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Bayesian Atlas Estimation for the Variability Analysis of Shape Complexes
Pietro Gori1,2, Olivier Colliot1,2, Yulia Worbe2, Linda Marrakchi-Kacem1,2,3, Sophie Lecomte1,2,3, Cyril Poupon3, Andreas Hartmann2, Nicholas Ayache4, and Stanley Durrleman1,2
1Aramis Project-Team, Inria Paris-Rocquencourt, Paris, France
2CNRS UMR 7225, Inserm UMR-S975, UPMC, CRICM, Paris, France
3Neurospin, CEA, Gif-Sur-Yvette, France
4Asclepios Project-Team, Inria Sophia Antipolis, Sophia Antipolis, France
Abstract. In this paper we propose a Bayesian framework for multi-object atlas estimation based on the metric of currents which permits to deal with both curves and surfaces without relying on point correspondence. This approach aims to study brain morphometry as a whole and not as a set of different components, focusing mainly on the shape and relative position of different anatomical structures which is fundamental in neuro-anatomical studies. We propose a generic algorithm to estimate templates of sets of curves (fiber bundles) and closed surfaces (sub-cortical structures) which have the same “form” (topology) of the shapes present in the population. This atlas construction method is based on a Bayesian framework which brings to two main improvements with respect to previous shape based methods. First, it allows to estimate from the data set a parameter specific to each object which was previously fixed by the user: the trade-off between data-term and regularity of deformations. In a multi-object analysis these parameters balance the contributions of the different objects and the need for an automatic estimation is even more crucial. Second, the covariance matrix of the deformation parameters is estimated during the atlas construction in a way which is less sensitive to the outliers of the population.
LNCS 8149, p. 267 ff.
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© Springer-Verlag Berlin Heidelberg 2013