# SS3 DNet-AF: A Single-Stage, Single-View 3D Reconstruction Network with Attention-Based Fusion
## 3 Proposed Methods
### Parameters Optimization and Gradient Loss  
Parameter optimization is a crucial step in updating model weights during training. The Chamfer distance (CD) was used as the primary loss function to evaluate the dissimilarity between the predicted point clouds \(M\) and the ground truth point clouds \(Y\). CD computes the average of the minimum squared Euclidean distances between points in the two sets. For each point in \(M\), the nearest point in \(Y\) is identified, and their squared distances are summed. This process is repeated for points in \(Y\) with respect to \(M\). The final Chamfer distance, a standard metric for point cloud reconstruction, guides the model towards more accurate predictions.  
\[\begin{split} loss&=\sum_{m\in M}\min_{y\in Y}\|m- y\|^{2}+\sum_{y\in Y}\min_{m\in M}\|m-y\|^{2},\\ \theta_{new}&=\theta_{old}-\alpha\cdot\frac{ \partial_{loss}}{\partial_{\theta}},\end{split} \tag{9}\]  
where \(\theta_{new}\) denotes the updated parameter, \(\theta_{old}\) represents the current parameter, and \(\alpha\) is the learning rate (set to 0.0001), which was tuned through various experiments. The results showed that a learning rate of \(3\times 10^{-2}\) achieved 63.13%, \(3\times 10^{-3}\) achieved 79.19%, and \(3\times 10^{-4}\) achieved 81.09%, with the lowest learning rate yielding the highest accuracy, and \(\
abla L(\theta_{old})\) indicates the gradient of the loss function. The Adam optimizer [40] was employed to update the parameters, providing a robust, adaptive approach that adjusts learning rates dynamically based on historical gradient information, enabling efficient convergence with minimal hyperparameter tuning. In this context, the integration of the  
Figure 8: 3D point clouds generated from input images on previously unseen data. Each input image is paired with its corresponding 3D point cloud, visualized from multiple perspectives. These results highlight the model’s capability to generalize and accurately reconstruct 3D shapes.  
Figure 7: Visualization of the 3D reconstruction process. The input image (first column) is followed by the initial random point cloud geometry (second column), the fusion with spherical prior for structural consistency (third column), and the final refinement using attention-based fusion layers (fourth column). This highlights the importance of geometric priors and attention mechanisms in achieving accurate and detailed reconstructions.  
Adam optimizer with the Chamfer distance loss ensures stable and effective parameter optimization, ultimately enhancing 3D reconstruction performance.  
Figure 9 displays the training loss on the dataset and Table 1 compares our method with state-of-the-art approaches like 3D-Reconstret [35], 3D-FEGNET [41], DetNet [38], and Pixel2 Point [37]. Results from other models were obtained from their publications or cited references. The proposed method shows better or more competitive results compared to most state-of-the-art algorithms, attributable to the deep fusion attention mechanism applied across both the image and point cloud branches. However, high reconstruction loss was observed for some object categories, which may be due to intricate geometries and fine details. Further analysis is needed to determine the precise reasons behind this performance gap. We will analyze these categories in our future work and will improve the results for these categories. Figure 10 presents the 3D point clouds generated by the proposed architecture.  
Figure 10: To assess model performance across diverse datasets with varying backgrounds, the Figure presents input images alongside the generated 3D models and their corresponding ground truth 3D representations.  
Figure 9: Training loss on the ShapeNet dataset: the first image displays the loss over the first 100 iterations, while the second image shows the loss for the remaining iterations.