Scale-based decomposable shape representations for medical image segmentation and shape analysis

In this thesis, we propose and evaluate two novel scale-based decomposable representations of shape for the segmentation and shape 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 description and a more fine-grained control over the deformation of models based on these representations, when compared to previous techniques. In particular, the decomposition of these shape representations can be localized both in space and in scale, enabling the construction of more descriptive, non-global, non-uniform shape priors to be included in the segmentation framework. For each representation, we derive a segmentation algorithm using the parameters of the shape representation to easily include and benefit from the prior in the optimization framework. We first review the two main classes of shape representation, parametric and implicit models, and discuss the impact of existing representations on the construction of data-driven or knowledge-driven shape priors and segmentation algorithms. In particular, we note that most shape priors fall either under the category of global priors, constraining the full shape model to a predefined shape space, or very local priors, constraining the smoothness of the model on a very local level. This thesis addresses the gap between the two categories by proposing and evaluating two novel multi-scale shape representations and shape probability priors adapted to particular classes of anatomical shapes. The first novel shape probability prior proposed by this thesis is a knowledge-driven semi-local prior using local shape filters that measure shape properties for implicit shape representations. 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. We introduce the concept of a scale-space shape filter that measures the deviation from a tubular shape in a local neighborhood of points, given a particular scale of analysis. 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. The second novel shape representation proposed by this thesis is a multi-scale parametric shape representation using spherical wavelets. This work is motivated by the need to compactly and accurately encode variations at multiple scales in the shape representation in order to drive the segmentation and shape analysis of deep brain structures, such as the caudate nucleus or the hippocampus. Our proposed shape representation can be optimized to compactly encode shape variations in a population at the needed scale and spatial locations, enabling the construction of more descriptive, non-global, non-uniform shape probability priors to be included in the segmentation and shape analysis framework. We apply this representation to two important medical imaging tasks, segmentation and shape analysis. For segmentation, we derive a parametric active surface evolution using the multiscale prior coefficients as parameters for our optimization procedure to naturally include the prior for segmentation. Additionally, the optimization method can be applied in a coarse-to-fine manner. Our results on synthetic and real data show that our algorithm is computationally efficient and outperforms the Active Shape Model (ASM) algorithm, by capturing finer shape details. For shape analysis, we use the coefficients of our shape representation as features to describe a population of shapes and perform hypothesis testing using an existing non-parametric permutation testing technique. The technique tests for shape differences in the caudate brain structure among twopopulation of patients with and without schizo-typal disorder. Our results show that significant differences are found among the group of patients, and in particular the spherical wavelet representation finds a greater number of locations on the shapes that exhibit a statistical shape difference among the shapes, when compared to a point distribution representation of the shapes.