Efficient Hyperelastic Regularization for Registration

  • Sune Darkner
  • Michael Sass Hansen
  • Rasmus Larsen
  • Mads F. Hansen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6688)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sune Darkner
    • 1
  • Michael Sass Hansen
    • 2
  • Rasmus Larsen
    • 2
  • Mads F. Hansen
    • 2
  1. 1.eScience Center, Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark
  2. 2.DTU InformaticsTechnical University of DenmarkLyngbyDenmark

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