Train-Free Segmentation in MRI with Cubical Persistent Homology
Anton François Raphaël Tinarrage
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.