Robust representation learning with topological and geometric constraints in medical imaging
File(s)
Author(s)
Santhirasekaram, Ainkaran
Type
Thesis
Abstract
Robust representation learning in medical imaging is crucial for the reliable application of deep learning models in critical tasks like clinical decision-making. The vulnerability of deep learning models to subtle perturbations, particularly when facing distributional shifts in test data not encountered during training, is well-documented. To enhance model robustness, common approaches involve data augmentation, adversarial training, and self-supervised learning strategies.
In this thesis, we will explore the importance of geometry and topology of the latent space in building robust representation for medical imaging. We start with restricting the latent space to a finite set of components using vector quantisation for downstream segmentation and classification tasks. We claim that imposing a compositional structure on the latent space enables a more robust representation. Next, we will explore the natural curvature in which to embed these components for segmentation. Specifically, we impose hierarchical compositionality in a latent space equipped with hyperbolic geometry to compose the segmentation output to improve robustness. We then explore an alternative geometric perspective by constraining the latent space to a dictionary of group equivariant shape components which is sampled to construct the segmentation output. We analyse equivariance to various groups and demonstrate how the order of the group affects model robustness. We follow up our exposition into robust segmentation with a discrete latent space by sampling the dictionary of shape components such that topology is preserved using persistent homology and cellular sheaf theory. We show the advantage of using cellular sheaf theory over persistent homology to extract richer geometric information. Finally, we show the importance of curvature for embedding symbols in neurosymbolic reasoning. Specifically, we develop robust hierarchical explanations in hyperbolic space for deep discriminative models.
We demonstrate the effectiveness of our methods to improve model robustness under various perturbations and in single domain generalisation tasks.
In this thesis, we will explore the importance of geometry and topology of the latent space in building robust representation for medical imaging. We start with restricting the latent space to a finite set of components using vector quantisation for downstream segmentation and classification tasks. We claim that imposing a compositional structure on the latent space enables a more robust representation. Next, we will explore the natural curvature in which to embed these components for segmentation. Specifically, we impose hierarchical compositionality in a latent space equipped with hyperbolic geometry to compose the segmentation output to improve robustness. We then explore an alternative geometric perspective by constraining the latent space to a dictionary of group equivariant shape components which is sampled to construct the segmentation output. We analyse equivariance to various groups and demonstrate how the order of the group affects model robustness. We follow up our exposition into robust segmentation with a discrete latent space by sampling the dictionary of shape components such that topology is preserved using persistent homology and cellular sheaf theory. We show the advantage of using cellular sheaf theory over persistent homology to extract richer geometric information. Finally, we show the importance of curvature for embedding symbols in neurosymbolic reasoning. Specifically, we develop robust hierarchical explanations in hyperbolic space for deep discriminative models.
We demonstrate the effectiveness of our methods to improve model robustness under various perturbations and in single domain generalisation tasks.
Version
Open Access
Date Issued
2024-02
Date Awarded
2024-06
Copyright Statement
Creative Commons Attribution Licence
License URL
Advisor
Glocker, Benjamin
Rockall, Andrea
Winkler, Mathias
Sponsor
Cancer Research UK
Grant Number
C309/A28804
Publisher Department
Department of Surgery and Cancer
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)