Learning Probabilistic Topological Representations Using Discrete Morse Theory

Abstract

Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we propose a novel deep learning based method to learn topological/structural. We use discrete Morse theory and persistent homology to construct a one-parameter family of structures as the topological/structural representation space. Furthermore, we learn a probabilistic model that can perform inference tasks in such a topological/structural representation space. Our method generates true structures rather than pixel-maps, leading to better topological integrity in automatic segmentation tasks. It also facilitates semi-automatic interactive annotation/proofreading via the sampling of structures and structure-aware uncertainty.

Cite

Text

Hu et al. "Learning Probabilistic Topological Representations Using Discrete Morse Theory." International Conference on Learning Representations, 2023.

Markdown

[Hu et al. "Learning Probabilistic Topological Representations Using Discrete Morse Theory." International Conference on Learning Representations, 2023.](https://mlanthology.org/iclr/2023/hu2023iclr-learning/)

BibTeX

@inproceedings{hu2023iclr-learning,
  title     = {{Learning Probabilistic Topological Representations Using Discrete Morse Theory}},
  author    = {Hu, Xiaoling and Samaras, Dimitris and Chen, Chao},
  booktitle = {International Conference on Learning Representations},
  year      = {2023},
  url       = {https://mlanthology.org/iclr/2023/hu2023iclr-learning/}
}