# PTRNet: Global Feature and Local Feature Encoding for Point Cloud Registration
## 1 Introduction  
In recent years, with the increasing maturity of laser technology, a variety of laser systems play an important role in cultural relic restoration, military aerospace, 3D topography measurement, target recognition and other applications. As one of the key technologies of laser 3D scanning and imaging, 3D point cloud registration has been widely studied and applied. Rigid point cloud registration refers to the problem of finding a transformation matrix T to align two point clouds. Registration plays a key role in many computer vision applications, such as 3D reconstruction, 3D positioning, and attitude estimation. Traditional point cloud registration methods are often called optimization-based point cloud registration frameworks. Such registration algorithms [1; 2; 3; 4; 5; 6; 7] obtain the optimal transformation matrix by iterating through two phases [8] correspondence search and transformation estimation. The correspondence search finds the corresponding (matching) points between the point clouds. Transformation estimation uses these corresponding relations to estimate the transformation matrix. The advantage of these methods is that they do not need training sets, relying on strict data theory to ensure their convergence. However, they need many complex strategies to overcome noise, outliers, density changes, and partial overlaps, all of which increase the computational cost. In recent years, the development of deep learning technology has enabled 3D point cloud registration to make great progress [9; 10; 11; 12; 13; 14]. Point cloud registration methods based on deep learning fall into two categories: feature learning methods [15; 16; 17; 18; 19] and end-to-end methods [20; 21; 22; 23; 24; 25; 26]. Feature learning methods use depth features to estimate accuratecorrespondences. After finding matching points, the transformation is estimated using one-step optimization (e.g., singular value decomposition (SVD) or random sample consensus (RANSAC)) without iteration between correspondence estimation and transformation estimation. [PERSON] et al. [16] estimated the correspondence of depth features based on the traditional iterative registration method of iterative closest point (ICP) [1] and used SVD to calculate the transformation to complete registration. [PERSON] et al. [17] used a differentiable Sinkhorn layer and annealing algorithm to determine corresponding points by learning the fusion features between spatial features and local geometric information. [PERSON] et al. [20] proposed an iterative distance-aware similarity matrix convolution network, which could be easily integrated with traditional feature methods (e.g., Fast Point Feature Histograms, FPFH [27]) or learning-based methods to perform registration. This approach provides robust and accurate correspondence searches, obtaining accurate registration results through a simple RANSAC (SVD) method. However, the registration performance of such methods declines sharply in unforeseen situations. If there is a large difference in the distributions between the actual scene and the training data, a large amount of training data is needed. Meanwhile, the separated training process learns a stand-alone feature extraction network, with the learned feature network only determining matching point pairs without the ability to complete the registration. The end-to-end learning-based methods solve the registration problem with a single neural network. Such methods accept two point clouds as inputs and produce the transformation matrix between the two point clouds as output. These methods transform the registration problem into a regression problem. [PERSON] et al. [11] proposed a local descriptor suitable for this task along with a network RelativeNet for relative pose regression on the basis of point cloud registration and point cloud relative pose estimation. [PERSON] et al. [21] proposed an end-to-end lightweight universal point cloud registration model with good performance in heritability. [PERSON] et al.