# Train-Free Segmentation in MRI with Cubical Persistent Homology

arXiv: https://arxiv.org/abs/2401.01160 · HTML: https://mlsanity.com/paper/2401.01160/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 171 references that are in the map.
- First posted on arXiv 2 Jan 2024.

## Builds on (most cited first, 30 of 34)

- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [The RSNA-ASNR-MICCAI BraTS 2021 Benchmark on Brain Tumor Segmentation and Radiogenomic Classification](https://mlsanity.com/paper/2107.02314/) (2021)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Efficient Multi-Scale 3D CNN with Fully Connected CRF for Accurate Brain Lesion Segmentation](https://mlsanity.com/paper/1603.05959/) (2016)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [An automatic multi-tissue human fetal brain segmentation benchmark using the Fetal Tissue Annotation Dataset](https://mlsanity.com/paper/2010.15526/) (2020)
- [Multi-Atlas Segmentation of Biomedical Images: A Survey](https://mlsanity.com/paper/1412.3421/) (2014)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Cardiac Segmentation with Strong Anatomical Guarantees](https://mlsanity.com/paper/2006.08825/) (2020)
- [Optimized U-Net for Brain Tumor Segmentation](https://mlsanity.com/paper/2110.03352/) (2021)
- [The Topology ToolKit](https://mlsanity.com/paper/1805.09110/) (2018)
- [Extending nn-UNet for brain tumor segmentation](https://mlsanity.com/paper/2112.04653/) (2021)
- [Explicit topological priors for deep-learning based image segmentation using persistent homology](https://mlsanity.com/paper/1901.10244/) (2019)
- [Fast and Accurate Tumor Segmentation of Histology Images using Persistent Homology and Deep Convolutional Features](https://mlsanity.com/paper/1805.03699/) (2018)
- [Cubical Ripser: Software for computing persistent homology of image and volume data](https://mlsanity.com/paper/2005.12692/) (2020)
- [Fetal Brain Tissue Annotation and Segmentation Challenge Results](https://mlsanity.com/paper/2204.09573/) (2022)
- [Redundancy Reduction in Semantic Segmentation of 3D Brain Tumor MRIs](https://mlsanity.com/paper/2111.00742/) (2021)
- [A Deep Attentive Convolutional Neural Network for Automatic Cortical Plate Segmentation in Fetal MRI](https://mlsanity.com/paper/2004.12847/) (2020)
- [A persistent homology-based topological loss function for multi-class CNN segmentation of cardiac MRI](https://mlsanity.com/paper/2008.09585/) (2020)
- [Volume Optimal Cycle: Tightest representative cycle of a generator on persistent homology](https://mlsanity.com/paper/1712.05103/) (2017)
- [Topology-Aware Focal Loss for 3D Image Segmentation](https://mlsanity.com/paper/2304.12223/) (2023)
- [Glioma Segmentation with Cascaded Unet](https://mlsanity.com/paper/1810.04008/) (2018)
- [Approaching Peak Ground Truth](https://mlsanity.com/paper/2301.00243/) (2022)
- [Duality in Persistent Homology of Images](https://mlsanity.com/paper/2005.04597/) (2020)
- [Segmentation of the cortical plate in fetal brain MRI with a topological loss](https://mlsanity.com/paper/2010.12391/) (2020)
- [Persistent 1-Cycles: Definition, Computation, and Its Application](https://mlsanity.com/paper/1810.04807/) (2018)
- [Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide](https://mlsanity.com/paper/2105.07025/) (2021)
- [HNF-Netv2 for Brain Tumor Segmentation using multi-modal MR Imaging](https://mlsanity.com/paper/2202.05268/) (2022)

## Built on by (most cited first, 1 of 1)

- [Data-driven techniques for translational neuroscience and personalized neuro-health](https://mlsanity.com/paper/2608.13749/) (2026)

## Abstract (arXiv)

We investigate a framework for train-free MRI segmentation based on Topological Data Analysis. The pipeline proceeds in three steps, first identifying the whole object to segment via automatic thresholding, then detecting a distinctive subset whose topology is known in advance, and finally deducing the various components of the segmentation. A key ingredient is the extraction of approximate representative cycles from persistence diagrams, which provides an interpretable link between persistent features and anatomical components. To clarify the method's scope, we make the underlying topological and intensity assumptions explicit, quantify when they hold on real data, and analyze typical failure modes. We evaluate the approach on glioblastoma and on fetal cortical plate segmentation, with comparisons to unsupervised and deep-learning references. By operating without large annotated datasets, the method is well suited to scarce-data settings and provides an interpretable baseline and practical initialization for expert refinement or learning-based pipelines.