352 Current Trends in Bayesian Methodology with Applications
surfaces termed square-root normal fields. This is the framework we describe
in the remainder of this chapter. In particular, we define a proper distance be-
tween shapes of surfaces under a s implified elastic Riemannian metric (hence
the title “elastic prior shape models”). We define a sha pe space of surfaces
and utilize it for statistical analysis. In particular, we describe a framework
for co mputing summary statistics of shapes such as the mean and covariance.
Using these, we learn Gaussian generative models o n the shape space and pro-
vide a recip e for random sampling. Obtaining representative random samples
of shapes of 3D objects is crucial in Bayesian modeling of shape data and