Efficient Hyperelastic Regularization for Registration

Sune Darkner, Michael Sass Hansen, Rasmus Larsen, Mads Fogtmann Hansen

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    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.
    Original languageEnglish
    Title of host publicationImage Analysis : 17th Scandinavian Conference, SCIA 2011 - Ystad, Sweden, May 2011 - Proceedings
    PublisherSpringer
    Publication date2011
    Pages295-305
    ISBN (Print)978-3-642-21226-0
    ISBN (Electronic)978-3-642-21227-7
    DOIs
    Publication statusPublished - 2011
    Event17th Scandinavian Conference on Image Analysis (SCIA) - Ystad Saltsjöbad, Ystad, Sweden
    Duration: 23 May 201127 May 2011
    http://www.maths.lth.se/vision/scia2011/

    Conference

    Conference17th Scandinavian Conference on Image Analysis (SCIA)
    LocationYstad Saltsjöbad
    CountrySweden
    CityYstad
    Period23/05/201127/05/2011
    Internet address
    SeriesLecture Notes in Computer Science
    Number6688
    ISSN0302-9743

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