## 2 Related Work
### Learning-Based Methods  
A number of deep learning approaches, including PCRNet [26], REGTR [27], PREDATOR [28], and others, have recently been suggested for registration. Two categories can be used to categorize learning-based registration: feature learning-based methods and end-to-end learning-based approaches.  
In contrast to the conventional point cloud registration techniques, feature learning-based approaches learn a robust feature correspondence search using a deep neural network. The transformation matrix is then finally computed via a one-step estimate (e.g., RANSAC) without the need for iterations. In order to identify soft correspondences between the overlap of two point clouds and extract contextual information for the purpose of learning more unique feature descriptors, PREDATOR uses an attention mechanism. Self-attention and cross-attention are used by REGTR to directly forecast a set of final point correspondences that are consistent. The goal of all these techniques is to estimate robust correspondences using the learned distinctive feature, and they all use deep learning as a tool for feature extraction. [PERSON] et al. [29] propose to describe 3 DSmoothNet for point cloud registration, a comprehensive approach to match 3D point clouds with a Siamese deep learning architecture with fully convolutional layers via a voxelized smoothed density value (SDV) representation. [PERSON] et al. [30] put forward PointDSC, which is a revolutionary deep neural network that explicitly uses spatial consistency to prune correspondences between outliers during point cloud registration.  
End-to-end neural networks are used in end-to-end learning-based approaches to overcome the registration challenge. Two point clouds are the network's input, and the transformation matrix that aligns the two point clouds is its output. The network not only can extract features of point clouds but can also estimate transformation. The network of the feature learning-based approach is distinct from the transformation estimation network of the end-to-end learning-based approach and concentrates on feature learning. After extracting global features with PointNet, PCRNet joins these features and feeds them into the MLP network for regression modification. To learn pose-invariant point-to-distribution parameter correspondences, DeepGMR [31] makes use of a neural network. The GMM optimization module then uses these correspondences to estimate the transformation matrix. For internal likelihood prediction, DGR [32] proposes a six-dimensional convolutional network design and uses a weighted Procrustes module to estimate the transformation.  
However, 3D point clouds with labeled tags are commonly used in deep learning methods, but the creation of the labeled tags is time consuming, making them difficult to use for some practical applications. Exceptions include point cloud registration technology based on deep learning, which still has problems, such as inaccurate error solving, certain randomness and instability of registration results, high algorithm complexity and long computation time, and limited generalization ability. Specifically, the issues with 3 DSmoonNet includes high efficiency in processing large-scale point clouds, strong hardware dependency, and low generalization ability. The shortcomings of PointDSC include severe performance dependence on initial matching, high computational complexity, etc.