We introduce a novel geometric framework for separating, analyzing and
modeling the $x$ (or horizontal) and the $y$ (or vertical) variability in
time-warped functional data of the type frequently studied in growth curve
analysis. This framework is based on the use of the Fisher-Rao Riemannian
metric that provides a proper distance for: (1) aligning, comparing and
modeling functions and (2) analyzing the warping functions.