This thesis presents a pipeline of methods that facilitate the analysis of biomarkers on the cortex of the brain. The pipeline includes a topology-aware Laplacian thickness, a novel method for the measurement of cortical thickness which incorporates global topology information; the SAVOR framework, a novel framework for registering intra- and inter-subject cortical surfaces based on topology-preserving surface projection of volumetrically aligned cortical surfaces; and a suite of established statistical tools that are well-suited for the analysis of small population, high-dimensional population studies. We present the formulation and validation of these methods and present an illustrative application of the pipeline to the study of Alzheimer's disease.
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