Topology-Aware Segmentation Using Discrete Morse Theory
This work addresses the need for topologically correct segmentation in natural and biomedical images, which is crucial for downstream analysis tasks, representing an incremental advancement by integrating discrete Morse theory into deep learning methods.
The paper tackled the problem of improving topological accuracy in image segmentation, such as vessel connectivity and membrane closure, by proposing a new training approach using discrete Morse theory, resulting in significant performance improvements on both DICE scores and topological metrics across diverse datasets.
In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream analysis tasks. In this paper, we propose a new approach to train deep image segmentation networks for better topological accuracy. In particular, leveraging the power of discrete Morse theory (DMT), we identify global structures, including 1D skeletons and 2D patches, which are important for topological accuracy. Trained with a novel loss based on these global structures, the network performance is significantly improved especially near topologically challenging locations (such as weak spots of connections and membranes). On diverse datasets, our method achieves superior performance on both the DICE score and topological metrics.