# Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation

arXiv: https://arxiv.org/abs/2411.03228 · HTML: https://mlsanity.com/paper/2411.03228/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [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)
- [The TopCoW Challenge -- Topology-Aware Circle of Willis Segmentation for CT and MR Angiography](https://mlsanity.com/paper/2312.17670/) (2023)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Skeleton Recall Loss for Connectivity Conserving and Resource Efficient Segmentation of Thin Tubular Structures](https://mlsanity.com/paper/2404.03010/) (2024)
- [A skeletonization algorithm for gradient-based optimization](https://mlsanity.com/paper/2309.02527/) (2023)
- [Topological Optimization with Big Steps](https://mlsanity.com/paper/2203.16748/) (2022)
- [Topologically Faithful Multi-class Segmentation in Medical Images](https://mlsanity.com/paper/2403.11001/) (2024)

## Built on by (most cited first, 17 of 17)

- [Topology-Preserving Image Segmentation with Spatial-Aware Persistent Feature Matching](https://mlsanity.com/paper/2412.02076/) (2024)
- [Pitfalls of topology-aware image segmentation](https://mlsanity.com/paper/2412.14619/) (2024)
- [Endowing Embodied Agents with Spatial Reasoning Capabilities for Vision-and-Language Navigation](https://mlsanity.com/paper/2504.08806/) (2025)
- [MATCH: Multi-faceted Adaptive Topo-Consistency for Semi-Supervised Histopathology Segmentation](https://mlsanity.com/paper/2510.01532/) (2025)
- [BackSplit: The Importance of Sub-dividing the Background in Biomedical Lesion Segmentation](https://mlsanity.com/paper/2511.19394/) (2025)
- [FMS2: Unified Flow Matching for Segmentation and Synthesis of Thin Structures](https://mlsanity.com/paper/2603.13659/) (2026)
- [Skelite: Compact Neural Networks for Efficient Iterative Skeletonization](https://mlsanity.com/paper/2503.07369/) (2025)
- [Topo-R1: Detecting Topological Anomalies via Vision-Language Models](https://mlsanity.com/paper/2603.13054/) (2026)
- [3D Cell Oversegmentation Correction via Geo-Wasserstein Divergence](https://mlsanity.com/paper/2502.01890/) (2025)
- [ContextLoss: Context Information for Topology-Preserving Segmentation](https://mlsanity.com/paper/2506.11134/) (2025)
- [Preserving instance continuity and length in segmentation through connectivity-aware loss computation](https://mlsanity.com/paper/2509.03154/) (2025)
- [SAMSEM -- A Generic and Scalable Approach for IC Metal Line Segmentation](https://mlsanity.com/paper/2603.16548/) (2026)
- [Effect of Input Resolution on Retinal Vessel Segmentation Performance: An Empirical Study Across Five Datasets](https://mlsanity.com/paper/2604.02977/) (2026)
- [Vesselpose: Vessel Graph Reconstruction from Learned Voxel-wise Direction Vectors in 3D Vascular Images](https://mlsanity.com/paper/2605.00538/) (2026)
- [SEMIR: Topology-Preserving Graph Minors for Thin-Structure Segmentation](https://mlsanity.com/paper/2606.24935/) (2026)
- [Topology-Aware Training and Spatial Diagnostics for Fiber Bundle Segmentation in Tracer Histology](https://mlsanity.com/paper/2609.04454/) (2026)
- [Sparse cubical complexes for efficient topology-preservation in image data](https://mlsanity.com/paper/2609.37177/) (2026)

## Abstract (arXiv)

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust topological guarantees, are limited to specific use cases, or impose high computational costs. In this work, we propose a novel, graph-based framework for topologically accurate image segmentation that is both computationally efficient and generally applicable. Our method constructs a component graph that fully encodes the topological information of both the prediction and ground truth, allowing us to efficiently identify topologically critical regions and aggregate a loss based on local neighborhood information. Furthermore, we introduce a strict topological metric capturing the homotopy equivalence between the union and intersection of prediction-label pairs. We formally prove the topological guarantees of our approach and empirically validate its effectiveness on binary and multi-class datasets. Our loss demonstrates state-of-the-art performance with up to fivefold faster loss computation compared to persistent homology methods.