Metrics on Shape Spaces

AOOD Program working group

Principal Component Analysis  depends on two metrics, a sample-based metric specified by a sample covariance matrix and a base metric usually specified by the identity matrix.  In Functional Data Analysis, the base metric is often specified in terms of a differential operator to ensure a certain level of smoothness.
In this group we shall explore how to adapt these ideas to shape spaces, e.g. of landmarks, curves and surfaces.