Efficient hyperelastic regularization for registration

TY - GEN

T1 - Efficient hyperelastic regularization for registration

AU - Darkner, Sune

AU - Hansen, Michael Sass

AU - Larsen, Rasmus

AU - Hansen, Mads F

N1 - Conference code: 17

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-642-21227-7_28

DO - 10.1007/978-3-642-21227-7_28

M3 - Article in proceedings

SN - 978-3-642-21226-0

T3 - Lecture notes in computer science

SP - 295

EP - 305

BT - Image Analysis

A2 - Heyden, Anders

A2 - Kahl, Fredrik

PB - Springer

T2 - 17th Scandinavian Conference on Image Analysis

Y2 - 23 May 2011 through 27 May 2011

ER -