# Feature-Preserved Point Cloud Simplification Based on Natural Quadric Shape Models
## 1 Introduction  
With the development of 3D scanning technology, a number of portable devices have appeared, and the application of 3D graphics has widened, for example, Microsoft's Kinect, Hololens, and Intel's RealSense are used in VR (virtual reality), reverse engineering, non-contact measurement, and so on. Regarding 3D scanning technology, point clouds, as the basic and most popular data type, are collected by a 3D scanner. Therefore, point cloud processing is becoming a hot topic in 3D graphics, which includes data denoising, data registration, data segmentation, data simplification, and surface reconstruction [1]. At present, for the application of point clouds in 3D graphics, the huge time and space consumption is the key problem that needs to be solved. Taking Kinect (V2) as an example, data can be collected at a rate of 12 MB per second. The large amount of data, which can be seen as dense point clouds, can be collected at a low cost. Obviously, the dense point clouds show more details of the surface of the measured object. However, dense point clouds produce a huge volume of data. The massive data volume produces unimaginable pressure for 3D processing, such as the reverse reconstruction of objects. Hence, the simplification of point cloud data is important and necessary for point cloud processing. In order to simplify the data volume, many algorithms have been provided so far. Among these algorithms, point cloud simplification by voxelization is the most widely used method, especially in reverse engineering [2; 3; 4]. For example, the grid-based simplificationalgorithm has a compelling advantage in terms of efficiency. Unfortunately, the grid-based algorithm has an influence on the quality of the reduced data. Therefore, in order to obtain a higher quality, the surface features are estimated and applied to point cloud simplification, for example, [PERSON] used the symmetrical features of objects [5]. At present, the point cloud simplification problem can be solved in two ways: mesh-based simplification [6] and point-based simplification [7]. Research into mesh-based simplification has been the focus for a long time, e.g., the vertex merging [8] and subdivision. In order to preserve the geometric features, the energy function is introduced into mesh-based simplification [9]. However, when mesh-based simplification is used, it is inevitable that mesh will be constructed by the original point clouds. Especially when facing huge original point clouds, the process of mesh construction will occupy a significant amount of the system's resources. Thus, in this paper, we pay more attention to the point-based simplification algorithm. According to the data attributes which are used by point cloud simplification, the state-of-the-art point-based simplification algorithms can be classified into three categories: space subdivision, geometric features, and extra attributes. The first kind of point cloud simplification involves reducing data via the division of measured space. Before simplification, the measured space is divided into different sub-spaces [10]. Then, the simplification algorithm is implemented for each sub-space [2]. To achieve more efficient algorithms, simplification based on space division is frequently adopted. In particular, grid-based simplification, a process in which the sub-space is divided by the unified grid, reduces the running time of the algorithm. The Octree [11; 12; 13; 14] simplification algorithms divide the measured space according to the Octree coding, and the sub-spaces are uneven. The cluster [15; 16; 17; 18; 19] gathers similar points together in the space and divides the data set into a series of sub-clusters. [PERSON] et al. [16] verified that the K-means is the suitable cluster algorithm for point cloud simplification compared to the hierarchical agglomerative. However, by just relying on the division of measured space, some critical geometric features would be missed; this can lead to mistakes in 3D measurement or reverse engineering.