Discrete Exterior Calculus and the Averaged Template Matching Equations

Anil Hirani
California Institute of Technology

Template matching is a common paradigm in computational anatomy and image
matching, in which one image or data set is morphed into another while minimizing some
energy. In order to solve the template matching PDEs on irregular meshes, one needs to
define discrete differential operators on such meshes, which need not be flat. One
approach, which we do not take, is to locally fit a smooth manifold to the mesh, and
define operators on that. We take a purely discrete approach, work with only the given
mesh, and develop operators that satisfy properties analogous to their smooth
counterparts. We will describe this calculus for meshes that we have developed recently
and which we call Discrete Exterior Calculus. We will also describe why such a calculus
might be useful in solving equations like the template matching PDEs.

For more details, please see

Presentation (PDF File)

Back to Graduate Summer School: Mathematics in Brain Imaging