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Description

A variety of anatomical structures in human brain can be represented as functions (curves or surfaces) on intervals or spheres. Examples of curves include DTI fiber tracts and sulcal folds while examples of surfaces include subcortical structures (hippocampus, thalamus, putamen, etc). Morphological analysis and statistical modeling of such data faces the following challenges: the representation spaces are curved, the data is seldom registered, the classical Hilbert structure is problematic, and (nowdays) there is a tremendous amount of data to deal with. Many current methods handle these challenges as pre-processing, using off the shelf software, resulting in sub-optimal solutions. Elastic FDA provides a unified framework for dealing with nonlinear geometries and simultaneous registration of function data, and leads to efficient computer algorithms. It has proven to outperform all recent methods in registering functional data. The FPCA, resulting from linearized representations under elastic Riemannian metrics, has been used for solving regression and testing under appropriate models. I will present some recent extensions of this work involving morphological analysis of tree-like structures such as neurons.