Scale-based decomposable shape representations for medical image segmentation and shape analysis
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In this thesis, we propose and evaluate two novel scale-based decomposable representations of shape for the segmentation and morphometric analysis of anatomical structures in medical imaging. We propose two representations that are adapted to a particular class of anatomical structures and allow for a richer shape description and a more fine-grained control over the deformation of models based on these representations, when compared to previous techniques. In the first part of this thesis, we introduce the concept of a scale-space shape filter for implicit shape representations that measures the deviation from a tubular shape in a local neighborhood of points, given a particular scale of analysis. We use these filters for the segmentation of blood vessels, and introduce the notion of segmentation with a soft shape prior, where the segmented model is not globally constrained to a predefined shape space, but is penalized locally if it deviates strongly from a tubular structure. Using this filter, we derive a region-based active contour segmentation algorithm for tubular structures that penalizes leakages. We present results on synthetic and real 2D and 3D datasets. In the second part of this thesis, we present a novel multi-scale parametric shape representation using spherical wavelets. Our proposed shape representation encodes shape variations in a population at various scales to be used as prior in a probabilistic segmentation framework. We derive a probabilistic active surface segmentation algorithm using the multi-scale prior coefficients as parameters for our optimization procedure. One nice benefit of this algorithm is that the optimization method can be applied in a coarse-to-fine manner. We present results on 3D sub-cortical brain structures. We also present a novel method of statistical surface-based morphometry based on the use of non-parametric permutation tests and the spherical wavelet shape representation. As an application, we analyze two sub-cortical brain structures, the caudate nucleus and hippocampus.