H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes

TL;DR

H2G introduces a hyperbolic affinity field that leverages foundation-model cues to enable hierarchical 3D scene grouping across multiple levels without relying on semantic labels.

Contribution

The paper presents a novel hyperbolic affinity field that encodes hierarchical 3D grouping, integrating foundation-model cues into a unified tree-structured representation.

Findings

Successfully derives semantically organized hierarchy supervision from foundation-model affinities.

Embeds hierarchical structure in a Lorentz hyperbolic feature field suitable for tree-like data.

Achieves multi-level 3D grouping grounded in 2D foundation-model knowledge.

Abstract

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.