Topology-Aware Segmentation Using Discrete Morse Theory
Xiaoling Hu, Yusu Wang, Li Fuxin, Dimitris Samaras, Chao Chen
Abstract
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.
BibTeX
@inproceedings{
hu2021topologyaware,
title={Topology-Aware Segmentation Using Discrete Morse Theory},
author={Xiaoling Hu and Yusu Wang and Li Fuxin and Dimitris Samaras and Chao Chen},
booktitle={International Conference on Learning Representations},
year={2021},
url={https://openreview.net/forum?id=LGgdb4TS4Z}
}