发表机构
University of Hull; Xiamen University; University of Washington; Chinese Academy of Sciences（赫尔大学; 厦门大学; 华盛顿大学; 中国科学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
NeuSOGA3D提出一种结合神经感知与符号几何推理的混合框架，通过正交投影、隐式样条和构造实体几何操作，从点云重建可解释且CAD兼容的三维几何，并在ModelNet40全部类别上验证了有效性。
AI 中文摘要
从无组织点云进行三维重建仍然是计算机视觉、几何建模和计算机辅助设计中的一个挑战性问题。虽然神经隐式方法实现了令人印象深刻的重建精度，但几何通常编码在潜在表示中，这限制了其在工程工作流中的可解释性和重用性。我们提出了NeuSOGA3D（三维神经符号几何抽象），这是一种混合框架，结合了从NeuSOGA继承的学习感知先验与显式符号几何推理。该方法将点云投影到主正交平面上，从所得观测构建符号隐式样条表示，并通过保形构造实体几何操作融合它们以生成粗略视觉外壳。额外的几何细节通过横截面分解和使用部分保形样条的体积重建来恢复。与传统的神经隐式方法不同，NeuSOGA3D逐步将观测转换为显式符号实体，包括控制多边形、隐式样条场、横截面和体积放样。在ModelNet40基准的所有四十个类别上的实验表明，该框架能够从多样化的点云观测中恢复结构上有意义且CAD兼容的几何表示。结果突出了将学习感知与符号几何推理相结合以实现可解释几何智能的潜力。
英文摘要
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 Observation-Guided 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.
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