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.

翻译：我们提出狄利克雷环绕重建（DiWR），一种从具有非均匀采样、噪声和离群点的无定向点云中重建水密表面的鲁棒方法。本方法使用广义环绕数（GWN）场作为目标隐式表示，并在单一流程中联合优化点的方向、逐点面积权重以及置信系数。该优化最小化所诱导环绕场的狄利克雷能量以及额外的基于GWN的约束，使得DiWR能够在重建过程中补偿非均匀采样、降低噪声影响并对离群点进行降权，且无需依赖独立的预处理步骤。我们在来自3D高斯泼溅（一种计算机视觉流程）的点云以及受损的图形学基准数据集上评估DiWR。实验表明，DiWR在这些具有挑战性的输入上能生成合理的水密表面，并且优于传统的多阶段流程以及近期联合方向-重建方法。