## 4 Experiment Results and Discussion
### Ablation Studies
* Option 11: To further validate the effectiveness of the deformation decoder (DD) and deformation loss \(L_{Def}\) in reconstructing finer topological structures, we add the DD to the network of option 10 while keeping the other settings unchanged. As shown in Figure 7, this variant generally reconstructs object shapes with more detailed topological structures compared to option 10. This further demonstrates the contribution of the DD in reconstructing finer topological structures of objects. However, it is worth noting that the variant still struggles to generate visually appealing object shapes compared to the standard ED\({}^{2}\)IF\({}^{2}\)-Net. This observation emphasizes the importance of the deformation loss \(L_{Def}\) in the reconstruction process. * Option 12: To further demonstrate the superiority of the proposed method in feature extraction, we replace the PVT-Tiny and PVT-Large image encoders in the standard ED\({}^{2}\)IF\({}^{2}\)-Net-T and ED\({}^{2}\)IF\({}^{2}\)-Net-L with DeiT-Tiny and DeiT-Base [37], respectively, while keeping the other settings unchanged. The qualitative results are presented in Figure 7. It can be observed that when the image encoders of ED\({}^{2}\)IF\({}^{2}\)-Net-T and ED\({}^{2}\)IF\({}^{2}\)-Net-L are replaced by DeiT-Tiny and DeiT-Base, respectively, the network tends to reconstruct inferior results, which exhibit poor topological structure and surface details. This further confirms the effectiveness of ED\({}^{2}\)IF\({}^{2}\)-Net in feature extraction. * Option 13: To further validate the effectiveness of HAM in the surface detail decoder for enhancing surface detail representation, all HAMs in the surface detail decoder of the standard model are replaced with CBAMs [45], while keeping the other settings unchanged. The qualitative reconstruction results are depicted in Figure 7. In comparison to the standard ED\({}^{2}\)IF\({}^{2}\)-Net, the variant encounters challenges in capturing and recovering clear surface details of the object, resulting in the presence of artifacts around the shape. This option further demonstrates that HAM is more effective than CBAM in enhancing the capability of ED\({}^{2}\)IF\({}^{2}\)-Net to handle surface details. * Option 14: The standard ED\({}^{2}\)IF\({}^{2}\)-Net proposed in this paper, including all components and the loss function with WS. The visualization and quantitative results of the ablation studies are presented in Figure 7 and Table 2, respectively. Overall, the weighted sampling strategy enables the network to reconstruct small-scale details effectively. Additionally, the deformation decoder, which refines the coarse implicit field, plays a crucial role in capturing the object's topology. The deformation decoder performs optimally when trained with the deformation loss term \(L_{Def}\), while the coarse shape decoder benefits from the \(L_{Coa}\). The deformed implicit field, derived from the deformation decoder, serves as a solid foundation for reconstructing the object's surface, which is further fused with the forward displacement map generated by the surface detail decoder trained by \(L_{Lap}\) to recover the surface details of the object. Moreover, the backward displacement map from the surface detail decoder compensates for the deformed implicit field, ensuring the correct topology reconstruction. Furthermore, compared to using ResNet18 as an encoder, the standard ED\({}^{2}\)IF\({}^{2}\)-Net achieves higher-fidelity results. Importantly, the presence of the deformation decoder and the utilization of the deformation loss term \(L_{Def}\) contribute to the reconstruction of ED\({}^{2}\)IF\({}^{2}\)-Net with finer topological structures. Furthermore, the PVT architecture, which generates multi-scale hierarchical local features, is more suitable as an image encoder for ED\({}^{2}\)IF\({}^{2}\)-Net compared to other conventional transformers such as DeiT.