Efficient hyperelastic regularization for registration
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Efficient hyperelastic regularization for registration. / Darkner, Sune; Hansen, Michael Sass; Larsen, Rasmus; Hansen, Mads F.
Image Analysis: 17th Scandinavian Conference, SCIA 2011, Ystad, Sweden, May 2011. Proceedings. ed. / Anders Heyden; Fredrik Kahl. Springer, 2011. p. 295-305 (Lecture notes in computer science, Vol. 6688).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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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
Y2 - 23 May 2011 through 27 May 2011
ER -
ID: 170212111