Traditional longitudinal analysis begins by extracting desired clinical measurements, such as volume or head
circumference, from discrete imaging data. Typically, the continuous evolution of a scalar measurement is
estimated by choosing a 1D regression model, such as kernel regression or fitting a polynomial of fixed degree.
This type of analysis not only leads to separate models for each measurement, but there is no clear anatomical
or biological interpretation to aid in the selection of the appropriate paradigm. In this paper, we propose a
consistent framework for the analysis of longitudinal data by estimating the continuous evolution of shape over
time as twice differentiable flows of deformations. In contrast to 1D regression models, one model is chosen to
realistically capture the growth of anatomical structures. From the continuous evolution of shape, we can simply
extract any clinical measurements of interest. We demonstrate on real anatomical surfaces that volume extracted
from a continuous shape evolution is consistent with a 1D regression performed on the discrete measurements.
We further show how the visualization of shape progression can aid in the search for significant measurements.
Finally, we present an example on a shape complex of the brain (left hemisphere, right hemisphere, cerebellum)
that demonstrates a potential clinical application for our framework.