Diffeomorphic registration using geodesic shooting and Gauss-Newton optimisation

This paper presents a nonlinear image registration algorithm based on the setting of Large Deformation Diffeomorphic Metric Mapping (LDDMM). but with a more efficient optimisation scheme - both in terms of memory required and the number of iterations required to reach convergence. Rather than perform a variational optimisation on a series of velocity fields, the algorithm is formulated to use a geodesic shooting procedure, so that only an initial velocity is estimated. A Gauss-Newton optimisation strategy is used to achieve faster convergence. The algorithm was evaluated using freely available manually labelled datasets, and found to compare favourably with other inter-subject registration algorithms evaluated using the same data. (C) 2011 Elsevier Inc. All rights reserved

PDE-constrained LDDMM via geodesic shooting and inexact Gauss-Newton-Krylov optimization using the incremental adjoint Jacobi equations

The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. Inexact Newton-Krylov optimization has shown an excellent numerical accuracy and an extraordinarily fast convergence rate in this framework. However, the Galerkin representation of the non-stationary velocity fields does not provide proper geodesic paths. In this work, we propose a method for PDE-constrained LDDMM parameterized in the space of initial velocity fields under the EPDiff equation. The derivation of the gradient and the Hessian-vector products are performed on the final velocity field and transported backward using the adjoint and the incremental adjoint Jacobi equations. This way, we avoid the complex dependence on the initial velocity field in the derivations and the computation of the adjoint equation and its incremental counterpart. The proposed method provides geodesics in the framework of PDE-constrained LDDMM, and it shows performance competitive to benchmark PDE-constrained LDDMM and EPDiff-LDDMM methods

An Algorithm for Learning Shape and Appearance Models without Annotations

This paper presents a framework for automatically learning shape and appearance models for medical (and certain other) images. It is based on the idea that having a more accurate shape and appearance model leads to more accurate image registration, which in turn leads to a more accurate shape and appearance model. This leads naturally to an iterative scheme, which is based on a probabilistic generative model that is fit using Gauss-Newton updates within an EM-like framework. It was developed with the aim of enabling distributed privacy-preserving analysis of brain image data, such that shared information (shape and appearance basis functions) may be passed across sites, whereas latent variables that encode individual images remain secure within each site. These latent variables are proposed as features for privacy-preserving data mining applications. The approach is demonstrated qualitatively on the KDEF dataset of 2D face images, showing that it can align images that traditionally require shape and appearance models trained using manually annotated data (manually defined landmarks etc.). It is applied to MNIST dataset of handwritten digits to show its potential for machine learning applications, particularly when training data is limited. The model is able to handle ``missing data'', which allows it to be cross-validated according to how well it can predict left-out voxels. The suitability of the derived features for classifying individuals into patient groups was assessed by applying it to a dataset of over 1,900 segmented T1-weighted MR images, which included images from the COBRE and ABIDE datasets.Comment: 61 pages, 16 figures (some downsampled by a factor of 4), submitted to MedI

Flexible Bayesian Modelling for Nonlinear Image Registration

We describe a diffeomorphic registration algorithm that allows groups of images to be accurately aligned to a common space, which we intend to incorporate into the SPM software. The idea is to perform inference in a probabilistic graphical model that accounts for variability in both shape and appearance. The resulting framework is general and entirely unsupervised. The model is evaluated at inter-subject registration of 3D human brain scans. Here, the main modeling assumption is that individual anatomies can be generated by deforming a latent 'average' brain. The method is agnostic to imaging modality and can be applied with no prior processing. We evaluate the algorithm using freely available, manually labelled datasets. In this validation we achieve state-of-the-art results, within reasonable runtimes, against previous state-of-the-art widely used, inter-subject registration algorithms. On the unprocessed dataset, the increase in overlap score is over 17%. These results demonstrate the benefits of using informative computational anatomy frameworks for nonlinear registration.Comment: Accepted for MICCAI 202

Symmetric diffeomorphic modeling of longtudinal structural MRI

This technology report describes the longitudinal registration approach that we intend to incorporate into SPM12. It essentially describes a group-wise intra-subject modeling framework, which combines diffeomorphic and rigid-body registration, incorporating a correction for the intensity inhomogeneity artifact usually seen in MRI data. Emphasis is placed on achieving internal consistency and accounting for many of the mathematical subtleties that most implementations overlook. The implementation was evaluated using examples from the OASIS Longitudinal MRI Data in Non-demented and Demented Older Adults

Diffeomorphic brain shape modelling using Gauss-Newton optimisation

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