Quantitative Analysis of Open Curves in Brain Imaging: Applications to White Matter Fibers and Sulci

Meenakshi Mani 1
1 VisAGeS - Vision, Action et Gestion d'informations en Santé
INSERM - Institut National de la Santé et de la Recherche Médicale : U746, Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : There are about a hundred sulci in the human brain and over a hundred billion white matter fibers. These two anatomical structures differ in their number, their physical arrangements and in the function they serve but they do share a common geometric description: they are both open continuous curves. This thesis is a study of how the physical attributes of open curves can be used to advantage in the many varied quantitative applications of sulci and white matter fibers. Shape, scale, orientation and position, the four physical features associated with open curves, have different properties so the usual approach has been to design different metrics and spaces to treat them individually. We take an alternative approach using a comprehensive Riemannian framework where joint feature spaces allow for analysis of combinations of features. We can compare curves by using geodesic distances which quantify their differences. We validate the metrics we use, demonstrate practical uses and apply the tools to important clinical problems. To begin, specific tract configurations in the corpus callosum are used to showcase clustering results that depend on the Riemannian distance metric used. This nicely argues for the judicious selection of metrics in various applications, a central premise in our work. The framework also provides tools for computing statistical summaries of curves. We represent fiber bundles with a mean and variance which describes their essential characteristics. This is both a convenient way to work with a large volume of fibers and is a first step towards statistical analysis. Next, we design and implement methods to detect morphological changes which can potentially track progressive white matter disease. With sulci, we address the specific problem of labeling. An evaluation of physical features and methods such as clustering leads us to a pattern matching solution in which the sulcal configuration itself is the best feature
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Meenakshi Mani. Quantitative Analysis of Open Curves in Brain Imaging: Applications to White Matter Fibers and Sulci. Medical Imaging. Université Rennes 1, 2011. English. ⟨tel-00851505⟩

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