Train-Free Segmentation in MRI with Cubical Persistent Homology
This provides a modular, interpretable solution for medical image segmentation, particularly beneficial in domains with limited labeled data, though it is incremental as it builds on existing TDA methods.
The authors tackled MRI segmentation without large annotated datasets by developing a train-free framework using cubical persistent homology, achieving competitive performance on glioblastoma, myocardium, and cortical plate detection compared to supervised and unsupervised baselines.
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.