  A shape sensitive, variational approach for the matching of surfaces
considered as thin elastic shells is investigated. The elasticity functional to
be minimized takes into account two different types of nonlinear energies: a
membrane energy measuring the rate of tangential distortion when deforming the
reference shell into the template shell, and a bending energy measuring the
bending under the deformation in terms of the change of the shape operators
from the undeformed into the deformed configuration. The variational method
applies to surfaces described as level sets. It is mathematically well-posed
and an existence proof of an optimal matching deformation is given. The
variational model is implemented using a finite element discretization combined
with a narrow band approach on an efficient hierarchical grid structure. For
the optimization a regularized nonlinear conjugate gradient scheme and a
cascadic multilevel strategy are used. The features of the proposed approach
are studied for synthetic test cases and a collection of geometry processing
examples.
