# Growing Neural Gas with Different Topologies for 3D Space Perception
## 1 Introduction  
Three-dimensional space perception is one of the most important capabilities for an autonomous mobile robot in order to operate a task in an unknown environment adaptively since the autonomous robot needs to detect the target object and estimate the 3D pose of the target object for performing given tasks efficiently [1; 2; 3; 4; 5; 6; 7]. In the research field of 3D space perception, many research studies use an RGB-D camera, such as Microsoft Kinect [8] and Intel Realsense [9], that can measure the color and depth of an image simultaneously in real time. After the 3D point cloud is measured, the autonomous robot needs to reconstruct a structure from the 3D point cloud with color information according to the given tasks since the point cloud is unstructured data. For realizing the 3D space perception, many kinds of 3D image processing based methods have been proposed. These methods were expanded to the 3D point cloud by utilizing camera image processing technologies, such as filtering methods [10], feature extractions [11; 12], and sample consensus methods [13]. However, these methods depend on feature or model descriptors, which have a problem with adaptability to environmental changes, such as geometry, texture and light conditions. To improve the adaptability, recently, the research studies of the information extraction from the point cloud weredeveloped by a deep neural network (DNN) [14]. In particular, many research works in autonomous robot and automatic driving have proposed a DNN-based semantic segmentation method (e.g., PointNet [15], PointCNN [16] and VoxNet [17]) that can label and give the point cloud meaning. The DNN-based methods give highly accurate segmentation results by using big data with the teaching signal. However, one of the problems of the supervised learning method is application to unknown data. If the learned network is applied to the unknown environment or label not including the output layer, the network fails to segment the point cloud. In the environment where the autonomous robots are expected to perform the task, the autonomous robot needs to recognize the unknown target object and environment. Therefore, the point cloud processing method without prior knowledge is required for realizing the robot that can perform the given tasks in the unknown environment. Self-organization map (SOM) [18] based methods are one of the main streams based on unsupervised learning for the point cloud processing [19]. The other methods that are well known in this field are neural gas (NG) [20], growing cell structure (GCS) [21], and growing neural gas [22]. Basically, these methods are called unsupervised learning when applied to an unknown data distribution without teaching signals and using the competitive learning method based on the winner-take-all approach. The SOM can project the input vectors in a high dimensional space to a topological structure in a low dimensional space, according to the data distribution. The SOM is easy to apply to many problems by determining the number of nodes and topologies, while it is difficult to design these things to the unknown data distribution. NG does not need to determine the number of nodes since the NG has node addition and deletion in the learning algorithm. However, the topological structure is updated according to the order of the data input. On the other hand, GCS and GNG can dynamically change the topological structure based on the adjacency relation held in the referred node. GCS cannot delete the nodes and edges, while GNG can dynamically delete the nodes and edges by using the concept of the edge's age. Figure 1 shows an example result of each method applied to a 2D simulation point cloud. There are redundant nodes and edges in SOM and GCS, while GNG can preserve the 2D point cloud space appropriately. In addition, GNG can cluster the unknown ring data (Rings A, B and C) by utilizing the topological structure since there is no adjacent relations between each ring (Figure 1e).