# Structure-Aware Image Segmentation with Homotopy Warping

arXiv: https://arxiv.org/abs/2112.07812 · HTML: https://mlsanity.com/paper/2112.07812/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 80 references that are in the map.
- First posted on arXiv 15 Dec 2021.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs](https://mlsanity.com/paper/1412.7062/) (2014)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [DeepGlobe 2018: A Challenge to Parse the Earth through Satellite Images](https://mlsanity.com/paper/1805.06561/) (2018)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Boundary loss for highly unbalanced segmentation](https://mlsanity.com/paper/1812.07032/) (2018)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.10030/) (2019)
- [Boundary-Aware Feature Propagation for Scene Segmentation](https://mlsanity.com/paper/1909.00179/) (2019)
- [RoadTracer: Automatic Extraction of Road Networks from Aerial Images](https://mlsanity.com/paper/1802.03680/) (2018)
- [Beyond the Pixel-Wise Loss for Topology-Aware Delineation](https://mlsanity.com/paper/1712.02190/) (2017)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [iCurb: Imitation Learning-based Detection of Road Curbs using Aerial Images for Autonomous Driving](https://mlsanity.com/paper/2103.17118/) (2021)
- [Large Scale Image Segmentation with Structured Loss based Deep Learning for Connectome Reconstruction](https://mlsanity.com/paper/1709.02974/) (2017)

## Built on by (most cited first, 24 of 24)

- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [Learning Topological Interactions for Multi-Class Medical Image Segmentation](https://mlsanity.com/paper/2207.09654/) (2022)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [TopoCellGen: Generating Histopathology Cell Topology with a Diffusion Model](https://mlsanity.com/paper/2412.06011/) (2024)
- [Enhancing Modality-Agnostic Representations via Meta-Learning for Brain Tumor Segmentation](https://mlsanity.com/paper/2302.04308/) (2023)
- [Semi-supervised Segmentation of Histopathology Images with Noise-Aware Topological Consistency](https://mlsanity.com/paper/2311.16447/) (2023)
- [Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methods](https://mlsanity.com/paper/2404.18539/) (2024)
- [Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homology](https://mlsanity.com/paper/2407.04683/) (2024)
- [Spatial Diffusion for Cell Layout Generation](https://mlsanity.com/paper/2409.03106/) (2024)
- [Topology Optimization in Medical Image Segmentation with Fast Euler Characteristic](https://mlsanity.com/paper/2507.23763/) (2025)
- [GDDS: Pulmonary Bronchioles Segmentation with Group Deep Dense Supervision](https://mlsanity.com/paper/2303.09212/) (2023)
- [Universal Topology Refinement for Medical Image Segmentation with Polynomial Feature Synthesis](https://mlsanity.com/paper/2409.09796/) (2024)
- [Efficient Connectivity-Preserving Instance Segmentation with Supervoxel-Based Loss Function](https://mlsanity.com/paper/2501.01022/) (2025)
- [MATCH: Multi-faceted Adaptive Topo-Consistency for Semi-Supervised Histopathology Segmentation](https://mlsanity.com/paper/2510.01532/) (2025)
- [Topology-Preserving Downsampling of Binary Images](https://mlsanity.com/paper/2407.17786/) (2024)
- [Topology-Guaranteed Image Segmentation: Enforcing Connectivity, Genus, and Width Constraints](https://mlsanity.com/paper/2601.11409/) (2026)
- [TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy](https://mlsanity.com/paper/2503.03365/) (2025)
- [Disconnect to Connect: A Data Augmentation Method for Improving Topology Accuracy in Image Segmentation](https://mlsanity.com/paper/2503.05541/) (2025)
- [Topo-R1: Detecting Topological Anomalies via Vision-Language Models](https://mlsanity.com/paper/2603.13054/) (2026)
- [Towards High-Quality Image Segmentation: Improving Topology Accuracy by Penalizing Neighbor Pixels](https://mlsanity.com/paper/2603.18671/) (2026)
- [Conformable Convolution for Topologically Aware Learning of Complex Anatomical Structures](https://mlsanity.com/paper/2412.20608/) (2024)
- [ContextLoss: Context Information for Topology-Preserving Segmentation](https://mlsanity.com/paper/2506.11134/) (2025)
- [SAMSEM -- A Generic and Scalable Approach for IC Metal Line Segmentation](https://mlsanity.com/paper/2603.16548/) (2026)
- [Sparse cubical complexes for efficient topology-preservation in image data](https://mlsanity.com/paper/2609.37177/) (2026)

## Abstract (arXiv)

Besides per-pixel accuracy, topological correctness is also crucial for the segmentation of images with fine-scale structures, e.g., satellite images and biomedical images. In this paper, by leveraging the theory of digital topology, we identify pixels in an image that are critical for topology. By focusing on these critical pixels, we propose a new homotopy warping loss to train deep image segmentation networks for better topological accuracy. To efficiently identify these topologically critical pixels, we propose a new algorithm exploiting the distance transform. The proposed algorithm, as well as the loss function, naturally generalize to different topological structures in both 2D and 3D settings. The proposed loss function helps deep nets achieve better performance in terms of topology-aware metrics, outperforming state-of-the-art structure/topology-aware segmentation methods.