Section: New Results

Bayesian Atlas Estimation for the Variability Analysis of Shape Complexes

Participants : Pietro Gori [Correspondant] , Olivier Colliot, Yulia Worbe, Linda Marrakchi-Kacem, Sophie Lecomte, Cyril Poupon, Andreas Hartmann, Nicholas Ayache, Stanley Durrleman.

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.

Figure 4. Atlas construction from a data set of left caudate nucleus and its associated fiber bundle that were segmented in images of patients with Gilles de la Tourette syndrome and controls. An initial template complex determines the topology of the model. Its shape is optimized given the patients data or the controls data only, thus resulting in two atlases showing different distributions of the fibers on the surface of the nucleus.

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