Joint Orientation and Weight Optimization for Robust Watertight Reconstruction from Unoriented Points

We propose Dirichlet Winding Reconstruction (DiWR), a method for watertight surface reconstruction from unoriented point clouds affected by non-uniform sampling, noise, and outliers. DiWR represents geometry using a generalized winding number (GWN) field whose point-based discretization depends on point orientations and per-point contributions. Instead of treating each point's contribution as fixed, DiWR alternates between updating point orientations, area weights that compensate for local sampling density, and confidence coefficients that reduce the influence of unreliable samples. The optimization combines a sampled Dirichlet-energy regularizer with winding-number surface constraints, area-stability regularization, and confidence regularization. This joint treatment reduces reliance on separate denoising or outlier-removal stages and helps stabilize reconstruction on corrupted inputs. We evaluate the method using controlled stress tests and point clouds produced by 3D Gaussian Splatting and vision pipelines. In our experiments, DiWR improves robustness over classical multi-stage pipelines and several recent joint orientation-reconstruction methods on many challenging cases, while still assuming that the input sufficiently samples an underlying watertight manifold surface. The source code and test models are available at https://github.com/LaoChui999/DiWR.