H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes
This paper addresses the problem of unsupervised hierarchical 3D grouping for scene understanding, offering a novel way to embed 2D foundation-model knowledge into 3D representations.
H2G introduces a hyperbolic affinity field for hierarchical 3D grouping, using foundation-model cues to derive tree supervision and distilling it into a Lorentz hyperbolic feature field. The method achieves coherent multi-granularity grouping without semantic labels, outperforming prior works on hierarchical 3D scene understanding benchmarks.
Hierarchical 3D grouping aims to recover scene groups across multiple granularities, from fine object parts to complete objects, without relying on semantic labels or a fixed vocabulary. The main challenge is to transform 2D foundation-model cues into coherent hierarchy supervision and embed that hierarchy in a 3D representation. We propose H2G, a hyperbolic affinity field for hierarchical 3D grouping. Our method derives semantically organized tree supervision by interpreting foundation-model affinities through Dasgupta's objective for similarity-based hierarchical clustering. This supervision is distilled into a single Lorentz hyperbolic feature field, whose geometry is well suited for tree-like branching structures. A hierarchy-aware objective aligns the field with fine-level assignments, coarse object structure, compact feature clusters, and LCA (Lowest Common Ancestor) ordering. This formulation represents multiple grouping levels in one feature space, enabling semantic hierarchical grouping grounded in 2D foundation-model knowledge.