Train-Free Segmentation in MRI with Cubical Persistent Homology
To address the scarcity of annotated data in MRI segmentation, this paper proposes a training-free, fully unsupervised topological segmentation framework. Methodologically, it leverages cubical persistent homology to extract topological features—such as connected components and voids—from MRI volumes; employs automated threshold selection and spatial localization of representative cycles; and integrates anatomical geometric priors (e.g., spheres, cylinders, circles) to achieve precise segmentation of target structures—including glioblastoma, myocardium, and fetal cortical plate. Its key innovation lies in the first use of spatial coordinates of representative cycles to directly guide segmentation, thereby ensuring interpretability, topological stability, and geometric adaptability. Evaluated across multiple clinical MRI tasks, the method matches state-of-the-art supervised approaches in performance while requiring no labeled data—significantly enhancing robustness and clinical trustworthiness.