Subsequently, the rotation matrix \(R\) and translation matrix \(T\) are computed using the Singular Value Decomposition (SVD) algorithm, which has markedly improved the accuracy, robustness, and speed of point cloud registration [19]. These methods also incorporate strategies inspired by traditional point cloud registration techniques. However, these approaches typically assume a perfect one-to-one correspondence between the source and target point clouds during the training phase, making them less robust when faced with noise and non-overlapping areas. In practical engineering applications, the registration task is further complicated by factors such as acquisition time, angle, sensor noise, and variations between sensors [20]. Moreover, while significant progress has been made in enhancing the accuracy of point cloud registration, relatively little research has concentrated on optimizing registration speed. Additionally, the consumption of execution time and the storage requirements for point cloud data volumes have also received limited attention. Among the methods for feature extraction and processing in graph-structured data, mainstream technologies primarily utilize neural network models to learn the feature representations of nodes and edges. Specifically, the Graph Convolutional Network (GCN) [21] updates the feature representation of nodes by aggregating information from neighboring nodes. This process involves convolution operations that utilize the adjacency matrix and the node feature matrix of the graph. Additionally, graph kernel-based methods [22] achieve feature extraction by defining kernel functions between graphs to calculate their similarity. However, these methods encounter efficiency challenges when processing large-scale graph data. This inefficiency is primarily due to the high computational cost associated with calculating kernel functions between graphs. Furthermore, graph kernel methods lack flexibility in addressing dynamic changes in graph structures, as they predominantly focus on the static structural characteristics of graphs. DeepWalk [23] and Node2 Vec [24], both of which rely on random walks, may encounter limitations in memory and computational resources when processing large-scale graph data. This is due to the substantial resource requirements for generating node sequences with these methods and for subsequent model training. Furthermore, matrix factorization-based methods [25] may also experience challenges related to computational efficiency and memory usage when handling large-scale graph data. These approaches often struggle to effectively capture the local structural characteristics of graphs. This paper proposes a drawing structure registration method for building structures, aimed at achieving efficient and high-precision feature extraction and registration with limited point cloud data volume. The method integrates manual feature extraction with graph neural network-based feature extraction to enhance the robustness and accuracy of the registration process. To address the challenge of excessive point cloud data volume, a topological processing method for point cloud data is introduced. This approach offers the advantages of rapid processing and reduced data transmission, making it suitable for scenarios with constrained communication conditions. By pre-processing the topologized point cloud data on local devices, the proposed method can achieve high-precision registration while significantly minimizing data transmission requirements. This approach not only improves computational efficiency but also ensures that the registration process remains effective even in resource-limited environments. To address the challenges mentioned above, this paper proposes a method for registering drawing structures in building designs. The primary contributions of this work are summarized as follows:  
1. A point cloud registration framework based on feature metric geometry is introduced. This framework ensures high accuracy while enhancing improving computational efficiency.