# Growing Neural Gas with Different Topologies for 3D Space Perception
## 1 Introduction
Moreover, GNG can perform noise reduction [23; 24], 3D reconstruction [25; 26; 27; 28] and feature extraction using the topological structure [29; 30]. From these reasons, GNG is expected to utilize the unified perceptual system for the point cloud processing [31; 32; 33; 34; 35; 36; 37; 38; 39]. [PERSON] et al. applied GNG-based 3D feature extraction and the matching method to 3D object recognition [40]. This method just utilizes the node set for extracting features such as SHOT and spin image, which do not utilize the topological structure generated by GNG. Refs. [41; 42; 43; 44] reduced the calculation cost and improved the adaptability of the time-series data for realizing gesture recognition and 3D object-tracking methods in real time. Ref. [41] applied a uniform grid structure to GNG for reducing the calculation cost of the winner node selection and realized the real-time 3D object-tracking method. Refs. [43; 44] proposed the criteria for node addition and deletion. These methods are based on the probability density distribution of the data and nodes and verified the real-time adaptability for the point cloud data. In this way, many kinds of GNG-based methods have been proposed from the viewpoint of various research directions. However, the GNG-based perceptual system has unsolved problems. One of the problems is that GNG cannot preserve the 3D position space if the input vector is composed of not only the 3D point cloud (position information), but also additional information, such as RGB-D data (3D position with color information). Figure 2 represents a learning example using GNG from a 3D point cloud (\(x\), \(y\), \(z\)) with color information (\(R\), \(G\), \(B\)). The generated topological structure shown in Figure 2b cannot preserve the 3D position space of the point cloud since the topological structure is generated from both the position and color information, and the scale of the color information is a dominant scale compared with the scale of the position information in this dataset. In this way, GNG-based point cloud processing methods have the scalability problem between each feature vector if the input vector is composed of multiple properties. For solving this problem, there exist two main approaches. One is to utilize a background subtraction algorithm as preprocessing for extracting the target data and generating the topological structure of only the target object [45; 46]. The other is to apply a weighted distance measurement in the winner node selection according to the importance of each property [47; 48]. In the former approach, [PERSON], et al. proposed a background detection method based on mixture Gaussian distribution and CIE lab color space for generating topological structure of the human face and arm [45]. However, this kind of approach cannot preserve the appropriate position space if the background detection fails because of the sensor noises. In addition, the background detection needs detailed prior knowledge about the target object. Therefore, it is difficult to apply the background detection method to an unknown dataset. In the latter approach, [PERSON], et al. proposed the GNG attention method (GNGA) for extracting saliency from a 2D camera image [47]. GNGA uses the weighted distance measurement used in the selection of the 1 st and 2 nd winner nodes for generating the topological structure of the position space with color  
Figure 1: Examples of topological learning methods. In (**e**), each color indicates each cluster. (**a**) Input data, (**b**) SOM, (**c**) GCS, (**d**) GNG, (**e**) clustering. Figure 2: An example of GNG that applied to simulation data. Circles and lines respectively indicate node and edge of GNG in (**b,c**). (**a**) Image data, (**b**) result of GNG, (**c**) result of GNG with the weighted vector. information. In addition, the authors also proposed the weight-vector-based GNG method, called modified GNG with utility (GNG-U II) [48]. These methods can preserve the 2D/3D position spaces with color information by designing the appropriate weight.