# Learning Topological Representations for Deep Image Understanding

arXiv: https://arxiv.org/abs/2403.15361 · HTML: https://mlsanity.com/paper/2403.15361/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 12 references that are in the map.
- First posted on arXiv 22 Mar 2024.

## Builds on (most cited first, 8 of 8)

- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Trigger Hunting with a Topological Prior for Trojan Detection](https://mlsanity.com/paper/2110.08335/) (2021)
- [Learning Topological Interactions for Multi-Class Medical Image Segmentation](https://mlsanity.com/paper/2207.09654/) (2022)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [Enhancing Modality-Agnostic Representations via Meta-Learning for Brain Tumor Segmentation](https://mlsanity.com/paper/2302.04308/) (2023)
- [Confidence Estimation Using Unlabeled Data](https://mlsanity.com/paper/2307.10440/) (2023)
- [Deep Statistic Shape Model for Myocardium Segmentation](https://mlsanity.com/paper/2207.10607/) (2022)

## Abstract (arXiv)

In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning methods, they do not provide a satisfactory representation of these structures, thus creating significant barriers in scalable annotation and downstream analysis. In this dissertation, we tackle such challenges by proposing novel representations of these topological structures in a deep learning framework. We leverage the mathematical tools from topological data analysis, i.e., persistent homology and discrete Morse theory, to develop principled methods for better segmentation and uncertainty estimation, which will become powerful tools for scalable annotation.