LADA: Learned Decomposition and Assembly for Non-Manifold Surface Reconstruction

Explicit reconstruction of non-manifold surfaces remains challenging because, although most geometry is locally manifold-like, the global topology is governed by a small number of intricate non-manifold curves. Existing methods typically resolve this topology locally using marching-cubes-style algorithms, making them prone to missing, broken, or fragmented non-manifold edges. We view a non-manifold surface as a union of manifold patches meeting along non-manifold curves and propose a decomposition-and-assembly framework for explicit reconstruction from point clouds. First, a learned decomposition partitions the point cloud into overlapping blocks and predicts whether neighboring point pairs belong to the same manifold patch. Thresholding these affinities and applying union-find splits the points into a set of manifold patches as well as points on non-manifold curves. Second, the assembly step reconstructs each manifold patch with an off-the-shelf manifold surface reconstructor and stitches the patches with explicitly non-manifold edges. Because non-manifold structures are local, the network is trained only on shapes created by intersecting manifold meshes and generalizes zero-shot to unseen data. Across three benchmarks, including CAD models and point clouds sampled from neural implicit fields, our method matches strong baselines in Chamfer distance while achieving the lowest non-manifold Chamfer distance and substantially fewer topological errors on both clean and noisy inputs.