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/}
}