# A Point Cloud Registration Algorithm Based on Weighting Strategy for 3D Indoor Spaces
## 1 Introduction  
Various registration algorithms have significantly improved accuracy and efficiency, but their primary application is in the registration of small components. When facing complex 3D indoor spaces, existing registration algorithms struggle to attain a good balance between accuracy and efficiency. A 3D indoor space, like a room, contains objects of different shapes and sizes with large quantities of point clouds, which pose a challenge for both accuracy and efficiency. The idea behind this paper is to use a statistical weighting strategy to come up with a point cloud registration algorithm that is both accurate and quick for 3D indoor places. Point cloud registration typically serves 3D map reconstruction or navigation in 3D indoor spaces, necessitating higher weights for significant targets that impact navigation, tracking, or localization, such as chairs on the ground, tables in the room, or walls obstructing the path. We can appropriately reduce weights for other types of targets to save computational resources during registration, thereby enhancing the overall efficiency of the algorithm and the registration performance of key targets. This paper uses PointNet [1] for semantic segmentation, marking different targets in the point cloud of 3D indoor spaces. A statistical weighting strategy is introduced where the segmented parts of the point cloud are treated as evaluation criteria and various attributes of the pointcloud are set as samples for evaluation. We then use the weights of different parts of the point cloud as reference values to determine the minimum metric of the nonlinear objective function in the Iterative Closet Point (ICP) registration algorithm. We use a new technique to obtain closed-form answers to the nonlinear objective function in a 3D generalized metric. This makes the registration more accurate. Finally, experiments with 3D indoor space datasets verify the accuracy and efficiency of the proposed algorithm, demonstrating significant improvements over the traditional point cloud registration algorithms. We organize the remainder of this paper as follows: Section 2 introduces the weighting strategy, including the basic principles of objective weighting methods and a novel improvement to the calculation steps proposed in this paper. Section 3 describes the process of obtaining the ICP minimum metric solution with assigned weights. Section 4 analyzes the accuracy and efficiency of the proposed algorithm with registration experiments. Section 5 ultimately provides the conclusion and outlook. Point cloud registration is a vital technique in computer vision. It introduces a spatial transformation that maps one image onto another and ensures a one-to-one correspondence between points in both images of the same spatial location to achieve information fusion [2]. Over the years, research into point cloud registration has made great progress. In 1992, [PERSON] et al. proposed the Iterative Closest Point (ICP) algorithm [3]. By calculating the distances between corresponding points in the source point cloud and the target point cloud, a rotation-translation matrix RT is constructed. Then, the RT can be applied to transform the source point cloud and calculate the mean squared difference of the transformed points. If the mean squared difference satisfies a threshold condition, then the algorithm terminates. Otherwise, it continues iterating until the error meets the threshold condition or the maximum iteration count is reached. However, ICP is usually sensitive to initial values and may become stuck in local optima [4]. In 2009, [PERSON] proposed the normal distributions transform (NDT) as a great 3D surface representation with applications in point cloud registration [5]. The NDT utilizes statistical probability methods to determine corresponding point pairs based on the normal distribution of point clouds, thereby calculating the transformation relationship between the source point cloud and the target point cloud.