MeshNet: Mesh Neural Network for 3D Shape Representation

The evolution of 3D shape representation has transitioned from handcrafted descriptors like spherical harmonics to deep learning methods. Early approaches focused on explicit feature extraction, such as Lien and Kajiya’s moments or Zhang and Chen’s functional sums. With the advent of neural networks, volumetric grids (e.g., 3DShapeNets, VoxNet) and multi-view CNNs (MVCNN) gained popularity, offering improved recognition but at high computational costs. Point cloud methods like PointNet introduced permutation invariance, yet struggled with local detail capture. Mesh data, rich in geometric information, was underutilized due to irregularity and processing challenges. Recent efforts attempted handcrafted features or simple geometric descriptors, but lacked end-to-end learning frameworks. Mesh data’s potential for detailed shape understanding remains largely untapped, motivating the development of neural architectures like MeshNet.

The core challenge is to develop a neural network capable of directly learning from mesh face data, overcoming issues like irregular topology, variable face counts, and complex connectivity. Traditional methods rely on handcrafted features or indirect processing, which limit accuracy and generalization. Mesh data’s irregularity complicates neighborhood definition and feature aggregation, making it difficult to design scalable, robust models. Addressing these issues requires novel feature encoding strategies, such as face feature splitting and connectivity-aware convolution, to preserve geometric details while maintaining computational efficiency. Solving this problem is crucial for advancing high-fidelity 3D shape understanding in practical applications.

The primary innovation is the face feature splitting mechanism, dividing face attributes into spatial (position, normal) and structural (connectivity, corners) features, which enhances local detail encoding. Coupled with multi-scale Mesh Convolution layers that aggregate neighborhood information based on face adjacency, the model captures both local geometry and topological context. The encoding of face connectivity via adjacency matrices allows scalable, permutation-invariant processing. Additionally, the architecture supports end-to-end training with fewer parameters, maintaining high geometric fidelity. This approach differs from point cloud or voxel methods by directly modeling surface topology, enabling finer geometric discrimination and robustness to irregular meshes.

• �� Input: Triangular mesh faces with initial features (positions, normals, corners).
• �� Face feature splitting: Separate spatial features (face center, normal) and structural features (corner points, adjacency).
• �� Spatial descriptor: Use MLPs to encode position and normal information.
• �� Structural descriptor: Encode corners and connectivity patterns.
• �� Mesh convolution: Multi-scale neighborhood aggregation based on face adjacency, capturing local geometric details.
• �� Feature fusion: Combine spatial and structural features for each face.
• �� Global pooling: Aggregate face features into a shape-level representation.
• �� Training: End-to-end optimization with cross-entropy loss for classification or retrieval loss for similarity.
• �� Implementation details include neighbor sampling, feature normalization, and multi-layer stacking for hierarchical feature extraction.

The model was trained and validated on ModelNet40, with hyperparameters tuned via grid search. Baselines included SPH, PointNet, and multi-view CNNs. Metrics focused on classification accuracy and mean average precision (mAP). Ablation studies tested the impact of feature splitting and neighborhood aggregation. Training used Adam optimizer, with learning rate decay over 100 epochs. Results showed consistent improvements across various model complexities, confirming the effectiveness of face-based feature encoding. Computational costs were measured, demonstrating efficiency gains over volumetric models.

MeshNet achieved 92.3% accuracy on ModelNet40, outperforming PointNet (89.2%) and SPH descriptors (85.7%). In retrieval, it reached 0.87 mAP, surpassing multi-view approaches. Ablation results indicated that removing feature splitting or neighborhood aggregation reduced accuracy by 4-6%. The model parameters were approximately 2.5 million, with reduced inference time, validating its efficiency and effectiveness. These results confirm the advantage of face-based surface modeling for detailed geometric understanding.

MeshNet is suitable for CAD model classification, 3D object retrieval, and surface analysis in VR/AR applications. It requires mesh face data with connectivity information, making it ideal for industries like manufacturing, gaming, and robotics. Its ability to capture fine geometric details supports tasks such as defect detection, shape editing, and surface reconstruction. The model’s robustness to diverse mesh topologies broadens its industrial applicability, enabling more accurate and efficient 3D shape understanding in real-world scenarios.

The model’s performance declines on highly complex or irregular meshes with non-triangular faces. Its reliance on face adjacency limits handling of non-manifold or non-closed meshes. Computational costs increase with mesh complexity, posing scalability challenges. Currently, the architecture is tailored for triangular meshes, requiring extensions for polygonal or non-manifold geometries. Future work should focus on adaptive neighborhood definitions, multi-scale feature integration, and generalization to broader mesh types to address these issues.