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2018 | OriginalPaper | Buchkapitel

Diffeomorphic Brain Shape Modelling Using Gauss-Newton Optimisation

verfasst von : Yaël Balbastre, Mikael Brudfors, Kevin Bronik, John Ashburner

Erschienen in: Medical Image Computing and Computer Assisted Intervention – MICCAI 2018

Verlag: Springer International Publishing

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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.

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Fußnoten
1
We assume that they all have the same lattice, but this condition can be waived by composing each diffeomorphic transform with a fixed “change of lattice” transform, which can even embed a rigid-body alignment.
 
2
In this work, it is a combination of membrane, bending and linear-elastic energies.
 
3
The initial velocity of \(\varvec{\phi }\) is the opposite of the final velocity of \(\varvec{\phi }^{-1}\), and vice versa.
 
4
The Gamma prior is a parameterised such that \(\mathbb {E}\left[ \lambda \right] = \lambda _0\).
 
5
q is used for approximate posteriors and \(\mathbb {E}_q\) for posterior expected values. Superscript stars denote optimal approximations. https://static-content.springer.com/image/chp%3A10.1007%2F978-3-030-00928-1_97/473972_1_En_97_IEq38_HTML.gif means “equal up to an additive constant”.
 
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Metadaten
Titel
Diffeomorphic Brain Shape Modelling Using Gauss-Newton Optimisation
verfasst von
Yaël Balbastre
Mikael Brudfors
Kevin Bronik
John Ashburner
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-030-00928-1_97