Joint Orientation and Weight Optimization for Robust Watertight Surface Reconstruction via Dirichlet-Regularized Winding Fields

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.