Title: Train-Free Segmentation in MRI with Cubical Persistent Homology Show Chinese title

Title: 基于立方持久同调的MRI无训练分割

Abstract: 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. Show Chinese abstract

Abstract: 我们描述了一种使用拓扑数据分析（TDA）的新通用方法，用于MRI扫描中的分割，相比传统的机器学习方法具有多个优势。该方法分三步进行：首先通过自动阈值识别需要分割的整体对象，然后检测一个预先已知其拓扑结构的显著子集，最后推断出分割的不同组成部分。尽管采用了经典的TDA思想，但从未有单独提出过此类算法，而总是与深度学习方法结合。为了实现这一点，我们的方法除了考虑图像的同调性外，还考虑了代表性循环的定位，这一信息在此背景下似乎从未被利用过。特别是，它能够实现无需大规模标注数据集的分割。TDA还通过明确地将拓扑特征映射到分割组件上，提供了更可解释且更稳定的分割框架。通过调整要检测的几何对象，该算法可以适应各种数据分割挑战。我们仔细研究了脑部MRI中胶质母细胞瘤分割的例子（需要检测球体）、心脏MRI中心肌分割的例子（涉及圆柱体），以及胎儿脑MRI中皮质板检测的例子（其二维切片为圆形）。我们将我们的方法与最先进的算法进行了比较。