Neural implicit curve: A robust curve modeling approach on surface meshes

Abstract

Traditional implicit curve modeling methods on surface meshes, such as variational approaches, are often plagued by numerical instability and heavy reliance on mesh quality, severely limiting their reliability in practical applications. To address these challenges, we propose Neural Implicit Curve Modeling on Meshes (NICMM), a novel framework that integrates Neural Implicit Method with geometric constraints for robust curve design. NICMM leverages physics-driven loss functions to encode positional, smoothness, and other customized constraints, alleviates numerical instabilities and inaccuracies arising from low-quality meshes, such as convergence failures. The framework incorporates specialized modules (e.g., Efficient Channel Attention and Light GLU) to enhance feature extraction and computational efficiency and introduces a two-stage training strategy combining pre-training with rapid convergence optimization. Extensive experiments on the SHREC16 dataset demonstrate that NICMM has proven its mettle by outperforming traditional variational approaches in robustness. In the face of highly degraded meshes replete with elongated and near-degenerate elements, NICMM not only excels in generating high-fidelity curves but also maintains computational efficiency comparable to existing variational method, thereby showcasing its remarkable balance between accuracy and performance. Furthermore, NICMM also supports feature-aware curve design, enabling alignment with user-specified regions and obstacle avoidance through a unified guidance mechanism. This work establishes a new paradigm for manifold curve modeling, with significant potential in CAD/CAM systems, virtual surgery, and other domains that require precise and adaptive geometric design.