Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
A Method for Registration of 3-D Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
The Correlation Ratio as a New Similarity Measure for Multimodal Image Registration
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
MICCAI '02 Proceedings of the 5th International Conference on Medical Image Computing and Computer-Assisted Intervention-Part I
Optimal registration of deformed images
Optimal registration of deformed images
Analysis of deformation of the human ear and canal caused by mandibular movement
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention
Riemannian elasticity: a statistical regularization framework for non-linear registration
MICCAI'05 Proceedings of the 8th international conference on Medical image computing and computer-assisted intervention - Volume Part II
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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.