Recovering 3D geometry from unordered point clouds remains a challenging task in computer vision, geometric modeling, and CAD. Neural implicit methods achieve high reconstruction accuracy, yet the geometry is encoded in latent vectors, limiting interpretability and reuse in engineering pipelines.
NeuSOGA3D (Neuro‑Symbolic Geometric Abstraction in 3D) introduces a hybrid framework that merges perceptual priors learned by NeuSOGA with explicit symbolic geometric reasoning. The pipeline first projects the point cloud onto the three principal orthographic planes, yielding 2‑D observations. For each plane, a symbolic implicit spline representation is constructed, consisting of control polygons and implicit spline fields.
These planar splines are fused via shape‑preserving Constructive Solid Geometry (CSG) operations to produce a coarse visual hull. To recover finer details, the method performs cross‑sectional decomposition and volumetric reconstruction using Partial Shape‑Preserving Splines, resulting in volumetric lofts. Thus the observations are progressively transformed into explicit symbolic entities: control polygons → implicit spline fields → cross‑sections → volumetric lofts.
Experiments on all forty categories of the ModelNet40 benchmark show that NeuSOGA3D can recover structurally meaningful, CAD‑compatible geometric representations from diverse point‑cloud inputs, highlighting the promise of combining learned perception with symbolic geometric reasoning for explainable geometric intelligence.
Review