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Explore fiber bundle theory and its applications in probabilistic modeling for shapes and surfaces in this 54-minute lecture. Delve into geometric morphometrics, focusing on evolutionary biology and biomedical applications. Learn about three key problems: regression using shapes as covariates, sub-shape or variable selection, and Gaussian process models indexed via fiber bundles. Discover how integral geometry concepts are applied to the first two problems, and examine the extension of diffusion-based approaches on fiber bundles to develop a hierarchical Bayesian Gaussian process model for the third problem.
