Diffeomorphic brain shape modelling using Gauss-Newton optimisation

TL;DR

This paper introduces a generative shape model for brain images that captures deformation variability efficiently using Gauss-Newton optimization, enabling detailed 3D neuroimaging analysis without reducing model flexibility.

Contribution

The paper presents a novel diffeomorphic shape modelling approach with an efficient inference scheme that maintains deformation complexity for accurate brain shape analysis.

Findings

Successfully trained on OASIS brain data

Generated meaningful deformation trajectories

Achieved consistent fitting scores on unseen data

Abstract

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.