# Multi-Scale Indoor Scene Geometry Modeling Algorithm Based on Segmentation Results
## 1 Introduction  
With the continuous advancement of point cloud data acquisition technology and processing algorithms, more and more researchers are paying attention to the application and optimization methods of point cloud scene geometric modeling. For example, point cloud scene geometric modeling can be applied in areas such as virtual reality [1], autonomous driving [2], environment detection [3], and robotics [4], providing more efficient and safe experiences and services. In daily work, there are a large number of geometric primitives involved, such as planes, spheres, cylinders, and cones. Many complex objects can also be seen as composed of these geometric primitives, and these primitives have mathematical models. By representing the collected three-dimensional point cloud with basic model parameters, the storage space is greatly reduced, compressing the model. Geometric modeling of three-dimensional point clouds [5] not only enhances the autonomy of industrial robot grasping but also provides more information for the field of 3D reconstruction [6], helping to make the reconstruction results more in line with real scenes. This is particularly important in virtual reality applications as it provides more support for virtual and real-world integration. In addition, geometric modeling techniques are also very important in the field of surveying and mapping. They not only enable automatic surveying and mapping, reducing human workload, but also provide security guarantees in certain dangerous measurement environments.  
Solving the problem of automatically identifying geometric primitives, such as planes, spheres, cylinders, and cones, from three-dimensional point clouds is a fundamental problem in robot perception of the environment. Solving this problem can reduce the difficulty of robot perception of the environment and bridge the semantic gap between high-level semantics and low-level visual features. Many existing point cloud registration techniques and point cloud polygon mesh reconstruction techniques can reconstruct the collected 3D information well, but these techniques only reconstruct the surrounding environment or study the topology of objects, without recognizing the objects semantically. Therefore, using segmentation results as input is beneficial for achieving comprehensive scene analysis. Typically, the operating scenes of indoor robots consist of objects with regular structures, and with the gradual application of mathematical models in three-dimensional space, combining point cloud segmentation and geometric analysis can achieve modeling of regular objects, which helps reduce the perception difficulty of robots in unknown environments [7].  
The main contributions of this paper are as follows: (1) Introducing multiscale neighborhood search to address the instability of feature value computation at a single scale, enabling accurate determination of planar and curved surface types based on dimensional features and curvature features. (2) Utilizing the normal vector relationship between planes or surfaces as prior knowledge, using the Random Sample Consensus (RANSAC) algorithm to verify and extract parameters of known types of geometric primitives. The entire process does not require a training dataset and can quickly and accurately complete the geometric parsing and modeling of indoor scenes.