as HDBSCAN is utilized. HDBSCAN is a density-based hierarchical clustering method that analyzes cluster structures across multiple density levels, enabling automatic determination of the number of clusters while effectively identifying noise points. Unlike traditional DBSCAN, HDBSCAN measures the connectivity between sample points using the mutual reachability distance. The core of the method involves computing the mutual reachability distance between any two points as defined by Equation (6). \[d_{\text{mreach}}(a,b)=\max(\text{core}_{k}(a),\text{core}_{k}(b),d(a,b)), \tag{6}\]  
Here, \(d(a,b)\) denotes the Euclidean distance, while \(\text{core}_{k}(x)\) represents the distance from point \(x\) to its \(k\)-th nearest neighbor, which serves as a measure of the point's local density. As shown in Figure 6, the mutual reachability distance from the red point to the blue point corresponds directly to the distance between them, since this distance exceeds both core distances. The algorithm proceeds by modeling the distance structure among samples through the construction of a minimum spanning tree (MST). A graph is formed by connecting each point to its nearest neighbors within its reachable range, with edge weights defined by the mutual reachability distance described previously. [PERSON]'s algorithm is then applied to generate the MST, preserving the most critical density-based connectivity among data points. Edges in the MST are subsequently removed in descending order of mutual reachability distance to form a hierarchical cluster structure. Initially, each point constitutes  
Figure 6: Mutual reachability distance visualization. an individual cluster, and clusters are iteratively merged based on proximity, producing a hierarchical clustering tree. Following the construction of the hierarchical clustering tree, a condensation process compresses the large tree into multiple smaller sub-clusters. HDBSCAN introduces a parameter, minimum cluster size, to govern the splitting of the hierarchical tree. The condensation begins at the root node, where the entire dataset is treated as a single cluster. For each cluster represented by a node, the algorithm first evaluates its sample size. Clusters with fewer samples than the minimum cluster size are considered invalid and are either discarded or labeled as noise. Clusters meeting the minimum size threshold are further examined for their sub-cluster structures. Through this recursive exploration and filtering, the original hierarchical clustering tree is reduced to a set of appropriately sized, well-defined subtrees. Each subtree's root node represents a stable cluster that satisfies the parameter criteria. HDBSCAN enhances the algorithm's adaptability by eliminating the need for users to predefine the number of clusters. Instead, it automatically determines the clustering structure based on the data's density features and cluster stability. Noise points are removed during the condensation process, which improves the robustness of the clustering results. Moreover, HDBSCAN introduces cluster stability as a metric for evaluating clustering quality. The core idea is that the longer a sample remains within a cluster, the higher the confidence in its membership.