# Learning Topological Interactions for Multi-Class Medical Image Segmentation

arXiv: https://arxiv.org/abs/2207.09654 · HTML: https://mlsanity.com/paper/2207.09654/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 56 references that are in the map.
- First posted on arXiv 20 Jul 2022.

## Builds on (most cited first, 16 of 16)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (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)
- [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)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Trigger Hunting with a Topological Prior for Trojan Detection](https://mlsanity.com/paper/2110.08335/) (2021)
- [Structure-Aware Image Segmentation with Homotopy Warping](https://mlsanity.com/paper/2112.07812/) (2021)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [Higher-order Segmentation via Multicuts](https://mlsanity.com/paper/1305.6387/) (2013)
- [A Topology-Attention ConvLSTM Network and Its Application to EM Images](https://mlsanity.com/paper/2202.03430/) (2022)

## Built on by (most cited first, 28 of 28)

- [Position: Topological Deep Learning is the New Frontier for Relational Learning](https://mlsanity.com/paper/2402.08871/) (2024)
- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [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)
- [Topologically Faithful Multi-class Segmentation in Medical Images](https://mlsanity.com/paper/2403.11001/) (2024)
- [Semi-supervised Segmentation of Histopathology Images with Noise-Aware Topological Consistency](https://mlsanity.com/paper/2311.16447/) (2023)
- [S-SAM: SVD-based Fine-Tuning of Segment Anything Model for Medical Image Segmentation](https://mlsanity.com/paper/2408.06447/) (2024)
- [NexToU: Efficient Topology-Aware U-Net for Medical Image Segmentation](https://mlsanity.com/paper/2305.15911/) (2023)
- [TopoDiffusionNet: A Topology-aware Diffusion Model](https://mlsanity.com/paper/2410.16646/) (2024)
- [Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homology](https://mlsanity.com/paper/2407.04683/) (2024)
- [Probing the Limits and Capabilities of Diffusion Models for the Anatomic Editing of Digital Twins](https://mlsanity.com/paper/2401.00247/) (2023)
- [Spatial Diffusion for Cell Layout Generation](https://mlsanity.com/paper/2409.03106/) (2024)
- [BrainMRDiff: A Diffusion Model for Anatomically Consistent Brain MRI Synthesis](https://mlsanity.com/paper/2504.04532/) (2025)
- [MATCH: Multi-faceted Adaptive Topo-Consistency for Semi-Supervised Histopathology Segmentation](https://mlsanity.com/paper/2510.01532/) (2025)
- [FAS-UNet: A Novel FAS-driven Unet to Learn Variational Image Segmentation](https://mlsanity.com/paper/2210.15164/) (2022)
- [Pairwise-Constrained Implicit Functions for 3D Human Heart Modelling](https://mlsanity.com/paper/2307.08716/) (2023)
- [A Diffusion Model for Simulation Ready Coronary Anatomy with Morpho-skeletal Control](https://mlsanity.com/paper/2407.15631/) (2024)
- [Preserving Cardiac Integrity: A Topology-Infused Approach to Whole Heart Segmentation](https://mlsanity.com/paper/2410.10551/) (2024)
- [Topology-Aware Wavelet Mamba for Airway Structure Segmentation in Postoperative Recurrent Nasopharyngeal Carcinoma CT Scans](https://mlsanity.com/paper/2502.14363/) (2025)
- [TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy](https://mlsanity.com/paper/2503.03365/) (2025)
- [Morphology Edge Attention Network and Optimal Geometric Matching Connection model for vascular segmentation](https://mlsanity.com/paper/2306.01808/) (2023)
- [PnPNet: Pull-and-Push Networks for Volumetric Segmentation with Boundary Confusion](https://mlsanity.com/paper/2312.08323/) (2023)
- [Learning Topological Representations for Deep Image Understanding](https://mlsanity.com/paper/2403.15361/) (2024)
- [Scalar Function Topology Divergence: Comparing Topology of 3D Objects](https://mlsanity.com/paper/2407.08364/) (2024)
- [Conformable Convolution for Topologically Aware Learning of Complex Anatomical Structures](https://mlsanity.com/paper/2412.20608/) (2024)
- [Leveraging Textual Anatomical Knowledge for Class-Imbalanced Semi-Supervised Multi-Organ Segmentation](https://mlsanity.com/paper/2501.13470/) (2025)
- [Modality-AGnostic Image Cascade (MAGIC) for Multi-Modality Cardiac Substructure Segmentation](https://mlsanity.com/paper/2506.10797/) (2025)

## Abstract (arXiv)

Deep learning methods have achieved impressive performance for multi-class medical image segmentation. However, they are limited in their ability to encode topological interactions among different classes (e.g., containment and exclusion). These constraints naturally arise in biomedical images and can be crucial in improving segmentation quality. In this paper, we introduce a novel topological interaction module to encode the topological interactions into a deep neural network. The implementation is completely convolution-based and thus can be very efficient. This empowers us to incorporate the constraints into end-to-end training and enrich the feature representation of neural networks. The efficacy of the proposed method is validated on different types of interactions. We also demonstrate the generalizability of the method on both proprietary and public challenge datasets, in both 2D and 3D settings, as well as across different modalities such as CT and Ultrasound. Code is available at: https://github.com/TopoXLab/TopoInteraction