Efficient Hyperelastic Regularization for Registration.
ABSTRACT For most image registration problems a smooth one-to-one mapping is desirable, a diffeomorphism. This can be obtained using
priors such as volume preservation, certain kinds of elasticity or both. The key principle is to regularize the strain of
the deformation which can be done through penalization of the eigen values of the stress tensor. We present a computational
framework for regularization of image registration for isotropic hyper elasticity. We formulate an efficient and parallel
scheme for computing the principal stain based for a given parameterization by decomposing the left Cauchy-Green strain tensor
and deriving analytical derivatives of the principal stretches as a function of the deformation, guaranteeing a diffeomorphism
in every evaluation point. Hyper elasticity allows us to handle large deformation without re-meshing. The method is general
and allows for the well-known hyper elastic priors such at the Saint Vernant Kirchoff model, the Ogden material model or Riemanian
elasticity. We exemplify the approach through synthetic registration and special tests as well as registration of different
modalities; 2D cardiac MRI and 3D surfaces of the human ear. The artificial examples illustrate the degree of deformation
the formulation can handle numerically. Numerically the computational complexity is no more than 1.45 times the computational
complexity of Sum of Squared Differences.
- SourceAvailable from: ftp-sop.inria.frMedical Image Computing and Computer-Assisted Intervention - MICCAI 2005, 8th International Conference, Palm Springs, CA, USA, October 26-29, 2005, Proceedings, Part II; 01/2005
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ABSTRACT: We describe a framework for registering a group of images together using a set of non-linear diffeomorphic warps. The result of the groupwise registration is an implicit definition of dense correspondences between all of the images in a set, which can be used to construct statistical models of shape change across the set, avoiding the need for manual annotation of training images. We give examples on two datasets (brains and faces) and show the resulting models of shape and appearance variation. We show results of experiments demonstrating that the groupwise approach gives a more reliable correspondence than pairwise matching alone.Computer Vision - ECCV 2004, 8th European Conference on Computer Vision, Prague, Czech Republic, May 11-14, 2004. Proceedings, Part IV; 01/2004