Riemannian elasticity: a statistical regularization framework for non-linear registration.

Abstract : 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.
Type de document :
Communication dans un congrès
J. Duncan and G. Gerig. International Conference on Medical Image computing and Computer-Assisted Intervention, Oct 2005, Palm Springs, CA, United States. Springer-Verlag, 3750 (Pt 2), pp.943-50, 2005, Lecture notes in computer science. 〈10.1007/11566489_116〉
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https://hal.inria.fr/inria-00502675
Contributeur : Pierre Fillard <>
Soumis le : jeudi 15 juillet 2010 - 14:34:15
Dernière modification le : jeudi 11 janvier 2018 - 16:39:58

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Xavier Pennec, R. Stefanescu, V. Arsigny, Pierre Fillard, Nicholas Ayache. Riemannian elasticity: a statistical regularization framework for non-linear registration.. J. Duncan and G. Gerig. International Conference on Medical Image computing and Computer-Assisted Intervention, Oct 2005, Palm Springs, CA, United States. Springer-Verlag, 3750 (Pt 2), pp.943-50, 2005, Lecture notes in computer science. 〈10.1007/11566489_116〉. 〈inria-00502675〉

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