Algebraic Topology Preservation Learning for Image Segmentation



This project aims to achieve significant improvements in topology-preserving segmentation of medical imagery by incorporating recent theoretical and computational advances in persistent homology established by PI Bauer. Specifically, the method of induced matchings, a key part of the foundational algebraic stability theorem of persistent homology, will be utilized to obtain a faithful identification of topological features between training data and ground truth in a deep learning approach to segmentation, overcoming the shortcomings of previous methods based on persistent homology. Taking advantage of the algebraic structure of persistent homology, we leverage connections between algebraic objects through homomorphisms to obtain a more faithful feature identification between ground truth and likelihood function during the training of a convolutional neural network.