Tomographic Segmentation from Limited Projection Data

Computed Tomography (CT) enables analyzing the internal structures of objects from projections data. The projections data measures the attenuation of penetrating radiations such as X-rays. The conventional CT pipeline includes reconstructing an image from projections and segmenting the reconstructed image for quantitative analysis.

However, in challenging situations, when projection data are noisy or limited, the reconstructed images can be degenerate, which can lead to incorrect segmentation results. Instead of reconstructing images, the main goal of the thesis is to develop direct tomographic segmentation methods from projections for homogeneous objects.

This goal is achieved by representing objects using triangle meshes and deforming them to be aligned with the boundaries of the scanned objects. In this regard, we propose two direct segmentation methods. The first method addresses mesh deformation in 2D space with the advantage of topological adaptivity during deformation.

The second proposed method tackles 3D shape estimation directly from projections. We extend recent results on differentiable rendering to tomographic reconstruction and this extension enables optimizing 3D shapes from projections. The experimental results in electron tomography show the effectiveness of our method for reconstructing shapes of some nano-particles.

Also, we investigate another representation of objects using coordinate-based neural networks for tomographic reconstruction. Finally, the thesis studies a regularization term using a vectorial total variation norm for spectral CT. The proposed regularization term is demonstrated to benefit spectral CT data with the potential to be of practical use in security applications.