# 3D Shape Generation via Variational Autoencoder with
## 4 Experiments
### Performance Evaluation  
A framework named 3D-VAE-SDFRaGAN, which can infer a 3D shape from its associated 2D image, is proposed in this paper. The results of the proposed model, which learns to build SDFs of _chair_, _table_, _car_, and _sofa_ from their associated 2D images, are shown in Figure 4. The marching cubes algorithm is employed to extract triangular surfaces from the SDFs, which are then smoothed using Laplacian smoothing to generate the final 3D shapes, as presented in Figure 4c. Several state-of-the-art models are compared against the proposed 3D-VAE-SDFRaGAN, following the evaluation process outlined in [46]. The volumetric outputs of the 3D-R2N2 model are converted into a mesh representation using the marching cubes algorithm, and the quality of the generated model is compared with the proposed model. The chamfer distance (CD) [9; 46] is used for evaluating the accuracy of the 3D-VAE-SDFRaGAN model, which measures the difference between the generated 3D mesh and the ground truth mesh for the six categories presented in Table 4. Also, the proposed model is compared with state-of-the-art models in Table 5.  
Figure 4: Examples of 2D images and SDFs of the object, and the generated meshes. The 2D images and SDFs of objects are shown in (**a,b**). The generated mesh-based shape is shown in (**c**). Figure 3: Training process flow for our proposed framework. Table 4 also presents the results of this evaluation. The performance of the proposed 3D-VAE-SDFRaGAN was evaluated by computing the CD scores for the six categories. The chamfer distance (CD) is a standard evaluation metric in 3D deep learning, which is used to assess the similarity between two meshes by calculating the distance between the points of each mesh and the nearest surface point of the other mesh. The computation is performed by determining the closest point in the opposite mesh for each point in each mesh and then summing up the square of the distances between the two sets of points. The accuracy of the object is better measured when the CD score is smaller. The equation of the CD is defined as  
\[d_{CD}(S_{1},S_{2})=\sum_{x\in S_{1}}\min_{y\in S_{2}}\|x-y\|_{2}^{2}+\sum_{y \in S_{2}}\min_{x\in S_{1}}\|x-y\|_{2}^{2} \tag{12}\]  
where \(S_{1}\) and \(S_{2}\) are the original mesh and generated mesh, respectively, and x and y are vertices of the original mesh and generated mesh, respectively. The results of the experiment demonstrated that other state-of-the-art methods were surpassed in all categories by the proposed model. This was attributed to the significant improvement in the stability of the 3D-VAE-SDFRaGAN network, which was achieved by incorporating a relativistic discriminator and a non-standard GAN loss function, without any additional computational cost. Superior quality in generating 3D shapes was exhibited by the results of the proposed method, and a comparative analysis with other models was performed. Objects with finer details that cannot be achieved with 3D-R2N2 using different model views [30] were generated by our proposed model, which demonstrated its efficacy. Additionally, the 3D-R2N2 algorithm was based on a 3D-autoencoder that inherited the limitations of autoencoder algorithms and was primarily used for reconstruction purposes, unlike our proposed method, which was designed for the generation task. The proposed model had the capability to generate objects with diverse topologies, unlike the N3 MR approach, which lacked this feature [48]. The proposed model also addressed a key issue with the SIF method by utilizing SDF data representation to accurately capture the intricate details of an object's structure [47]. Furthermore, a well-detailed 3D shape is produced by the proposed model, which is sacrificed by the MeshSDF framework [51]. Finally, the proposed 3D-VAE-SDFRaGAN not only effectively scaled, but also produced highly detailed shape representations that were previously unattainable with the DISN model.