NeuSOGA3D explains 3D shapes from point clouds using symbolic geometry
NeuSOGA3D: A Neuro-Symbolic Framework for Explainable 3D Geometric Reconstruction
Artificial Intelligence
Summary
Turning scattered 3D points into clear, usable shapes is tricky because many smart methods hide the shape details in hard-to-understand codes. The authors created NeuSOGA3D, which combines learned knowledge from neural networks with explicit symbolic shapes like splines and polygons. This approach gradually builds understandable geometric parts from raw points, making the 3D shapes easier to interpret and use in engineering. Tests showed it works well on many different object types, creating 3D models that fit engineering and design needs better.
What this means in practice
- •For cad engineers: Create engineering-compatible 3D models from raw point cloud scans for reuse in design workflows.
- •For 3d modeling software developers: Integrate explainable symbolic geometry extraction to improve model interpretability and editing capabilities.
Authors
Qingde Li, Qingqi Hong, Zihan Li, Jie Tian
Abstract
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.