Diffeomorphic brain shape modelling using Gauss-Newton optimisation
This work addresses the problem of flexible and efficient brain shape modeling for neuroimaging researchers, offering an incremental improvement over previous methods.
The paper tackles the computational complexity of shape modeling with dense deformation models like diffeomorphisms, which often requires reducing dimensionality and limits flexibility for complex shapes like brains. It presents a generative model that captures deformation covariance without domain reduction, using Gauss-Newton optimization to process 3D neuroimaging data, achieving equivalent fitting scores on unseen data from the OASIS database.
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.