# 3D Shape Generation via Variational Autoencoder with
## 2 Related Work
### 3D Shape Generation via Deep Neural Networks  
Recently, researchers have made significant advancements in creating distributions that can depict shapes without relying on prior knowledge. This has been achieved by learning complex functions from data and parameterizing them to generate distributions [7; 26]. A number of algorithms have been proposed to achieve this, including deep convolutional autoencoders [27], autodecoders [28], variational autoencoders [9], convolutional neural networks [29], recurrent neural networks [30], deep belief networks [3], and generative adversarial networks [6; 31]. These algorithms use various data representations, such as voxels, point clouds, and meshes.  
[PERSON], [PERSON] et al. [3] used volumetric data representation as an input to perform 3D shape completion and recognition tasks. [PERSON], [PERSON] et al. [6] proposed the use of a generative adversarial network (GAN) to generate 3D shapes from a probabilistic latent space. [PERSON] et al. [32] introduced PrGANs, a 3D generative model that was trained using the GANs framework and was able to match the input distributions of 2D views. [PERSON] et al. [8] proposed an architecture that used a GANs framework and incorporated a 2D image enhancer network to efficiently train the 3D model generator network. The output of the architecture was a voxel-based 3D shape, which is computationally expensive and requires a large memory footprint.  
[PERSON] et al. [33] introduced the SP-GAN, a novel generative model that represented 3D shapes as point clouds. The input latent vector was disentangled into a global prior (sphere points) and a local prior (random latent vector), and the generator network used style embedding and adaptive instance normalization to develop the 3D shape. [PERSON] et al. [34] proposed GET3D, which leveraged the success of differentiable surface modeling, differentiable rendering, and training GAN models from 2D images. GET3D produced high-quality and textured 3D meshes with complex topologies, rich geometric features, and high textures. The model was trained using adversarial losses and used a rasterization-based differentiable renderer to obtain 2D RGB and silhouettes. However, GET3D only relies on generated data for evaluation purposes and needs to be evaluated on real-world data for a more accurate evaluation. [PERSON] et al. [35] proposed GINA-3D, which uses implicit neural representations to generate 3D models. It uses generative adversarial networks (GANs) to learn from a dataset of 3D scans of real-world objects and generates 3D models that are both realistic and diverse. GINA-3D introduces a novel neural network architecture that can efficiently represent 3D geometry in an implicit form and uses a combination of adversarial and perceptual losses to improve the quality of the generated 3D models. However, the 3D-VAE-SDFRaGAN can generate 3D shapes with fine details from 2D images.  
In contrast to the existing works, our proposed model seeks to use a similar framework but with a signed distance function as a 3D data representation and a RaGAN loss function to train the model to produce mesh-based 3D shapes. The generated 3D shape is of better quality and is less computationally expensive with a smaller memory footprint. To the best of our knowledge, no work has directly mapped 2D images using the VAE-GAN framework and relativistic average GAN loss function to 3D mesh-based shapes.