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.

翻译：我们研究了一种基于拓扑数据分析的无训练MRI分割框架。该流程分三步进行：首先通过自动阈值识别待分割的完整对象，接着检测一个拓扑结构已知的独特子集，最后推导出分割的各个组成部分。关键环节是从持续图中提取近似代表回路，这为持续特征与解剖成分之间建立了可解释的关联。为明确该方法适用范围，我们明确了其依赖的拓扑与强度假设，量化了这些假设在真实数据上的成立条件，并分析了典型失效模式。我们在胶质母细胞瘤和胎儿皮质板分割任务上评估该方法，并与无监督及深度学习基准方法进行对比。由于无需大量标注数据集即可运行，该方法特别适用于数据稀缺场景，同时为专家修正或基于学习的流程提供了可解释的基线及实用的初始化方案。