# Hyperbolic Image Segmentation

arXiv: https://arxiv.org/abs/2203.05898 · HTML: https://mlsanity.com/paper/2203.05898/

## Key facts

- Cited by 102 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 54 references that are in the map.
- First posted on arXiv 11 Mar 2022.

## Builds on (most cited first, 30 of 40)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [COCO-Stuff: Thing and Stuff Classes in Context](https://mlsanity.com/paper/1612.03716/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Segmentation Transformer: Object-Contextual Representations for Semantic Segmentation](https://mlsanity.com/paper/1909.11065/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [Context Encoding for Semantic Segmentation](https://mlsanity.com/paper/1803.08904/) (2018)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Hierarchical Multi-Scale Attention for Semantic Segmentation](https://mlsanity.com/paper/2005.10821/) (2020)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Evaluating Bayesian Deep Learning Methods for Semantic Segmentation](https://mlsanity.com/paper/1811.12709/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Open Vocabulary Scene Parsing](https://mlsanity.com/paper/1703.08769/) (2017)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [Squeeze-and-Attention Networks for Semantic Segmentation](https://mlsanity.com/paper/1909.03402/) (2019)
- [Bayesian Layers: A Module for Neural Network Uncertainty](https://mlsanity.com/paper/1812.03973/) (2018)
- [Differentiating through the Fr'echet Mean](https://mlsanity.com/paper/2003.00335/) (2020)

## Built on by (most cited first, 30 of 102)

- [Hyperbolic Image-Text Representations](https://mlsanity.com/paper/2304.09172/) (2023)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [E^2VPT: An Effective and Efficient Approach for Visual Prompt Tuning](https://mlsanity.com/paper/2307.13770/) (2023)
- [Hyperbolic Contrastive Learning for Visual Representations beyond Objects](https://mlsanity.com/paper/2212.00653/) (2022)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representations](https://mlsanity.com/paper/2303.06242/) (2023)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Learn to Categorize or Categorize to Learn? Self-Coding for Generalized Category Discovery](https://mlsanity.com/paper/2310.19776/) (2023)
- [Poincar'e ResNet](https://mlsanity.com/paper/2303.14027/) (2023)
- [HypLiLoc: Towards Effective LiDAR Pose Regression with Hyperbolic Fusion](https://mlsanity.com/paper/2304.00932/) (2023)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [Hyperbolic Category Discovery](https://mlsanity.com/paper/2504.06120/) (2025)
- [Hyperbolic Audio-visual Zero-shot Learning](https://mlsanity.com/paper/2308.12558/) (2023)
- [Emergent Visual-Semantic Hierarchies in Image-Text Representations](https://mlsanity.com/paper/2407.08521/) (2024)
- [Hyperbolic Active Learning for Semantic Segmentation under Domain Shift](https://mlsanity.com/paper/2306.11180/) (2023)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Hyperbolic Uncertainty Aware Semantic Segmentation](https://mlsanity.com/paper/2203.08881/) (2022)
- [HYPE: Hyperbolic Entailment Filtering for Underspecified Images and Texts](https://mlsanity.com/paper/2404.17507/) (2024)
- [Hyperbolic Safety-Aware Vision-Language Models](https://mlsanity.com/paper/2503.12127/) (2025)
- [HLFormer: Enhancing Partially Relevant Video Retrieval with Hyperbolic Learning](https://mlsanity.com/paper/2507.17402/) (2025)
- [Hyperbolic Contrastive Learning](https://mlsanity.com/paper/2302.01409/) (2023)
- [Hyperbolic Dataset Distillation](https://mlsanity.com/paper/2505.24623/) (2025)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [HyperVQ: MLR-based Vector Quantization in Hyperbolic Space](https://mlsanity.com/paper/2403.13015/) (2024)
- [HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules](https://mlsanity.com/paper/2504.08912/) (2025)
- [Improving Visual Recognition with Hyperbolical Visual Hierarchy Mapping](https://mlsanity.com/paper/2404.00974/) (2024)
- [Dynamic Hyperbolic Attention Network for Fine Hand-object Reconstruction](https://mlsanity.com/paper/2309.02965/) (2023)
- [Understanding Hyperbolic Metric Learning through Hard Negative Sampling](https://mlsanity.com/paper/2404.15523/) (2024)
- [Hyperbolic Learning with Multimodal Large Language Models](https://mlsanity.com/paper/2408.05097/) (2024)

## Abstract (arXiv)

For image segmentation, the current standard is to perform pixel-level optimization and inference in Euclidean output embedding spaces through linear hyperplanes. In this work, we show that hyperbolic manifolds provide a valuable alternative for image segmentation and propose a tractable formulation of hierarchical pixel-level classification in hyperbolic space. Hyperbolic Image Segmentation opens up new possibilities and practical benefits for segmentation, such as uncertainty estimation and boundary information for free, zero-label generalization, and increased performance in low-dimensional output embeddings.