Conference Paper

Efficient Hyperelastic Regularization for Registration.

DOI: 10.1007/978-3-642-21227-7_28 Conference: Image Analysis - 17th Scandinavian Conference, SCIA 2011, Ystad, Sweden, May 2011. Proceedings
Source: DBLP

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.

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