## 3 Methods  
### Problem Statement  
As shown in Figure 3, our method takes an eyeglass frame sketch as input, and our goal is to reconstruct the corresponding D3 DM of the eyeglass frame. We assume that the sketch represents a shape drawn in perspective. We define a binary sketch as \(\mathcal{I}\subseteq\{0,1\}^{H\times W}\), where zero denotes pixels covered by pen strokes, and one denotes uncovered pixels. An encoder \(\mathcal{E}\) and a decoder \(\mathcal{D}\) are trained, whose composite function, \(\mathcal{D}\circ\mathcal{E}(\mathcal{I})\), constructs a mesh \(\mathcal{M}(\theta)=(\mathcal{V},\mathcal{F})\), where \(\mathcal{V}\) denotes vertex positions in \(\mathbb{R}^{3}\) and \(\mathcal{F}\) denotes faces. In this formulation, \(\mathcal{Z}=\mathcal{E}(\mathcal{I})\), \(\mathcal{Z}\in\mathbb{R}^{n}\) is the latent vector that defines the 3D geometry of mesh. We describe the encoder and the decoder in Sections 3.2 and Section 3.3, respectively. The main objective of obtaining the 3D eyeglass frame mesh model is to enhance the parameter \(\theta\) to align the projection of 3D mesh \(f(\mathcal{M})\) with the 2D sketch \(\mathcal{I}\). This enhancement occurs by minimizing the 2D Chamfer distance between the projected mesh and the input sketch (Section 3.4). Section 3.5 detail optimization based on the symmetry of the eyeglass frame, emphasizing that the symmetrical property improves the accuracy of 3D reconstructions derived from FDS. Finally, we present implementation details in Section 3.6. Figure 4 illustrates the architecture of the DINOV2 model, providing a comprehensive view of its layered structure and the flow of data through various network components. The model consists of multiple layers, including convolutional layers (Conv), normalization layers (Norm), and activation functions such as ReLU and Tanh, each playing a pivotal role in feature extraction and data processing. These components work collaboratively to progressively refine extracted features, enhancing the model's ability to handle complex structures in image data. The network is divided into three primary layers, each with distinct functionality that contributes to the model's performance. Layer 1 serves as the initial stage of feature extraction, where convolutional and normalization layers process raw input data to capture fundamental image features, with ReLU further enhancing the network's capacity to learn nonlinear relationships. Layer 2 builds upon this foundation, incorporating additional convolutional and normalization layers to refine the features learned in Layer 1, enabling the model to discern more intricate patterns. Layer 3 continues this refinement process, using further convolutional and normalization layers to extract highly abstract and complex features. The data flows through the network in a clear progression, with each layer extracting progressively more sophisticated features essential for accurate predictions or specific tasks. Regarding computational efficiency and resource usage, we recognize the importance of these factors in evaluating the practicality of the DINOV2 framework. While powerful, the model demands significant computational resources due to the use of multiple convolutional layers, normalization, and activation functions, which increase both memory and processing requirements. However, the modular design allows for a flexible trade-off between performance and resource consumption, depending on the application and available hardware. For example, increasing the number of convolution layers in Layers 2 and 3 enhances feature extraction but also raises the computational load. This trade-off is critical in real-time applications, where balancing accuracy and efficiency is essential. Additionally, techniques like batch normalization and activation functions improve convergence speed and model stability, enhancing training efficiency. Figure 3: Pipeline. Our reconstruction approach starts with feature extraction from a fixed self-supervised backbone acting as an encoder (Section 3.2).