# A Voxel Generator Based on Autoencoder
## 1 Introduction  
Recently, Facebook announced a name change to Meta and the launch of the Metaverse project, dedicated to creating a virtual world which allows people to work and live in a virtual environment, thereby overcoming the limitations of space via networks and VR/AR devices. To popularize the Metaverse, many international manufacturers have invested in the development of software and hardware such as virtual/augmented reality headsets and 3D digital content to provide reasonable device prices and optimal applications for users. At present, virtual/augmented reality (VR/AR) is being applied in various fields. For example, virtual medical imaging [1, 2] allows doctors and medical staff to conduct accurate surgical treatment diagnoses or training through real-time high-resolution virtual organ images. Virtual museums [3] enable the public to view antiquities in 360 degrees. Virtual shopping malls [4] allow consumers to watch and try products without going to physical stores. Virtual classrooms [5] support students operating virtual instruments and equipment, allowing them to conduct experiments and interact with each other, which can also reduce the risk of the spread of diseases due to crowds gathering in confined spaces. In virtual/augmented reality games, players can be immersed in the game world through a combination of virtual and real scenes. As previously described, VR/AR has dramatically enriched people's life experience and improved work convenience and efficiency. However, the traditional process of developing VR/AR content and applications is very time-consuming and expensive. To emulate the real world, generating 3D image models for real-world objects is essential. Digital content developers usually have to manually use 3D drawing software such as 3 ds Max [6] or Solidwork [7] to draw objects, or use expensive equipment such as light detection and ranging (LiDAR) to scan objects. Fortunately, with the recent rapid development of Graphics Processing Units (GPUs), artificial intelligence (AI) has undergone tremendous development. Moreover, large-scale 3D model datasets such as ShapeNet [8] and ModelNet [9] have been released to support deeplearning models to learn to reconstruct 3D object models from 2D images. Therefore, the deep learning approach to 3D model reconstruction has recently become a research hotspot and a cost-effective solution to minimize the development cost of VR/AR applications. The methods of constructing a 3D object model from a 2D image can be divided into three categories [10]: voxel, point cloud, and mesh, which is the output structure of the 3D model. The full name of a voxel is volume pixel; this represents a value on a regular grid in three-dimensional space. A point cloud is composed of high-density points in a limited 3D space. A mesh is a triangle or quadrilateral surface composed of points and edges in space. The point cloud is easy to render. The mesh can make the surface of the object models smooth by increasing the number of polygons. Both the point cloud and mesh are represented by a geometric form. By contrast, voxels are represented by a rasterized format. Consequently, they can be directly used by convolution neural networks (CNNs) [11] to extract object features in order to construct 3D models. This paper focuses on the discussion and research of voxel-based 3D model reconstruction methods. In the past, voxel-based 3D model reconstruction methods often required additional image data or precise condition control to achieve acceptable quality. For example, the method proposed by [12; 13] requires cameras with depth sensors to create the depth data of images. Some approaches [14] require multi-view images of objects. This equipment and data collection requirements restrict the development of AR/VR applications. To overcome this restriction, recent research [15; 16; 17] proposed several methods to construct a voxel-based model using only a single image. The architecture of these methods may be divided into two parts.