Spinal imaging is an invaluable tool for visualizing and assessing spinal pathologies. Segmentation of vertebrae in computed tomography (CT) images is a fundamental basis for the quantitative analysis of medical images, crucial for clinical diagnosis and spinal surgery planning. Although convolutional or transformer-based neural networks generally dominate the segmentation of medical images, where the U-Net architecture is frequently employed, alternative methodologies could offer potential advantages. Among promising approaches are deep implicit statistical shape models (DISSMs), which are notable for creating high-quality surfaces without discretization artefacts, ensuring anatomically plausible shapes, and accounting for the biological variability of shapes. These advantages enable the DISSM method to effectively tackle the challenges presented by medical images, such as three-dimensional (3D) CT images of the spine. The DISSM method comprises two key parts: a shape decoder and a pose estimation encoder. The shape decoder learns an implicit model of shape, which in our case describes anatomically plausible shapes of lumbar vertebrae, while the position estimation encoder allows for precise determination of vertebrae positions in the 3D space of CT images using transformations such as translation, rotation, and isotropic scaling. Additionally, it learns the weights for principal components (PCA) that capture the essential shape features of the vertebrae. In this thesis, I explore the use and enhancement of the DISSM method for the segmentation of lumbar vertebrae on two data collections: VerSe2020 and Colonog-CTSpine1K, which together contain 920 3D CT images and corresponding segmentations of vertebrae. This approach offers a new potential tool for improving the accuracy and applicability of vertebra segmentation, especially in cases where traditional segmentation methods are limited due to the complexity of clinical samples. The preprocessing and learning techniques are based on the open-source software package AshStuff/dissm with custom modifications. For evaluating the results, we employed three established metrics in the field of semantic segmentations: the Dice similarity coefficient (DSC), 95th percentile of Hausdorff distance (HD95), and average symmetric surface distance (ASSD). The results are promising with DSC of 87.4 ± 2.6%, HD95 of 2.73 ± 0.95 mm and ASSD of 0.82 ± 0.20 mm.
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