cs.CVOct 24, 2026

Can One Hear Geometry? Gauge-Invariant Spectral Descriptors for Text-to-B-rep Retrieval

Authors: Hongzhu Yi, Hao Liu, Tao Yu, Tiankun Yang, Yujia Yang, Zhenghao Zhang, Tianyu Zong, Zhenyu Guan, 

Organizations: University of Chinese Academy of Sciences · Institute of Automation, Chinese Academy of Sciences · Institute of Information Engineering, Chinese Academy of Sciences · Tencent

Abstract

Text-to-3D solid retrieval faces a fundamental representation gap: while natural language describes intrinsic shapes, Boundary Representation (B-rep) entangles precise geometry with arbitrary variations in pose, scale, and boundary encoding conventions. Existing methods either discretize B-reps at the cost of analytic precision, or learn features from topological graphs without explicit invariance guarantees. We propose a text-to-B-rep retrieval framework based on geometric equivalence classes and spectral invariants, mathematically eliminating representation ambiguities prior to cross-modal alignment. Formalizing translation, rotation, reflection, uniform scaling, and contour re-indexing via group actions, we exploit the planar-profile-and-extrusion structure of engineering solids to construct a unified spectral descriptor across cross-sectional regions, contour boundaries, and extrusion depths. On public benchmarks, our method achieves state-of-the-art recall performance across all evaluation metrics.

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