Learning Topological Representations for Deep Image Understanding
This work targets biomedical applications where accurate structure delineation is critical for downstream analysis, offering incremental improvements in deep learning methods for specific domains.
The dissertation addresses the challenge of delineating complex fine-scaled structures like neurons and vessels in biomedical images by proposing novel topological representations using persistent homology and discrete Morse theory, aiming to improve segmentation and uncertainty estimation for scalable annotation.
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.