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Riemannian Elasticity: A Statistical Regularization Framework

Summary: Riemannian Elasticity: A Statistical
Regularization Framework
for Non-linear Registration
X. Pennec, R. Stefanescu, V. Arsigny, P. Fillard, and N. Ayache
INRIA Sophia - Projet Epidaure, 2004 Route des Lucioles BP 93,
06902 Sophia Antipolis Cedex, France
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 deforma-
tion from a rigid transformation. By changing the Euclidean metric for a
more suitable Riemannian one, we define a consistent statistical frame-
work 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


Source: Ayache, Nicholas - INRIA


Collections: Computer Technologies and Information Sciences; Engineering