# Cube of Space Sampling for 3D Model Retrieval
## 1 Introduction  
In the last few years, 3D images and models have gradually extended to different applications and become more popular, such as in Computer-Aided Design (CAD) [1], molecular biology, virtual reality, video and computer games, movies etc. These applications usually require managing a large number of 3D models. In addition, since the number of 3D models is rapidly increasing, there is an urgent need to effectively search from 3D model databases. As a result, 3D model retrieval has become a very important research issue.  
In fact, in the field of Computer-Aided Design, a productive approach is to reuse and modify similar existing models instead of always creating new ones [2]. Therefore, for CAD datasets, accurate identification and retrieval of all components is necessary in order to efficiently reuse existing designs [2]. According to [PERSON] et al. [2], there are two basic types of approaches for the matching and retrieval of 3D CAD data: manufacturing feature-based techniques and shape content-based techniques.  
In image retrieval, images usually have to be processed in several steps before they can be queried, including: segmentation; feature extraction; representation; and query processing. Similarly, 3D models or objects also require several steps of processing before retrieval. Figure 1 shows the process of 3D model retrieval [3].  
However, although various approaches have been developed for content-based 3D model classification, recognition and retrieval, none of them have achieved high performance on all shape classes [4]. Moreover, some of the existing feature extraction methods are only based on 2D images, which use many different views per image to represent a 3D model. Compared with some of these methods, image-based approaches have shown to produce some promising results, but they are not effective over various types of 3D models. Therefore, we believe that using the image-based approach to represent 3D modelsis likely to omit some important information, which has limited discriminative power for 3D model classification.  
In image-based 3D model retrieval, using a large number of 2D images to represent a 3D model is impractical, since it is time consuming and requires a very large storage space. Moreover, some important information would not be fully extracted when 3D models are described by images only, such as: fine features; spatial features; global features; etc. In other words, the method of using limited pictures to represent a 3D model has a limited potential to extract better representative feature descriptors for 3D models. Therefore, we propose a method to extract both global and localized features to represent 3D models.  
The main objective of this paper is to construct a space-based concept 3D model feature representation, namely CSS (Cube of Space Sampling). The CSS method is a branch of the voxelization method. Although voxel data has been widely used in some previous studies [5; 6; 7], most of the voxelization methods or voxel data are used in the visualization field. In contrast to these studies, this paper focuses on voxel-based features, i.e., based on the voxel data rather than the visual display. It is worth mentioning that we believe that the voxel-based feature approach has great potential and robustness for 3D model retrieval, and that our experiments confirm this argument.  
In CSS, cube space 3D model sampling is used to extract whole, new features from 3D models. In addition, the extracted features not only provide the global distribution of information, but also provide information on local features.  
The rest of this paper is organized as follows: Section 2 overviews related work of 3D model retrieval and feature representation; Section 3 introduces the proposed feature extraction approach; and experimental results and the conclusion are provided in Sections 4 and 5, respectively.