动态调整曲率正则化强度，提升CAD模型重建精度
Scheduling the Off-Diagonal Weingarten Loss of Neural SDFs for CAD Models
- 引入变权重策略，初期强正则化稳定优化，后期弱化以保留细节
- 在ABC CAD数据集上，切比雪夫距离提升最高达35%
- 适合需要高精度几何重建的CAD建模与逆向工程场景
神经符号距离函数（SDF）已成为点云几何重建的强大表示方法，但通常需要梯度与曲率双重正则化以抑制伪形变并保持结构保真度。FlatCAD提出非对角魏格纳特（ODW）损失作为高效二阶先验，近似全海森正则化，计算成本约为一半。然而，FlatCAD在整个训练过程中使用固定权重，效果不佳：强正则化虽能稳定早期优化，却抑制后期细节恢复。本文提出对ODW损失的调度策略，初始赋予高权重以稳定优化，随后逐步衰减以允许细粒度重构。我们考察了恒定、线性、五次、阶梯及渐增预热等多种调度方式。在ABC CAD数据集上的实验表明，时变调度始终优于固定权重。所提方法相较FlatCAD基线，切比雪夫距离最高提升35%，证明调度是鲁棒CAD重建中曲率正则化的简单而有效扩展。
原文摘要 · Abstract (English)
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.
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