# Feature-Preserved Point Cloud Simplification Based on Natural Quadric Shape Models
## 1 Introduction
The second kind of point cloud simplification is the extensive method in the academic research field, which reduces the data volume and preserves the geometric features. However, the estimation and protection of the geometric features is complicated and time-consuming. Usually, the geometric features vary, i.e., distance, curvature, normal, and density. Like the space division method, distance can be seen as a geometric feature by moving the least squares [20]. Furthermore, [PERSON] et al. [21] reduced the closed point sets. Similar to the distance, the density [22; 23], which derives from distance, is used for point cloud simplification. Curvature is the main factor that determines the geometric feature in point cloud data analysis. For example, [PERSON] et al. [24] first showed that the use of discrete curvature as the simplification criterion is better than using distance, especially in the high-curvature region. Then, Gaussian curvature [25] was estimated as the geometric feature. Some researchers tried to extract the curvature of point clouds by combining this process with sub-space division [7; 26]. Moreover, the normal and vectorial angles are important point cloud features [27; 28; 29]. Furthermore, the boundary [30], symmetry [31] and shape features also play roles in simplification, especially if the shape feature is difficult to estimate and measure, but is important for the point clouds. Among the shape features, the plane is easy to describe and extract for point cloud simplification [32; 33]. In this paper, FPPS (feature-preserved point cloud simplification) is used to measure and describe the multi-shape features, which are used for point cloud simplification. The last kind of method is to reduce data using the extra attributes. However, extra attributes incur extra costs, such as the device capturing fee. [PERSON] et al. [34] provide a point cloud simplification method on the basis of panorama images, where the data are projected into different geometry structures, and the data volume can be greatly compressed, based on the geometry. Additionally, similar and redundant information can be found according to the color of the point clouds or the intensity of reflected light [35]. The second method is to simplify data with the location information, which is usually applied in the remote sensing field. Using the auxiliary GPS information, the volume of data can be reduced [36; 37; 38]. For the purpose of preserving the geometric features, this paper provides the FPPS algorithm, and FPPS algorithm processing starts with the extraction of key points from the point cloud. The key points can reveal scale-independent and spin-independent features, surface profile features, and curved features. Taking the key point as the center, we create the neighbor of each key point. We consider the neighbor of each key point to be important and include rich, diverse geometric features. For the neighbor of each key point, it is difficult to represent the geometric features' representation. In addition, the scale-independent, spin-independent, surface profile, and curved features which are used for key points, are insufficient to express the neighbors' geometric features. Therefore, the regular shape, i.e., natural quadric surface, is seen as the simplification model of point clouds to estimate the neighbors' geometric features, which are considered as the shape features in FPPS. Then, according to the model, we create the simplification rules. Finally, the point cloud simplification is accomplished. The contributions of this paper are as follows:  
1. The point cloud simplification method (FPPS) is proposed. By using FPPS, the data volume can be reduced while preserving the rich geometric features. Based on key points, including the estimation of geometric features, FPPS performs the simplification on the key points and their neighbors with a lower reduction ratio, so that geometric features are well preserved. The FPPS algorithm provides the adaptive reduction ratio, which changes with different shape features. 2.