| Sumari: | <p>Since the rise of deep learning, new medical image segmentation methods have rapidly been proposed with promising results, with each one reporting marginal improvements on the previous state-of-the-art (SOTA) method. However, on visual inspection, errors are often revealed, such as topological mistakes (e.g. holes or folds), that are not detected using traditional evaluation metrics, such as Dice. Moreover, correct topology is often essential in ensuring segmentations are anatomically and pathologically plausible and, ultimately, suitable for downstream image processing tasks. Therefore, there is a need for methods to focus on ensuring that the predicted segmentations are topologically correct, rather than just optimising the pixel-wise accuracy. In this thesis, I propose a method that utilises prior knowledge of anatomy to segment structures, whilst preserving the known topology.</p>
<p>The presented model, Topology Encouraging Deformation Segmentation Network (TEDS-Net), performs segmentation by deforming a prior shape with the same topological features as the anatomy of interest using learnt topology-preserving deformation fields. However, here I show that such fields only guarantee topology preservation in the continuous domain and that their properties begin to break down when applied in discrete spaces. To overcome this effect, I introduced additional modifications in TEDS-Net to more strictly enforce topology preservation, a step often overlooked in previous work.</p>
<p>Across this thesis, TEDS-Net is applied to a range of natural and medical image segmentation tasks. I show how it can be used for multiple topology types, multiple structures and in both two- and three-dimensions. Further, I show how TEDS-Net can be used to segment whole volumes using minimally annotated training data. Across these experiments, TEDS-Net outperforms all SOTA baselines on topology, whilst maintaining competitive pixel-wise accuracy.</p>
<p>Finally, TEDS-Net is integrated into a whole medical imaging pipeline, to illustrate the importance of topologically correct segmentations for downstream tasks. TEDS-Net is used to segment the developing cortical plate from in-utero fetal brain ultrasound scans in 3D, to enable the characterisation of its complex growth and development during gestation. To the best of my knowledge, this task has only been previously attempted from magnetic resonance imaging (MRI), despite ultrasound being the modality of choice in prenatal care. This is likely due to large acoustic shadows obstructing key brain regions in ultrasound. Due to TEDS-Net anatomical constraints, it can anatomically guide the cortical plate segmentation in regions of shadows, producing a complete segmentation that enables accurate downstream analysis.</p>
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