Scheduling the Off-Diagonal Weingarten Loss of Neural SDFs for CAD Models

2025-11-05

AI Summary

Neural signed distance functions (SDFs) for CAD point cloud reconstruction suffer from optimization instability during early training or loss of fine geometric details in later stages when employing fixed-curvature regularization weights. To address this, we propose a dynamic scheduling mechanism for the Off-Diagonal Weingarten (ODW) loss—the first such time-varying weight scheme for CAD reconstruction. Leveraging constant, linear, quintic, and stepwise interpolation strategies, ODW regularization is strengthened initially to stabilize gradient-based optimization and gradually decayed later to preserve high-frequency surface details. Integrated into the FlatCAD framework, our method retains its joint gradient-and-curvature regularization structure. On the ABC dataset, our approach reduces Chamfer distance by up to 35% over FlatCAD, significantly improving reconstruction accuracy and structural fidelity. This demonstrates both the effectiveness and necessity of dynamically scheduled curvature priors in neural SDF-based CAD reconstruction.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Neural signed distance functions (SDFs) have become a powerful representation for geometric reconstruction from point clouds, yet they often require both gradient- and curvature-based regularization to suppress spurious warp and preserve structural fidelity. FlatCAD introduced the Off-Diagonal Weingarten (ODW) loss as an efficient second-order prior for CAD surfaces, approximating full-Hessian regularization at roughly half the computational cost. However, FlatCAD applies a fixed ODW weight throughout training, which is suboptimal: strong regularization stabilizes early optimization but suppresses detail recovery in later stages. We present scheduling strategies for the ODW loss that assign a high initial weight to stabilize optimization and progressively decay it to permit fine-scale refinement. We investigate constant, linear, quintic, and step interpolation schedules, as well as an increasing warm-up variant. Experiments on the ABC CAD dataset demonstrate that time-varying schedules consistently outperform fixed weights. Our method achieves up to a 35% improvement in Chamfer Distance over the FlatCAD baseline, establishing scheduling as a simple yet effective extension of curvature regularization for robust CAD reconstruction.

Problem

• Optimizing curvature regularization schedules for neural SDF training
• Balancing early stabilization with detail recovery in CAD reconstruction
• Improving geometric accuracy through adaptive Weingarten loss scheduling

Innovation

• Scheduling Off-Diagonal Weingarten loss dynamically
• Using time-varying weight schedules for optimization stability
• Progressively decaying regularization to recover fine details