Topology preserving and robust variational image segmentation models with applications in medical imaging
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Computer vision refers to the process of enabling computers to mimic the human visual system. The central concern of this thesis is a sub-task of computer vision known as image segmentation, which refers to the decomposition of an image into its most relevant regions. Image segmentation by its nature is a poorly defined task, considering that what constitutes the `best' decomposition of an image changes according to the task at hand. In this context, the specific focus of this thesis is to investigate the general topic of segmentation robustness; toward this goal, three aspects of this topic have been explored, with a new algorithm proposed in each case.The first algorithm addresses the problem of boundary detection in low-contrast images. The proposed technique consists in solving the well-known Mumford-Shah functional using a highly efficient convex segmentation scheme, the output of which is a simplified binary representation of the original image. Using this binary representation, an edge detector is generated, the output of which is input into a geodesic active contour scheme to produce the final curve representing the boundary of the structure. Results indicate that the proposed scheme yields enhanced performance compared to existing methods. The second algorithm addresses the issue of robustness with respect to topology preservation. In this context, a segmentation model is proposed that consists of a non-local topology preserving constraint and a data fidelity constraint that increases robustness in the presence of noise. Results indicate that the proposed method performs better than existing methods at imposing a topology prior in the presence of noise. The third algorithm consists of a novel approach for lung nodule candidate detection in Computed Tomography which is based on the application of global segmentation methods combined with mean curvature minimisation and simple rule-based filtering. Nodules with vascular connection tend to be characterised by irregular geometrical features that make them difficult to detect using local image metrics. Experimental results indicate that the proposed method can accurately detect nodules exhibiting a diverse range geometrical features. Taken together, the proposed techniques improve robustness in three important areas; namely, robustness with respect to image features, robustness with respect to topology preservation and finally, robustness with respect to diverse geometrical features of the target object.
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