## 2 Related Works
### Implicit Methods for Single-View 3D Reconstruction  
Since the object shapes in this work are represented with implicit functions, this section focuses on reviewing the implicit methods for single-view 3D reconstruction. There are mainly two popular forms of data in deep-learning-based single-view implicit 3D reconstructions: occupancy probability and SDF. Specifically, the implicit models learn the scalar value of each query point under the supervision of the ground-truth occupancy probability or SDF. Earlier implicit methods, such as Occupancy Network [20] and IM-Net [19], tend to adopt a straightforward idea. There, the latent vectors of the input image are firstly extracted via an image encoder, and are subsequently combined with the features or coordinates of the query points for the MLP inputs, and then the occupancy probability or SDF for each query point can be predicted. Recently, a few novel CNN-based implicit 3D reconstruction models [24; 25; 26; 27; 28; 29] have been proposed that take into account local features, resulting in more promising reconstruction performance. The most relevant works to ours are DISN [24], MDISN [25], and D\({}^{2}\)IM-Net [29]. Specifically, both DISN and MDISN predict the camera parameters of the input image to extract local features corresponding to each query point. In DISN, query point features are concatenated with global and local features. Two concatenated features are decoded to obtain two predicted values, which are summed to derive the final SDF. MDISN deforms the randomly generated SDF for each query point from coarse resolutions to fine ones depending on the variation of local features. D\({}^{2}\)IM-Net predicts the camera pose and decomposes the reconstruction of the object's implicit field into two parts: the reconstruction of coarse shapes and the recovery of details. DISN and MDISN achieve better experimental results than earlier approaches, yielding shapes with more structure details. However, they still fail to recover the surface details of an object. While D\({}^{2}\)IM-Net is capable of recovering good surface details, it often results in poor topological structures. Although a variant of D\({}^{2}\)IM-Net, called D\({}^{2}\)IM-Net\({}_{GL}\), uses both global and local features in the basic decoder, it still struggles to reconstruct a satisfactory shape and even produces blurry surface details. Compared to DISN, MDISN and D\({}^{2}\)IM-Net, ED\({}^{2}\)IF\({}^{2}\)-Net is the first to employ a transformer to solve single-view implicit 3D reconstruction, which alleviates the negative effects brought by convolution in CNN-based models. This paper proposes a novel paradigm that disentangles the reconstruction of an object into reconstruction of more accurate topological structures and enhanced surface details. The finer-grained topological structure details and enhanced surface details are obtained through iterative refinement of the coarse implicit field using the multiple IFDBs, as well as enhancement of the surface detail features in both spatial and channel dimensions using HAMs, as shown in Figure 1. The core difference lies in the construction of individual specific loss terms for all learned fields, including the coarse implicit field, deformed implicit field, and enhanced displacement field. This disentanglement of the deformed implicit field, which contains most of the topological structures, from the enhanced displacement field allows for better learning, resulting in the recovery of enhanced surface details. Actually, a novel deformation loss for learning structure details from ground truth is introduced in our combined loss function, while the surface details can be learned from ground-truth normal maps by applying a Laplacian loss. Extensive qualitative and quantitative comparisons conducted in the experimental Section 4 unequivocally demonstrate the remarkable capabilities of our proposed ED\({}^{2}\)IF\({}^{2}\)-Net.