author = {Iglesias, J.~A. and Rumpf, M. and Scherzer, O.},
  title = {Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies},
  journal = {Found. Comput. Math.},
  year = {2017},
  volume = {Online First},
  abstract = {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 applications.},
  doi = {https://doi.org/10.1007/s10208-017-9357-9},
  fjournal = {Foundations of Computational Mathematics},
  url = {https://link.springer.com/content/pdf/10.1007%2Fs10208-017-9357-9.pdf}