Metrics on the Space of Shapes, and Applications to Biology
Joel Hass (Davis and IAS)
Abstract: The problem of comparing shapes turns up in different guises in numerous
fields. I will discuss a new metric on the space of smooth Riemannian
2-spheres that is well suited for comparing geometric similarity. The
metric is based on a distortion energy defined on the space
of diffeomorphisms between a pair of genus-zero surfaces.
I’ll also discuss a related idea based on hyperbolic orbifold structures
on a surface.
I will also present results of experiments on applying these ideas to biological
data.
This involves comparing the similarity of collections of teeth, bones, proteins and
brain cortices.
This is joint work with Patrice Koehl.