联合优化点方向与权重，实现噪声和采样不均下的鲁棒水密表面重建
Joint Orientation and Weight Optimization for Robust Watertight Surface Reconstruction via Dirichlet-Regularized Winding Fields
- 用广义绕数场作为隐式表示，统一优化点方向、面积权重和置信度
- 在3DGS和受污染图形基准上重建出合理水密表面，优于传统多阶段方法
- 无需预处理即可抗噪声、去异常值，适合真实场景点云重建
我们提出狄利克雷绕数重建（DiWR），一种从无方向点云中重建水密表面的鲁棒方法，适用于非均匀采样、噪声和异常值。该方法以广义绕数（GWN）场为隐式表示，通过单一流程联合优化点方向、每点面积权重及置信系数。优化目标最小化诱导绕数场的狄利克雷能量，并引入基于GWN的约束，使DiWR能补偿非均匀采样，降低噪声影响，抑制异常值，且无需额外预处理。我们在3D高斯溅射（3D Gaussian Splatting）生成的点云及受污染的图形基准数据集上评估了DiWR。实验表明，DiWR能在这些挑战性输入上生成合理的水密表面，性能优于传统多阶段流程以及近期的联合方向-重建方法。
原文摘要 · Abstract (English)
We propose Dirichlet Winding Reconstruction (DiWR), a robust method for reconstructing watertight surfaces from unoriented point clouds with non-uniform sampling, noise, and outliers. Our method uses the generalized winding number (GWN) field as the target implicit representation and jointly optimizes point orientations, per-point area weights, and confidence coefficients in a single pipeline. The optimization minimizes the Dirichlet energy of the induced winding field together with additional GWN-based constraints, allowing DiWR to compensate for non-uniform sampling, reduce the impact of noise, and downweight outliers during reconstruction, with no reliance on separate preprocessing. We evaluate DiWR on point clouds from 3D Gaussian Splatting, a computer-vision pipeline, and corrupted graphics benchmarks. Experiments show that DiWR produces plausible watertight surfaces on these challenging inputs and outperforms both traditional multi-stage pipelines and recent joint orientation-reconstruction methods.
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