Discrete Exterior Calculus and the Averaged Template Matching Equations
Anil Hirani
California Institute of Technology
ITS
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 an energy functional. To solve the template matching partial differential equations (PDEs) on irregular meshes, one must define discrete differential operators on such meshes, which need not be flat.
One possible approach, which we do not adopt, is to locally fit a smooth manifold to the mesh and define operators on that manifold. Instead, we take a purely discrete approach, working directly with the given mesh and developing operators that satisfy properties analogous to those of their smooth counterparts.
We describe this recently developed calculus for meshes, which we call Discrete Exterior Calculus. We also discuss why such a framework may be useful for solving equations such as the template matching PDEs.
For more details, see the referenced materials by the author.
