# A Point Cloud Registration Algorithm Based on Weighting Strategy for 3D Indoor Spaces
## 1 Introduction
It is a discrete global registration algorithm that, in discretized coordinate space, maximizes the score of the probability density of the normal distribution calculated for the source points voxelized in the target point cloud. It employs probability density functions and optimal solving methods to compute the transformation relationship between the point clouds to be registered. Compared to ICP, the NDT significantly decreases consumption of hardware resources and enhances registration accuracy. However, since all point cloud data need to be discretized, the NDT has longer running times than ICP, leading to lower efficiency. In 2019, [PERSON] et al. proposed the PointNetLK, a deep-learning-based point cloud registration algorithm [6]. In PointNetLK, PointNet is treated as a learnable \"imaging\" function and is utilized for point cloud registration by modifying the classic Lucas-Kanade (LK) algorithm used for image alignment to integrate with PointNet [7]. Unlike ICP and its variants, PointNetLK does not require large amounts of computation resources, offering advantages in terms of registration accuracy, robustness to initialization, and computational efficiency. On the other hand, due to the explicit encoding of the alignment process in the network architecture, PointNetLK shows significant generalization performance for unseen objects, which implies that the network only needs to learn point cloud representations without the necessity to learn the alignment task. In summary, existing point cloud registration algorithms can be broadly categorized into several types: iterative, optimization-based algorithms such as ICP and its variants Point-to-plane ICP, NICP, Go-ICP, and IMLS-ICP, etc. [8; 9; 10; 11]; statistical, Gaussian distribution-based algorithms such as NDT and its variant MSKM-NDT [12]; and deep-learning-based algorithms such as PointNetLK, DeepVCP, and PCGAN [13; 14]. In the last few years there have been other papers, such as [15], which provides an overview of traditional and learning-based methods for point cloud registration and outlier rejection. It discusses the limitations of existing approaches and sets the stage for the pro posed PointDSC model. Ref. [15] discusses traditional point cloud registration algorithms, such as RANSAC and its variants, which are popular outlier rejection methods but have drawbacks in terms of slow convergence and low accuracy in cases with large outlier ratios. It also mentions the limitations of 3D descriptors in traditional methods due to irregular density and a lack of useful texture, highlighting the importance of geometric consistency, such as length constraints under rigid transformation, which are commonly utilized by traditional outlier rejection algorithms. In addition, it presents learning-based outlier rejection methods, such as DGR and 3 DRegNet, which formulate outlier rejection as an inlier/outlier classification problem. These methods use operators like sparse convolution and pointwise MLP for feature embedding, but they overlook the spatial compatibility between inliers. The section also highlights the limitations of existing outlier rejection methods, as well as the need for spatial consistency in outlier rejection for robust 3D point cloud registration. In the related work section of [15], certain algorithms are suggested, including RANSAC [16], spectral matching [17], DGR [18], and 3 DRegNet [19]. This section gives a full picture of all the current methods used for point cloud registration and outlier rejection. Ref. [20] focuses on the recent developments in point cloud registration, including same-source and cross-source methods, as well as the connections between optimization-based and deep learning techniques. The authors emphasize the need for a comprehensive survey to summarize recent advances in point cloud registration, as existing reviews mainly focus on conventional point cloud registration and deep learning techniques, with limited coverage of cross-source point cloud registration.