用双曲空间建模3D场景层次分组，无需语义标签即可自动识别从零件到整体的结构。
H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes
- 基于2D模型相似性构建树状监督信号，通过双曲几何编码层次结构。
- 统一在单个特征场中表示多粒度分组，实现细粒度与整体结构对齐。
- 适合无标注3D理解、场景解析与生成任务，尤其适用于复杂物体结构建模。
层次化3D分组旨在不依赖语义标签或固定词汇表的情况下，从细粒度部件到完整物体跨多个粒度恢复场景分组。核心挑战在于将2D基础模型的提示转化为连贯的层次监督，并将其嵌入3D表示中。我们提出H2G，一种用于层次化3D分组的双曲亲和场方法。该方法通过解读基础模型的亲和性并应用Dasgupta的相似性聚类目标，生成语义组织的树状监督信号。该监督被提炼为单一洛伦兹双曲特征场，其几何结构非常适合树状分支结构。一个层次感知的目标函数使特征场与细粒度分配、粗粒度物体结构、紧凑特征簇以及最低公共祖先（LCA）排序保持一致。该形式在一个特征空间中同时表示多个分组层级，实现了基于2D基础模型知识的语义层次分组。
原文摘要 · Abstract (English)
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.
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