NeuSOGA3D: A Neuro-Symbolic Framework for Explainable 3D Geometric Reconstruction

Three-dimensional reconstruction from unorganized point clouds remains a challenging problem in computer vision, geometric modeling, and computer-aided design. While neural implicit methods achieve impressive reconstruction accuracy, geometry is typically encoded in latent representations that limit interpretability and reuse within engineering workflows. We present NeuSOGA3D (Neuro-Symbolic Geometric Abstraction in 3D), a hybrid framework that combines learned perceptual priors inherited from NeuSOGA with explicit symbolic geometric reasoning. The method projects point clouds onto principal orthographic planes, constructs symbolic implicit spline representations from the resulting observations, and fuses them through shape-preserving constructive solid geometry operations to generate a coarse visual hull. Additional geometric detail is recovered through cross-sectional decomposition and volumetric reconstruction using Partial Shape-Preserving Splines. Unlike conventional neural implicit approaches, NeuSOGA3D progressively transforms observations into explicit symbolic entities, including control polygons, implicit spline fields, cross-sections, and volumetric lofts. Experiments on all forty categories of the ModelNet40 benchmark demonstrate the ability of the framework to recover structurally meaningful and CAD-compatible geometric representations from diverse point-cloud observations. The results highlight the potential of combining learned perception with symbolic geometric reasoning for explainable geometric intelligence.