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Train-Free Segmentation in MRI with Cubical Persistent Homology

Anton François, Raphaël Tinarrage

TL;DR

This work tackles MRI segmentation without training data by leveraging cubical persistent homology. A three-module pipeline localizes the whole object, identifies a geometrically distinctive subset via persistent cycles, and deduces remaining components, enabling interpretable segmentations in glioblastoma, cardiac, and fetal cortical plate cases. Results show competitive performance with unsupervised baselines in some tasks and highlight limitations when topological assumptions fail, while offering clear avenues for integration with deep learning. The approach promises applicability in scarce-data settings and provides topological guarantees and explainability for clinical use.

Abstract

We present a new general framework for segmentation of MRI scans based on Topological Data Analysis (TDA), offering several advantages over traditional machine learning approaches. 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. Unlike most prior TDA uses in medical image segmentation, which are typically embedded within deep networks, our approach is a standalone method tailored to MRI. A key ingredient is the localization of representative cycles from the persistence diagram, which enables interpretable mappings from topological features to anatomical components. In particular, the method offers the ability to perform segmentation without the need for large annotated datasets. Its modular design makes it adaptable to a wide range of data segmentation challenges. We validate the framework on three applications: glioblastoma segmentation in brain MRI, where a sphere is to be detected; myocardium in cardiac MRI, forming a cylinder; and cortical plate detection in fetal brain MRI, whose 2D slices are circles. We compare our method with established supervised and unsupervised baselines.

Train-Free Segmentation in MRI with Cubical Persistent Homology

TL;DR

This work tackles MRI segmentation without training data by leveraging cubical persistent homology. A three-module pipeline localizes the whole object, identifies a geometrically distinctive subset via persistent cycles, and deduces remaining components, enabling interpretable segmentations in glioblastoma, cardiac, and fetal cortical plate cases. Results show competitive performance with unsupervised baselines in some tasks and highlight limitations when topological assumptions fail, while offering clear avenues for integration with deep learning. The approach promises applicability in scarce-data settings and provides topological guarantees and explainability for clinical use.

Abstract

We present a new general framework for segmentation of MRI scans based on Topological Data Analysis (TDA), offering several advantages over traditional machine learning approaches. 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. Unlike most prior TDA uses in medical image segmentation, which are typically embedded within deep networks, our approach is a standalone method tailored to MRI. A key ingredient is the localization of representative cycles from the persistence diagram, which enables interpretable mappings from topological features to anatomical components. In particular, the method offers the ability to perform segmentation without the need for large annotated datasets. Its modular design makes it adaptable to a wide range of data segmentation challenges. We validate the framework on three applications: glioblastoma segmentation in brain MRI, where a sphere is to be detected; myocardium in cardiac MRI, forming a cylinder; and cortical plate detection in fetal brain MRI, whose 2D slices are circles. We compare our method with established supervised and unsupervised baselines.
Paper Structure (52 sections, 8 equations, 18 figures, 4 tables)

This paper contains 52 sections, 8 equations, 18 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related works
  3. Segmentation tasks and datasets
  4. Glioblastomas
  5. Myocardium
  6. Cortical plate
  7. Segmentation methods
  8. Unsupervised methods
  9. Deep learning
  10. TDA for MRI analysis
  11. Unsupervised methods in TDA
  12. Deep learning in TDA
  13. Background on TDA
  14. Homology
  15. Filtrations
  16. ...and 37 more sections

Figures (18)

  • Figure 1: TDA segmentation overview. We demonstrate a simple concept for segmentation using Topological Data Analysis (TDA) on three datasets. Each row focuses on a particular organ to segment, from top to bottom: myocardium in ACDC, glioblastoma in BraTS 2025, and cortical plate in STA. First column: In each case, we are provided with a 3D MRI and aim at detecting a component of a given topology. Second column: We automatically select components by analyzing persistence diagrams. Third column: Eventually, through the strategies detailed in this article, we deduce a segmentation.
  • Figure 2: Glioblastoma segmentation in BraTS 2025. Rows contain horizontal MRI slices of a patient (modalities T1, T1ce, T2, FLAIR) and the provided segmentation (TC: red, ET: orange, ED: blue).
  • Figure 3: Ventricles/myocardium segmentation in ACDC.Left: axial slice of a CMR at ED (top) or ES (bottom). Right: ground-truth segmentation (Myo: orange, LV: red, RV: blue).
  • Figure 4: Cortical plate segmentation in STA. The rows contain sagittal slices of the same MRI, for gestational week 30 (top) and 38 (bottom), with ground-truth cortical plate segmentation (orange).
  • Figure 5: A 2D binary image.
  • ...and 13 more figures