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

Overview & Synopsis

Text-to-3D solid retrieval requires aligning natural language with precise geometry despite variations in pose, scale, and recording conventions. Existing methods discretize Boundary Representation (B-rep) models into point clouds or meshes, or learn features from faces, edges, and topology, risking information loss or lacking explicit invariance guarantees. We propose a text-to-B-rep retrieval framework based on group actions and spectral geometric invariants, making invariance an explicit constraint on descriptor construction. Specifically, we use group actions to characterize equivalence transformations induced by translation, rotation, reflection, uniform scaling, and contour recording conventions. For sketch-extrusion solids, we construct a fixed 280-dimensional spectral geometric descriptor by integrating geometric information from three complementary levels, including cross-sectional regions, contour boundaries, and extrusion structures. Furthermore, we use descriptor-consistent multi-positive sets and geometric attribute supervision to promote structural alignment between text and solids. On Text-to-3D solid retrieval, our method achieves 88.6% Recall@5, exceeding the previous state of the art by 13.6 percentage points and demonstrating the effectiveness of explicit geometric invariants for precise 3D solid retrieval.