Conceitos Básicos
Novel representations of topological structures in deep learning frameworks improve segmentation accuracy and uncertainty estimation.
Resumo
This dissertation explores topological representations in deep learning for image understanding. It addresses challenges in segmenting fine-scaled structures accurately, proposing topological losses and homotopy warping methods. The work leverages mathematical tools like persistent homology and discrete Morse theory to enhance segmentation performance and annotation speed. Key highlights include:
Introduction to topological data analysis and its application in deep learning.
Development of topology-preserving methods for image segmentation.
Application of topological priors in trojan detection.
Proposal of a method to learn structural representations directly from images.
Estatísticas
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.
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.
Citações
"Despite the strong predictive power of deep learning methods, they do not provide a satisfactory representation of these structures." - Xiaoling Hu