NeuSOGA3D: A Neuro-Symbolic Framework for Explainable 3D Geometric Reconstruction
NeuSOGA3D combines learned perception with symbolic spline reasoning to produce explainable, CAD-compatible 3D reconstructions from point clouds across all forty ModelNet40 categories.
The hybrid neuro-symbolic framework projects point clouds onto principal orthographic planes, constructs symbolic implicit spline representations, and fuses them via shape-preserving constructive solid geometry into a coarse visual hull. Cross-sectional decomposition and Partial Shape-Preserving Splines recover additional detail, yielding explicit control polygons, implicit spline fields, cross-sections, and volumetric lofts. Experiments across all forty ModelNet40 categories demonstrate interpretable, engineering-workflow-compatible reconstruction from diverse point clouds.
- Hybrid neuro-symbolic framework fuses learned priors with symbolic spline geometry
- Produces explicit control polygons, spline fields, and volumetric lofts for interpretability
- Shape-preserving CSG operations build a coarse visual hull from orthographic projections
- Evaluated on all forty ModelNet40 categories for CAD-compatible reconstruction
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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.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.20323