## 2 Related Work
### Graph Attention Network  
Recently, the development of the GAT [46] contributes to simplifying CNN into graph representations. Even though there are often common traits with on-set deep learning, the GAT can aggregate more powerful features along the edges and nodes. Previously, [PERSON] et al. [47] presented an application of deep neural networks for finding the similarity matrix in graph matching. [PERSON] et al. [48] introduced another GAT-based network for the image domain. Its framework consists of a feature extractor in the image, a graph embedding component, an affinity metric function, and a permutation prediction. Typically, the graph matching problem is mathematically formulated as a quadratic assignment problem, which consists of finding the assignment that maximizes an objective function of local compatibilities (a linear term) and structural compatibilities (a quadratic term) [47; 49]. Many algorithms have been proposed to find a locally optimal solution for the above matching problem. One popular method is to use an approximation of the objective function. By using the Hungarian method proposed by [PERSON] [50], the problem can be solved for minimizing total cost (or) maximizing the profit. As an approximate version of the Hungarian method, a Sinkhorn network [51] is developed for linear assignment learning with a predefined assignment cost which is designated to enforce doubly-stochastic regulation on any non-negative square matrix. However, very few studies have focused on using GAT to solve the point cloud registration problem. The proposed methodology using GAT improves performance but still saves the computational cost of the registration point cloud.  
In the MDGAT-matcher [4], a dynamic GAT was introduced to embed the geometry feature from the FPFH descriptor to create more robust feature for the matching process. Because of the limitations of handcrafted descriptors, their results are sensitive and rotation-variant to rigid transformation in Euclidian space. Recently, [PERSON] et al. [28] proposed D3 Feat which is invariant in density, representative, and has outstanding adaptive capability across untrained scenarios. However, it either requires the calculation of the point density or relies on random points selection to achieve rotation robustness. This is often unfeasible and is insufficient when there are limited computing resources. However, the proposed method not only selectively exploits the rich spatial and contextual information of the D3 Feat, but also takes advantage of the flexible GAT to find high-quality point-wise correspondences in 3D point cloud feature matching.  
The main focus of this study is to use a learning-based approach to overcome the limitations of manual methods. For indoor datasets, early works such as 3 dMatch [25]use a 3D convolutional network to learn geometric features by training on positive and negative pairs. The fully convolutional geometric features approach (FCGF) [27] used a fully convolutional network for descriptors and achieved rotation invariance. The SpinNet approach [35] used a spatial point transformer to project the input point to a cylindrical space followed by a series of powerful neural networks. It learns rotation-invariant, compact, and highly descriptive local representations. Similar to the FCCF, the D3 Feat approach uses a fully convolutional network [28], but unlike FCGC, the D3 Feat extracts global descriptors using dense deep features through a KPConv backbone [36]. [PERSON] and [PERSON] [52] used a weakly-supervised network to extract features in outdoor scenes. However, these descriptors are the result of random or full sampling. To overcome the above drawbacks, an effective combination of a keypoint and a descriptor is proposed to provide better registration performance.