Learning Probabilistic Topological Representations Using Discrete Morse Theory
Xiaoling Hu, Dimitris Samaras, Chao Chen
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.
BibTeX
@inproceedings{
hu2023learning,
title={Learning Probabilistic Topological Representations Using Discrete Morse Theory},
author={Xiaoling Hu and Dimitris Samaras and Chao Chen},
booktitle={The Eleventh International Conference on Learning Representations },
year={2023},
url={https://openreview.net/forum?id=cXMHQD-xQas}
}