Multiresolution elastic matching
Computer Vision, Graphics, and Image Processing
Non-linear Registration with the Variable Viscosity Fluid Algorithm
IPMI '99 Proceedings of the 16th International Conference on Information Processing in Medical Imaging
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Fast and simple calculus on tensors in the log-euclidean framework
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Extrapolation of sparse tensor fields: application to the modeling of brain variability
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Statistical Computing on Manifolds: From Riemannian Geometry to Computational Anatomy
Emerging Trends in Visual Computing
Mean template for tensor-based morphometry using deformation tensors
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention
Efficient hyperelastic regularization for registration
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
A log-euclidean framework for statistics on diffeomorphisms
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Simultaneous multiscale polyaffine registration by incorporating deformation statistics
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
Computer Vision and Image Understanding
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In inter-subject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the re-introduction in a registration algorithm is not easy. In this paper, we interpret the elastic energy as the distance of the Green-St Venant strain tensor to the identity, which reflects the deviation of the local deformation from a rigid transformation. By changing the Euclidean metric for a more suitable Riemannian one, we define a consistent statistical framework to quantify the amount of deformation. In particular, the mean and the covariance matrix of the strain tensor can be consistently and efficiently computed from a population of non-linear transformations. These statistics are then used as parameters in a Mahalanobis distance to measure the statistical deviation from the observed variability, giving a new regularization criterion that we called the statistical Riemannian elasticity. This new criterion is able to handle anisotropic deformations and is inverse-consistent. Preliminary results show that it can be quite easily implemented in a non-rigid registration algorithms.