# 3D Shape Generation via Variational Autoencoder with
## 4 Experiments
### Performance Evaluation
This was because the shape representation in DISN's model was limited to a fixed-length feature vector, which only captured the global shape and was unable to represent fine details [52]. Figures 5-7 present a graph to show the performance of CD metrics on a chair, cabinet categories, and average chamfer distance of the proposed model with other state-of-the-art models. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Category** & **3D-R2N2 [30]** & **SIF [47]** & **N3 MR [48]** & **MeshSDF [49]** & **DISN [50]** & **Ours** \\ \hline Chair & 1.432 & 1.540 & 2.084 & 0.590 & 0.754 & 0.589 \\ Table & 1.116 & 1.570 & 2.383 & 1.070 & 1.329 & 0.672 \\ Car & 0.845 & 1.080 & 2.298 & 0.960 & 0.492 & 0.491 \\ Lamb & 4.009 & 3.420 & 3.013 & 1.490 & 2.273 & 0.662 \\ Sofa & 1.135 & 0.800 & 3.512 & 0.780 & 0.871 & 0.566 \\ Cabinet & 0.750 & 1.100 & 2.555 & 0.780 & 1.130 & 0.314 \\ Average & 1.545 & 1.585 & 2.641 & 0.945 & 1.142 & 0.578 \\ \hline \end{tabular}
\end{table} 
Table 4: Performance comparison of the proposed method with state-of-the-art on the ShapeNet dataset. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Criteria** & **3D-R2N2 [30]** & **SIF [47]** & **N3 MR [48]** & **MeshSDF [49]** & **DISN [50]** & **Ours** \\ \hline \multirow{4}{*}{Approach} & Multi-view & \multirow{4}{*}{Reconstruction using 3D} & \multirow{4}{*}{Reconstruction using implicit} & \multirow{4}{*}{Reconstruction shapes from learned feature maps} & \multirow{4}{*}{Reconstruction using implicit} & \multirow{4}{*}{Reconstruction using implicit functions and source extraction} & \multirow{4}{*}{Learning a generative model for 3D shapes via 2D images} \\  & & & & & & \\ \cline{1-1} \cline{5-5}  & & & & & & \\ \cline{1-1} \cline{5-5}  & & & & & & \\ \hline \multirow{4}{*}{Architecture} & 2D-CNN + 3D-LSTM + 3D-DCNN & Multi-layer perceptron & \multirow{4}{*}{ \begin{tabular}{c} Neural network \\ with geometric encoding \\ \end{tabular}  } & \multirow{4}{*}{ \begin{tabular}{c} Multi-layer perceptron \\ \end{tabular}  } & \multirow{4}{*}{\ \begin{tabular}{c} Convolutional \\ neural network \\ \end{tabular}  } & \multirow{4}{*}{ \begin{tabular}{c} VAE- \\ SDFRaGAN \\ \end{tabular}  } \\ \cline{1-1} \cline{5-5}  & & ShapeNet and & & & & \\ \cline{1-1} \cline{5-5}  & & & & & \\ \cline{1-Figure 5: Performance of chamfer distance evaluation metrics on the proposed model and some of the state-of-the-art methods on the chair category. Figure 6: Performance of chamfer distance evaluation metrics on the proposed model and some of the state-of-the-art methods on the cabinet category. Figure 7: Performance of the average chamfer distance metrics on our proposed model and some of the state-of-the-art methods. In Figure 8, the qualitative comparison of the generated samples and the learned representations of the proposed model with other 3D GAN-based models for visual evaluation is shown. (a) Sample of car, chair, and table generated by [PERSON] et al. [6]. (b) Sample of car, chair, and table generated by [PERSON] et al. [8]. (c) Sample of chair and table generated by [PERSON] et al. [7]. (d) Sample of car, chair, and table generated by [PERSON] et al. [36]. (e) Sample of car, chair, and table generated by [PERSON] et al. [37]. (f) Sample of car, chair, and table generated by our model. It can be observed that noticeably better and higher qualitative performance is obtained by the smooth meshed surfaces recovered from signed distance function fields powered by the proposed 3D-VAE-SDFRaGAN framework and 2D image features in our work. The results of [PERSON] et al. [37] is compared with the generated samples in Figure 8f, despite the complete 3D data used in their work. This shows that the low-cost 2D images readily available with corresponding SDFs from the proposed method are better dataset options for training 3D mesh-based generator models leveraging relativistic average GAN loss function. Moreover, better mesh-based 3D shape generation with the proposed 3D VAE-SDFRaGAN model is aided by the combination of 2D images and the SDFs dataset.