A Probabilistic Approach To Non-Rigid Medical Image Registration

Non-rigid image registration is an important tool for analysing morphometric differences in subjects with Alzheimer's disease from structural magnetic resonance images of the brain. This thesis describes a novel probabilistic approach to non-rigid registration of medical images, and explores the benefits of its use in this area of neuroimaging. Many image registration approaches have been developed for neuroimaging. The vast majority suffer from two limitations: Firstly, the trade-off between image fidelity and regularisation requires selection. Secondly, only a point-estimate of the mapping between images is inferred, overlooking the presence of uncertainty in the estimation. This thesis introduces a novel probabilistic non-rigid registration model and inference scheme. This framework allows the inference of the parameters that control the level of regularisation, and data fidelity in a data-driven fashion. To allow greater flexibility, this model is extended to allow the level of data fidelity to vary across space. A benefit of this approach, is that the registration can adapt to anatomical variability and other image acquisition differences. A further advantage of the proposed registration framework is that it provides an estimate of the distribution of probable transformations. Additional novel contributions of this thesis include two proposals for exploiting the estimated registration uncertainty. The first of these estimates a local image smoothing filter, which is based on the registration uncertainty. The second approach incorporates the distribution of transformations into an ensemble learning scheme for statistical prediction. These techniques are integrated into standard frameworks for morphometric analysis, and are demonstrated to improve the ability to distinguish subjects with Alzheimer's disease from healthy controls

Fast Predictive Multimodal Image Registration

We introduce a deep encoder-decoder architecture for image deformation prediction from multimodal images. Specifically, we design an image-patch-based deep network that jointly (i) learns an image similarity measure and (ii) the relationship between image patches and deformation parameters. While our method can be applied to general image registration formulations, we focus on the Large Deformation Diffeomorphic Metric Mapping (LDDMM) registration model. By predicting the initial momentum of the shooting formulation of LDDMM, we preserve its mathematical properties and drastically reduce the computation time, compared to optimization-based approaches. Furthermore, we create a Bayesian probabilistic version of the network that allows evaluation of registration uncertainty via sampling of the network at test time. We evaluate our method on a 3D brain MRI dataset using both T1- and T2-weighted images. Our experiments show that our method generates accurate predictions and that learning the similarity measure leads to more consistent registrations than relying on generic multimodal image similarity measures, such as mutual information. Our approach is an order of magnitude faster than optimization-based LDDMM.Comment: Accepted as a conference paper for ISBI 201

Validating Dose Uncertainty Estimates Produced by AUTODIRECT: An Automated Program to Evaluate Deformable Image Registration Accuracy.

Deformable image registration is a powerful tool for mapping information, such as radiation therapy dose calculations, from one computed tomography image to another. However, deformable image registration is susceptible to mapping errors. Recently, an automated deformable image registration evaluation of confidence tool was proposed to predict voxel-specific deformable image registration dose mapping errors on a patient-by-patient basis. The purpose of this work is to conduct an extensive analysis of automated deformable image registration evaluation of confidence tool to show its effectiveness in estimating dose mapping errors. The proposed format of automated deformable image registration evaluation of confidence tool utilizes 4 simulated patient deformations (3 B-spline-based deformations and 1 rigid transformation) to predict the uncertainty in a deformable image registration algorithm's performance. This workflow is validated for 2 DIR algorithms (B-spline multipass from Velocity and Plastimatch) with 1 physical and 11 virtual phantoms, which have known ground-truth deformations, and with 3 pairs of real patient lung images, which have several hundred identified landmarks. The true dose mapping error distributions closely followed the Student t distributions predicted by automated deformable image registration evaluation of confidence tool for the validation tests: on average, the automated deformable image registration evaluation of confidence tool-produced confidence levels of 50%, 68%, and 95% contained 48.8%, 66.3%, and 93.8% and 50.1%, 67.6%, and 93.8% of the actual errors from Velocity and Plastimatch, respectively. Despite the sparsity of landmark points, the observed error distribution from the 3 lung patient data sets also followed the expected error distribution. The dose error distributions from automated deformable image registration evaluation of confidence tool also demonstrate good resemblance to the true dose error distributions. Automated deformable image registration evaluation of confidence tool was also found to produce accurate confidence intervals for the dose-volume histograms of the deformed dose

GOGMA: Globally-Optimal Gaussian Mixture Alignment

Gaussian mixture alignment is a family of approaches that are frequently used for robustly solving the point-set registration problem. However, since they use local optimisation, they are susceptible to local minima and can only guarantee local optimality. Consequently, their accuracy is strongly dependent on the quality of the initialisation. This paper presents the first globally-optimal solution to the 3D rigid Gaussian mixture alignment problem under the L2 distance between mixtures. The algorithm, named GOGMA, employs a branch-and-bound approach to search the space of 3D rigid motions SE(3), guaranteeing global optimality regardless of the initialisation. The geometry of SE(3) was used to find novel upper and lower bounds for the objective function and local optimisation was integrated into the scheme to accelerate convergence without voiding the optimality guarantee. The evaluation empirically supported the optimality proof and showed that the method performed much more robustly on two challenging datasets than an existing globally-optimal registration solution.Comment: Manuscript in press 2016 IEEE Conference on Computer Vision and Pattern Recognitio

Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data

Mathematical and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observation regimes. Our ability to do this relies on the specification of strongly informative prior models over the amplitude component of function variability. We provide two strategies for this critical choice: a data-driven approach that defines an empirical basis for the amplitude subspace based on available training data, and a shape-restricted approach when the relative location and number of local extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to separately model amplitude and phase variability inherent in functional data. We emphasize the importance of uncertainty quantification and visualization of these two components as they provide complementary information about the estimated functions. We validate the proposed framework using simulation studies, and real applications to estimation of fractional anisotropy profiles based on diffusion tensor imaging measurements, growth velocity functions and bone mineral density curves.No embarg

Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach

This paper introduces Quicksilver, a fast deformable image registration method. Quicksilver registration for image-pairs works by patch-wise prediction of a deformation model based directly on image appearance. A deep encoder-decoder network is used as the prediction model. While the prediction strategy is general, we focus on predictions for the Large Deformation Diffeomorphic Metric Mapping (LDDMM) model. Specifically, we predict the momentum-parameterization of LDDMM, which facilitates a patch-wise prediction strategy while maintaining the theoretical properties of LDDMM, such as guaranteed diffeomorphic mappings for sufficiently strong regularization. We also provide a probabilistic version of our prediction network which can be sampled during the testing time to calculate uncertainties in the predicted deformations. Finally, we introduce a new correction network which greatly increases the prediction accuracy of an already existing prediction network. We show experimental results for uni-modal atlas-to-image as well as uni- / multi- modal image-to-image registrations. These experiments demonstrate that our method accurately predicts registrations obtained by numerical optimization, is very fast, achieves state-of-the-art registration results on four standard validation datasets, and can jointly learn an image similarity measure. Quicksilver is freely available as an open-source software.Comment: Add new discussion