# Color Point Cloud Registration Algorithm Based on [PERSON]
## 1 Introduction  
With the development of three-dimensional scanning equipment, reconstruction technology has been more and more widely used. For example, dental repairs in the medical field, virtual reconstructions of roles in the film and television industry, and restoration of cultural relics in archaeology are all areas that have found application. Reconstruction is an important method of modeling in which registration technology plays a crucial role. Because the collection field of the three-dimensional scanning device is limited, only part of the whole scene data can be obtained in one operation. In order to gain complete data, collection operations must be performed several times and then spliced together to obtain the whole data. The point cloud is an important form of data, and its registration is the process to estimate the transformation between different point cloud according to the overlap between them, then different data collected at the different positions can be spliced together according to the transformation relationship between the point clouds to form a whole scene data. One of the most classical methods for this task is the Iterative Closest Point (ICP) algorithm proposed by [PERSON] [1]. ICP uses the nearest point principle to create corresponding point pairs between the target and source point cloud under the current transform, then obtains a new transform by minimizing the mean square error (RMSE) between the corresponding point pairs and updates the current transform. This process is repeated until the best transform is obtained. the ICP algorithm has been widely used in engineering because of its simplicity, efficiency, and accuracy, but the use of coordinate information alone is not enough to constrain the optimization process. For example, when two point clouds with duplicate structures are registered, the alignment effect using ICP algorithm forpoint cloud registration is not good, which may cause sliding, resulting in a large error [2; 3]. Therefore, in recent years, many extended ICP algorithms [4; 5; 6; 7] based on the classical ICP algorithm have been derived. In recent years, the neural network has made great achievements in image and point cloud processing, and its combination with ICP algorithm is an important trend in point cloud registration. Two studies [8; 9] used the neural network method to improve the traditional ICP algorithm by making correspondence through learned features of the point cloud. Although these two algorithms work well, they require a long training time on the dataset. When applying the algorithm, the result will not be good if the test data have large differences compared with training data. Therefore, the improved ICP algorithm based on the neural network has strict limitations on data. With the development of sensor technology, many industrial 3D scanners are equipped with color cameras, which can acquire the color information of point clouds, which is helpful for registration. A common way to introduce color information to registration is to extend the coordinate with color information and form a four or six-dimensional space, which contains color information [10; 11; 12; 13]. However, for the points that have large distances but similar colors, it will sometimes introduce an incorrect correspondence, which will cause the error function to converge in the wrong direction, thus obtaining the incorrect final transformation. The method [14] proposed by [PERSON] et al. solves this problem by establishing a corresponding relationship through the nearest point principle, and like Point-to-Plane ICP, they use the color distribution on the tangent plane to introduce the color information. The error function consists of color and geometric parts, which makes it possible to unify the color and geometric information in registration. However, the color information used by the algorithm [14] is gray.