author = {Droske, M. and Rumpf, M.},
  title = {A Variational Approach to Non-Rigid Morphological Registration},
  journal = {SIAM Journal on Applied Mathematics},
  year = {2004},
  volume = {64},
  pages = {668--687},
  number = {2},
  abstract = {A variational method to non rigid registration of multi-modal image
	data is presented. A suitable deformation will be determined via
	the minimization of a morphological, i.e., contrast invariant, matching
	functional along with an appropriate regularization energy. The aim
	is to correlate the morphologies of a template and a reference image
	under the deformation. Mathematically, the morphology of images can
	be described by the entity of level sets of the image and hence by
	its Gauss map. A class of morphological matching functionals is presented
	which measure the defect of the template Gauss map in the deformed
	state with respect to the deformed Gauss map of the reference image.
	The problem is regularized by considering a nonlinear elastic regularization
	energy. Existence of homeomorphic, minimizing deformation is proved
	under assumptions on the class of admissible deformations. With respect
	to actual medical applications suitable generalizations of the matching
	energies and the boundary conditions are presented. Concerning the
	robust implementation of the approach the problem is embedded in
	a multi-scale context. A discretization based on multi-linear finite
	elements is discussed and first numerical results are presented.},
  digital = {1},
  pdf = { 1},
  printed = {1}