PatchGF: Feed-Forward Geometric Fields from Unoriented Point Clouds

Surface reconstruction and differential-quantity estimation from unoriented point clouds are often addressed separately, although both depend on the same local geometry. We present PatchGF, a feed-forward framework that jointly predicts patch-conditioned unsigned distance fields (UDFs), unoriented normals, mean-curvature magnitudes, and Gaussian curvatures. A shared Point Transformer encodes each patch; query-to-patch cross-attention predicts unsigned distances at nearby spatial locations, while dedicated heads estimate normals and curvatures. A single model is trained exclusively on synthetic quadratic patches and applied directly to unseen point clouds without fine-tuning or per-shape network optimization. Paired queries sampled along analytic normals, with curvature-adaptive offsets, supervise near-surface distance variation. At inference, fixed anchor-centered patches provide consistent local supports, and distance-weighted fusion combines overlapping predictions into a UDF over the observed surface region. Positive-level-set extraction and gradient-based projection provide an initial reconstruction, which can be refined through local surface fitting and adaptive remeshing guided by the predicted differential quantities. Experiments on standard benchmarks and real-world scans evaluate reconstruction and differential-quantity estimation and demonstrate accurate reconstruction under noise and outlier contamination.