We describe a new general method for segmentation in MRI scans using Topological Data Analysis (TDA), offering several advantages over traditional machine learning approaches. It works 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. Although convoking classical ideas of TDA, such an algorithm has never been proposed separately from deep learning methods. To achieve this, our approach takes into account, in addition to the homology of the image, the localization of representative cycles, a piece of information that seems never to have been exploited in this context. In particular, it offers the ability to perform segmentation without the need for large annotated data sets. TDA also provides a more interpretable and stable framework for segmentation by explicitly mapping topological features to segmentation components. By adapting the geometric object to be detected, the algorithm can be adjusted to a wide range of data segmentation challenges. We carefully study the examples of glioblastoma segmentation in brain MRI, where a sphere is to be detected, as well as myocardium in cardiac MRI, involving a cylinder, and cortical plate detection in fetal brain MRI, whose 2D slices are circles. We compare our method to state-of-the-art algorithms.

翻译：我们描述了一种利用拓扑数据分析（TDA）进行 MRI 扫描分割的新通用方法，与传统机器学习方法相比具有多项优势。该方法分三步进行：首先通过自动阈值分割识别待分割的整体对象，然后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。虽然该方法借鉴了 TDA 的经典思想，但此前从未有独立于深度学习方法之外的此类算法被提出。为此，我们的方法除考虑图像的同调性外，还纳入了代表性循环的定位——这一信息似乎从未在此类场景中被利用过。特别地，该方法无需大型标注数据集即可实现分割。TDA 还通过将拓扑特征显式映射到分割组件，提供了一个更具可解释性和稳定性的分割框架。通过调整待检测的几何对象，该算法可适用于多种数据分割挑战。我们仔细研究了脑部 MRI 中胶质母细胞瘤分割（需检测球体）、心脏 MRI 中心肌分割（涉及圆柱体）以及胎儿脑部 MRI 中皮质板检测（其二维切片为圆形）等示例。我们将我们的方法与最先进的算法进行了比较。