  Shape modelling describes methods aimed at capturing the natural variability
of shapes and commonly relies on probabilistic interpretations of
dimensionality reduction techniques such as principal component analysis. Due
to their computational complexity when dealing with dense deformation models
such as diffeomorphisms, previous attempts have focused on explicitly reducing
their dimension, diminishing de facto their flexibility and ability to model
complex shapes such as brains. In this paper, we present a generative model of
shape that allows the covariance structure of deformations to be captured
without squashing their domain, resulting in better normalisation. An efficient
inference scheme based on Gauss-Newton optimisation is used, which enables
processing of 3D neuroimaging data. We trained this algorithm on segmented
brains from the OASIS database, generating physiologically meaningful
deformation trajectories. To prove the model's robustness, we applied it to
unseen data, which resulted in equivalent fitting scores.
