# FMT: Unsupervised RGB-D Point Cloud Registration via Fusion Feature Matching with Transformer
## 2 Related Work  
### Point Cloud Registration  
Point cloud registration is a crucial research area in computer vision and computer graphics. Its primary objective is to align point cloud data from different coordinate systems, providing a geometric foundation for downstream tasks such as 3D reconstruction and pose estimation. Optimization-based methods achieve point cloud registration by defining matching criteria between point clouds and minimizing an error function. The classic Iterative Closest Point (ICP) algorithm [1] is a representative example of this approach. While the ICP algorithm is theoretically straightforward and easy to implement, it is highly sensitive to initial alignment conditions and prone to local minima. Moreover, its computational efficiency is limited when handling large-scale point cloud data. To address these issues, ref. [27] proposed an improved ICP algorithm based on point-to-plane distance, which enhances registration accuracy. However, this method still suffers from suboptimal computational efficiency. To enhance global search capability, RANSAC [28] has been introduced as a global optimization strategy, which identifies the optimal matching model through random sampling and consistency evaluation. This method demonstrates robustness against noise and outliers but exhibits low efficiency when handling high-dimensional point cloud data. In addition, Go-ICP [5] achieves globally optimal registration results by integrating global search with local optimization. Although Go-ICP is theoretically guaranteed, its search process remains computationally intensive, rendering it unsuitable for real-time applications. Feature-based methods achieve robust registration by extracting local or global geometric features from point clouds to establish correspondences. These methods are advantageous in handling point cloud data with noise and partial occlusion. Traditional approaches, such as FPFH [8], generate local features by computing point normals and geometric distributions, which are characterized by their simplicity and computational efficiency. Nonetheless, FPFH demonstrates limited effectiveness in scenarios involving sparse point clouds or significant occlusion. SHOT [12] refines the construction of feature descriptors, significantly improving matching accuracy, but its high computational complexity poses challenges for real-time applications. In recent years, deep learning methods have been extensively utilized for feature extraction. 3 DMatch [20] employs convolutional neural networks to learn features from RGB-D point clouds, greatly enhancing the robustness of descriptors. While 3 DMatch demonstrates superior registration accuracy, its reliance on labeled data for training limits its applicability in unlabeled scenarios. Furthermore, PPFNet [29] establishes connections between global and local features to improve adaptability to complex geometric scenes, but its high demand for computational resources remains a significant constraint. End-to-end approaches leverage deep learning networks to directly map point cloud inputs to transformation parameters. The advantage of such methods lies in their ability to fully exploit both global and local information from point clouds, achieving efficient and accurate registration. DCP [16] incorporates an attention mechanism to model the point cloud registration task as point-to-point correspondence learning. PRNet [17] employs a self-supervised framework to achieve partial-to-partial registration and addresses the non-convexity of alignment and partial correspondence problems. GeoTransformer [15] introduces a geometry-aware Transformer architecture that combines global attention with local geometric constraints, encoding pair-wise distances and triplet-wise angles. This design enhances robustness in scenarios with low overlap and remains invariant to rigid transformations.