Updates from Overleaf

Author: theo-barfoot

Abstract.tex

@@ -1 +1,11 @@
-I have a super abstract.
+Uncertainty and confidence estimation in medical image segmentation are crucial pillars for the clinical deployment of automated segmentation models. While deep learning-based methods have achieved impressive segmentation accuracy, they often struggle to accurately represent the confidence in their predictions and to communicate the underlying uncertainty inherent in the task. Capturing this uncertainty can provide valuable insights into the reliability of automated segmentations, enabling better-informed clinical decisions via interaction with more expressive and richer data structures. For example, modeling spatial correlation within the uncertainty measures is particularly important in medical imaging, as anatomical and pathological structures exhibit strong spatial dependencies that should be reflected in data communicated to clinical decision makers.
+
+Stochastic Segmentation Networks (SSNs) provide a framework for capturing spatially correlated aleatoric uncertainty by learning to a multivariate normal distribution over the output space, permitting multiple masks to be drawn as samples. Due to the high dimensional space of the prediction, a lower dimensional representation of the covariance must be employed. In this work, we extend SSNs by parametrising the covariance and precision matrices of multivariate normal distributions using structured sparse matrices. The use of such structured distributions allows for a more expressive representation of the uncertainty present in medical image data. Additionally, these predicted distributions can be conditioned on user input, which allows the model to improve the predicted distribution, leveraging the spatial correlation captured by structured Gaussians.
+
+To achieve this, we explore several covariance and precision parameterisations, including low-rank, sparse, and hybrid structures, focusing on their application to 3D medical imaging. We explore the utility and behaviour of these structured Gaussians on synthetic and real world medical image segmentation tasks. Our results show that incorporating structured covariance into SSNs enhances the model's ability to capture the complex spatial correlations inherent in medical imaging, leading to a more meaningful and powerful uncertainty estimation, that can provide a path for richer interaction with automated predictions.
+
+Our work also extends to the development of efficient sparse matrix operations for backpropagation via sparse gradients, including sparse matrix multiplication and linear solvers, which are critical for optimising models that utilise structured sparse representations. We provide implementations of these operations, including support for PyTorch, CuPy, and JAX, and have released it as a Python package, to facilitate broader adoption within the research community.
+
+In addition to our work on uncertainty estimation, we address the problem of model calibration in medical image segmentation by introducing novel calibration loss functions. We propose the use of marginal L1 average calibration error (mL1-ACE) as a differentiable loss to improve pixel-wise calibration, demonstrating significant improvements in calibration error metrics while preserving segmentation quality. Furthermore, we introduce dataset reliability histograms, which generalize traditional reliability diagrams to provide a more refined visual assessment of model calibration across the entire dataset.
+
+Overall, this thesis contributes to the advancement of uncertainty estimation and model calibration in medical image segmentation, aiming to enhance the reliability and interpretability of deep learning models in clinical settings. By leveraging structured sparse matrices, we provide a novel pathway for capturing the structured uncertainty that is often overlooked in traditional approaches, ultimately improving the trustworthiness of automated segmentation systems.

Chapter_1.tex

@@ -0,0 +1,24 @@
+\chapter[Sparse Matrix Operations]{Sparse Matrix Operations with Back propagation}
+\chaptermark{Sparse Matrices}
+\label{chap:sparse}
+\minitoc
+
+
+\section{Basics of Sparse Matrices}
+\subsection{COO and CSR encoding}
+\subsection{Limitation of PyTorch Sparse Graidents}
+\section{Sparse Matrix Multiplication}
+\subsection{Sparse Gradient Functions for SpMM}
+\section{Sparse Linear Solvers}
+\subsection{Comparing Solver Backbones}
+\begin{itemize}
+    \item CuPy
+    \item Jax
+    \item BICGSTAB
+    \item Conjugate Gradients
+    \item MINRES
+\end{itemize}
+\subsection{Sparse Gradients for Linear Solvers}
+
+Spanning on several pages
+

Chapter_2.tex

@@ -0,0 +1,23 @@
+\chapter[Structured Uncertainty In Medical Image Segmentation]{Modelling aleatoric uncertainty in medical image segmentation using stochastic segmentation networks predicting structured gaussian distributions}
+\chaptermark{Structured Uncertainty}
+\label{chap:uncertainty}
+\minitoc
+
+\section{Multivariate Normal Distributions}
+\subsection{Diagonal Covariance}
+\subsection{Low-Rank Covariance}
+\subsection{Low-Rank Precision}
+\subsection{Sparse Covariance}
+\subsection{Sparse Precision}
+\subsection{Symbolic Covariance}
+\subsection{Combining Low-Rank and Sparse}
+Maybe? 
+\section{Stochastic Segmentation Networks}
+\subsection{Low-Rank SSNs}
+Demonstrating on toy example and medical dataset
+\subsection{Sparse Structured SSNs}
+Demonstrating on toy example and medical dataset
+
+\newpage
+
+Spanning on several pages

Chapter_3.tex

@@ -0,0 +1,14 @@
+\chapter[Calibration in Medical Image Segmentation]{Using directly differential calibration errors as loss function for medical image segmentation}
+\chaptermark{Calibration in Medical Image Segmentation}
+\label{chap:calibration}
+\minitoc
+\section{Reliability Diagrams}
+\section{Calibration Error Metrics}
+\section{Calibration Losses}
+\subsection{Hard-Binned Calibration Losses}
+\subsection{ACE-DLIRIS MICCAI Paper}
+\subsection{Soft-Binned Calibration Losses}
+\subsection{Journal Extension Paper}
+\newpage
+
+Spanning on several pages

Introduction.tex

@@ -10,21 +10,35 @@ \chapter{Introduction}
 \end{minipage}
 \end{center}
 
+% \section{A section}
+% %
+% Youpi
+
+% \subsection{A sub-section}
+% %
+% Youpi
+
+% \subsubsection{A sub-sub-section}
+% %
+% Youpi
+
+% \paragraph{A paragraph}
+% %
+% Youpi
 
 From the beginning of times, men and women have written theses using Lorem Ipsum and Foo Bar language.
 
-\section{A section}
-%
-Youpi
+\section{Uncertainty in Medical Image Segmentation}
 
-\subsection{A sub-section}
+\subsection{Epistemic Uncertainty}
 %
-Youpi
 
-\subsubsection{A sub-sub-section}
-%
-Youpi
+\subsubsection{MC Drop-out}
+% etc etc
+\subsection{Aleatoric Uncertainty}
+\subsubsection{Stochastic Segmentation Networks}
 
-\paragraph{A paragraph}
-%
-Youpi
+\section{Reliability and Calibration in Medical Image Segmentation}
+\subsection{Reliability Diagrams}
+\subsection{Calibration Metrics}
+\subsection{Calibration Losses}

Thesis.tex

@@ -10,8 +10,8 @@
 \documentclass[british,a4paper,11pt,twoside]{ThesisStyle}
 
 \makeatletter
-\title{Lorem Ipsum}\let\thetitle\@title
-\author{Foo von Bar}\let\theauthor\@author
+\title{Structured Uncertainty and Reliability in Medical Image Segmentation}\let\thetitle\@title
+\author{Theodore Barfoot}\let\theauthor\@author
 \makeatother
 
 \input{FormatAndDefsBasic}
@@ -65,7 +65,9 @@ \chapter{Acknowledgments}
 
 \include{Introduction}
 
-\include{Methods}
+\include{Chapter_1}
+\include{Chapter_2}
+\include{Chapter_3}
 
 \include{Conclusion}
 

TitlePageKCL.tex

@@ -46,10 +46,10 @@
 \begin{tabular}{l p{3.3cm} l l}
 
 Technical Supervisor & & Technical Co-Supervisor \\
-\textbf{Pr. Paul Erdos} & & \textbf{Pr. Harold Hopkins}  \\
+\textbf{Pr. Tom Vercauteren} & & \textbf{Pr. Ben Glocker}  \\
  & & \\
-Clinical Supervisor & & \\
-\textbf{Pr. Godfrey N. Hounsfield} & & 
+Clinical Supervisor & & Industry Supervisor \\
+\textbf{Mr. Jonathan Shapey} & & \textbf{Dr. Oliver Hamilton} & 
 
 \end{tabular}
 \end{center}