Learning Topological Representations for Deep Image Understanding

TL;DR

This paper introduces a novel deep learning framework that incorporates topological data analysis tools like persistent homology and Morse theory to improve segmentation and uncertainty estimation of complex structures in biomedical images.

Contribution

It presents new topological representations within deep learning models, enhancing segmentation accuracy and uncertainty quantification for fine-scale biomedical structures.

Findings

Improved segmentation of neurons, tissues, and vessels.

Enhanced uncertainty estimation in deep models.

Facilitated scalable annotation processes.

Abstract

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.