Discrete Morse theory

This repository contains the implementation of discrete Morse theory "Topology-aware Segmentation Using Discrete Morse Theory", accepted to ICLR 2021 (Spotlight).

This folder contains two subfolders:

1. morse_DMT: this folder contains the implementation for real discrete morse theory and captures the real morse structure.

It works for 2D and 3D vessel data.

2. persistence_ws: this folder contains the implementation for persistence-based watershed algorithm. It's a relaxed version of morse structure.

It works for 2D and 3D volume data.

Citation

Please consider citing our papers if you find them useful.

@article{hu2019topology,
  title={Topology-preserving deep image segmentation},
  author={Hu, Xiaoling and Li, Fuxin and Samaras, Dimitris and Chen, Chao},
  journal={Advances in neural information processing systems},
  volume={32},
  year={2019}
}

@inproceedings{hu2021topology,
  title={Topology-Aware Segmentation Using Discrete Morse Theory},
  author={Hu, Xiaoling and Wang, Yusu and Fuxin, Li and Samaras, Dimitris and Chen, Chao},
  booktitle={International Conference on Learning Representations},
  year={2021}
}