# View-Consistent Hierarchical 3D Segmentation Using Ultrametric Feature Fields

arXiv: https://arxiv.org/abs/2405.19678 · HTML: https://mlsanity.com/paper/2405.19678/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 61 references that are in the map.
- First posted on arXiv 30 May 2024.

## Builds on (most cited first, 30 of 43)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Masked-attention Mask Transformer for Universal Image Segmentation](https://mlsanity.com/paper/2112.01527/) (2021)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [In-Place Scene Labelling and Understanding with Implicit Scene Representation](https://mlsanity.com/paper/2103.15875/) (2021)
- [Decomposing NeRF for Editing via Feature Field Distillation](https://mlsanity.com/paper/2205.15585/) (2022)
- [Dense Depth Priors for Neural Radiance Fields from Sparse Input Views](https://mlsanity.com/paper/2112.03288/) (2021)
- [Panoptic Neural Fields: A Semantic Object-Aware Neural Scene Representation](https://mlsanity.com/paper/2205.04334/) (2022)
- [Neural Feature Fusion Fields: 3D Distillation of Self-Supervised 2D Image Representations](https://mlsanity.com/paper/2209.03494/) (2022)
- [Panoptic Lifting for 3D Scene Understanding with Neural Fields](https://mlsanity.com/paper/2212.09802/) (2022)
- [SPIn-NeRF: Multiview Segmentation and Perceptual Inpainting with Neural Radiance Fields](https://mlsanity.com/paper/2211.12254/) (2022)
- [NeSF: Neural Semantic Fields for Generalizable Semantic Segmentation of 3D Scenes](https://mlsanity.com/paper/2111.13260/) (2021)
- [GARField: Group Anything with Radiance Fields](https://mlsanity.com/paper/2401.09419/) (2024)
- [Deep Hierarchical Semantic Segmentation](https://mlsanity.com/paper/2203.14335/) (2022)
- [Graphonomy: Universal Human Parsing via Graph Transfer Learning](https://mlsanity.com/paper/1904.04536/) (2019)

## Built on by (most cited first, 8 of 8)

- [PARTFIELD: Learning 3D Feature Fields for Part Segmentation and Beyond](https://mlsanity.com/paper/2504.11451/) (2025)
- [v-PuNNs: van der Put Neural Networks for Transparent Ultrametric Representation Learning](https://mlsanity.com/paper/2508.01010/) (2025)
- [Learning Part-Aware Dense 3D Feature Field for Generalizable Articulated Object Manipulation](https://mlsanity.com/paper/2602.14193/) (2026)
- [Hi-LSplat: Hierarchical 3D Language Gaussian Splatting](https://mlsanity.com/paper/2506.06822/) (2025)
- [Botany-Bot: Digital Twin Monitoring of Occluded and Underleaf Plant Structures with Gaussian Splats](https://mlsanity.com/paper/2510.17783/) (2025)
- [Material Magic Wand: Material-Aware Grouping of 3D Parts in Untextured Meshes](https://mlsanity.com/paper/2603.17370/) (2026)
- [H2G: Hierarchy-Aware Hyperbolic Grouping for 3D Scenes](https://mlsanity.com/paper/2605.11967/) (2026)
- [On Hamming-Lipschitz Type Stability of the Subdominant (Minmax) Ultrametric: Theory and Simple Proofs](https://mlsanity.com/paper/2608.04014/) (2026)

## Abstract (arXiv)

Large-scale vision foundation models such as Segment Anything (SAM) demonstrate impressive performance in zero-shot image segmentation at multiple levels of granularity. However, these zero-shot predictions are rarely 3D-consistent. As the camera viewpoint changes in a scene, so do the segmentation predictions, as well as the characterizations of "coarse" or "fine" granularity. In this work, we address the challenging task of lifting multi-granular and view-inconsistent image segmentations into a hierarchical and 3D-consistent representation. We learn a novel feature field within a Neural Radiance Field (NeRF) representing a 3D scene, whose segmentation structure can be revealed at different scales by simply using different thresholds on feature distance. Our key idea is to learn an ultrametric feature space, which unlike a Euclidean space, exhibits transitivity in distance-based grouping, naturally leading to a hierarchical clustering. Put together, our method takes view-inconsistent multi-granularity 2D segmentations as input and produces a hierarchy of 3D-consistent segmentations as output. We evaluate our method and several baselines on synthetic datasets with multi-view images and multi-granular segmentation, showcasing improved accuracy and viewpoint-consistency. We additionally provide qualitative examples of our model's 3D hierarchical segmentations in real world scenes. The code and dataset are available at https://github.com/hardyho/ultrametric_feature_fields