345 research outputs found
A Statistical Model for Simultaneous Template Estimation, Bias Correction, and Registration of 3D Brain Images
Template estimation plays a crucial role in computational anatomy since it
provides reference frames for performing statistical analysis of the underlying
anatomical population variability. While building models for template
estimation, variability in sites and image acquisition protocols need to be
accounted for. To account for such variability, we propose a generative
template estimation model that makes simultaneous inference of both bias fields
in individual images, deformations for image registration, and variance
hyperparameters. In contrast, existing maximum a posterori based methods need
to rely on either bias-invariant similarity measures or robust image
normalization. Results on synthetic and real brain MRI images demonstrate the
capability of the model to capture heterogeneity in intensities and provide a
reliable template estimation from registration
Uncertainty quantification in non-rigid image registration via stochastic gradient Markov chain Monte Carlo
We develop a new Bayesian model for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backpropagation and the variational inference by backpropagation frameworks, in order to efficiently draw samples from the posterior distribution of transformation parameters. To address the modelling issues, we formulate a Bayesian model for image registration that overcomes the existing barriers when using a dense, high-dimensional, and diffeomorphic transformation parametrisation. This results in improved calibration of uncertainty estimates. We compare the model in terms of both image registration accuracy and uncertainty quantification to VoxelMorph, a state-of-the-art image registration model based on deep learning
A model of brain morphological changes related to aging and Alzheimer's disease from cross-sectional assessments
In this study we propose a deformation-based framework to jointly model the
influence of aging and Alzheimer's disease (AD) on the brain morphological
evolution. Our approach combines a spatio-temporal description of both
processes into a generative model. A reference morphology is deformed along
specific trajectories to match subject specific morphologies. It is used to
define two imaging progression markers: 1) a morphological age and 2) a disease
score. These markers can be computed locally in any brain region. The approach
is evaluated on brain structural magnetic resonance images (MRI) from the ADNI
database. The generative model is first estimated on a control population,
then, for each subject, the markers are computed for each acquisition. The
longitudinal evolution of these markers is then studied in relation with the
clinical diagnosis of the subjects and used to generate possible morphological
evolution. In the model, the morphological changes associated with normal aging
are mainly found around the ventricles, while the Alzheimer's disease specific
changes are more located in the temporal lobe and the hippocampal area. The
statistical analysis of these markers highlights differences between clinical
conditions even though the inter-subject variability is quiet high. In this
context, the model can be used to generate plausible morphological trajectories
associated with the disease. Our method gives two interpretable scalar imaging
biomarkers assessing the effects of aging and disease on brain morphology at
the individual and population level. These markers confirm an acceleration of
apparent aging for Alzheimer's subjects and can help discriminate clinical
conditions even in prodromal stages. More generally, the joint modeling of
normal and pathological evolutions shows promising results to describe
age-related brain diseases over long time scales.Comment: NeuroImage, Elsevier, In pres
Doctor of Philosophy in Computing
dissertationAn important area of medical imaging research is studying anatomical diffeomorphic shape changes and detecting their relationship to disease processes. For example, neurodegenerative disorders change the shape of the brain, thus identifying differences between the healthy control subjects and patients affected by these diseases can help with understanding the disease processes. Previous research proposed a variety of mathematical approaches for statistical analysis of geometrical brain structure in three-dimensional (3D) medical imaging, including atlas building, brain variability quantification, regression, etc. The critical component in these statistical models is that the geometrical structure is represented by transformations rather than the actual image data. Despite the fact that such statistical models effectively provide a way for analyzing shape variation, none of them have a truly probabilistic interpretation. This dissertation contributes a novel Bayesian framework of statistical shape analysis for generic manifold data and its application to shape variability and brain magnetic resonance imaging (MRI). After we carefully define the distributions on manifolds, we then build Bayesian models for analyzing the intrinsic variability of manifold data, involving the mean point, principal modes, and parameter estimation. Because there is no closed-form solution for Bayesian inference of these models on manifolds, we develop a Markov Chain Monte Carlo method to sample the hidden variables from the distribution. The main advantages of these Bayesian approaches are that they provide parameter estimation and automatic dimensionality reduction for analyzing generic manifold-valued data, such as diffeomorphisms. Modeling the mean point of a group of images in a Bayesian manner allows for learning the regularity parameter from data directly rather than having to set it manually, which eliminates the effort of cross validation for parameter selection. In population studies, our Bayesian model of principal modes analysis (1) automatically extracts a low-dimensional, second-order statistics of manifold data variability and (2) gives a better geometric data fit than nonprobabilistic models. To make this Bayesian framework computationally more efficient for high-dimensional diffeomorphisms, this dissertation presents an algorithm, FLASH (finite-dimensional Lie algebras for shooting), that hugely speeds up the diffeomorphic image registration. Instead of formulating diffeomorphisms in a continuous variational problem, Flash defines a completely new discrete reparameterization of diffeomorphisms in a low-dimensional bandlimited velocity space, which results in the Bayesian inference via sampling on the space of diffeomorphisms being more feasible in time. Our entire Bayesian framework in this dissertation is used for statistical analysis of shape data and brain MRIs. It has the potential to improve hypothesis testing, classification, and mixture models
Image registration via stochastic gradient markov chain monte carlo
We develop a fully Bayesian framework for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images along with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backprop and the variational inference by backprop frameworks in order to efficiently draw thousands of samples from the posterior distribution. Regarding the modelling issues, we carefully design a Bayesian model for registration to overcome the existing barriers when using a dense, high-dimensional, and diffeomorphic parameterisation of the transformation. This results in improved calibration of uncertainty estimates
Learning Conditional Deformable Templates with Convolutional Networks
We develop a learning framework for building deformable templates, which play
a fundamental role in many image analysis and computational anatomy tasks.
Conventional methods for template creation and image alignment to the template
have undergone decades of rich technical development. In these frameworks,
templates are constructed using an iterative process of template estimation and
alignment, which is often computationally very expensive. Due in part to this
shortcoming, most methods compute a single template for the entire population
of images, or a few templates for specific sub-groups of the data. In this
work, we present a probabilistic model and efficient learning strategy that
yields either universal or conditional templates, jointly with a neural network
that provides efficient alignment of the images to these templates. We
demonstrate the usefulness of this method on a variety of domains, with a
special focus on neuroimaging. This is particularly useful for clinical
applications where a pre-existing template does not exist, or creating a new
one with traditional methods can be prohibitively expensive. Our code and
atlases are available online as part of the VoxelMorph library at
http://voxelmorph.csail.mit.edu.Comment: NeurIPS 2019: Neural Information Processing Systems. Keywords:
deformable templates, conditional atlases, diffeomorphic image registration,
probabilistic models, neuroimagin
Stochastic Algorithm For Parameter Estimation For Dense Deformable Template Mixture Model
Estimating probabilistic deformable template models is a new approach in the
fields of computer vision and probabilistic atlases in computational anatomy. A
first coherent statistical framework modelling the variability as a hidden
random variable has been given by Allassonni\`ere, Amit and Trouv\'e in [1] in
simple and mixture of deformable template models. A consistent stochastic
algorithm has been introduced in [2] to face the problem encountered in [1] for
the convergence of the estimation algorithm for the one component model in the
presence of noise. We propose here to go on in this direction of using some
"SAEM-like" algorithm to approximate the MAP estimator in the general Bayesian
setting of mixture of deformable template model. We also prove the convergence
of this algorithm toward a critical point of the penalised likelihood of the
observations and illustrate this with handwritten digit images
CLAIRE: Scalable GPU-Accelerated Algorithms for Diffeomorphic Image Registration in 3D
We present our work on scalable, GPU-accelerated algorithms for diffeomorphic
image registration. The associated software package is termed CLAIRE. Image
registration is a non-linear inverse problem. It is about computing a spatial
mapping from one image of the same object or scene to another. In diffeomorphic
image registration, the set of admissible spatial transformations is restricted
to maps that are smooth, one-to-one, and have a smooth inverse. We formulate
diffeomorphic image registration as a variational problem governed by transport
equations. We use an inexact, globalized (Gauss--)Newton--Krylov method for
numerical optimization. We consider semi-Lagrangian methods for numerical time
integration. Our solver features mixed-precision, hardware-accelerated
computational kernels for optimal computational throughput. We use the
message-passing interface for distributed-memory parallelism and deploy our
code on modern high-performance computing architectures. Our solver allows us
to solve clinically relevant problems in under four seconds on a single GPU. It
can also be applied to large-scale 3D imaging applications with data that is
discretized on meshes with billions of voxels. We demonstrate that our
numerical framework yields high-fidelity results in only a few seconds, even if
we search for an optimal regularization parameter
Gaussian Process Morphable Models
Statistical shape models (SSMs) represent a class of shapes as a normal
distribution of point variations, whose parameters are estimated from example
shapes. Principal component analysis (PCA) is applied to obtain a
low-dimensional representation of the shape variation in terms of the leading
principal components. In this paper, we propose a generalization of SSMs,
called Gaussian Process Morphable Models (GPMMs). We model the shape variations
with a Gaussian process, which we represent using the leading components of its
Karhunen-Loeve expansion. To compute the expansion, we make use of an
approximation scheme based on the Nystrom method. The resulting model can be
seen as a continuous analogon of an SSM. However, while for SSMs the shape
variation is restricted to the span of the example data, with GPMMs we can
define the shape variation using any Gaussian process. For example, we can
build shape models that correspond to classical spline models, and thus do not
require any example data. Furthermore, Gaussian processes make it possible to
combine different models. For example, an SSM can be extended with a spline
model, to obtain a model that incorporates learned shape characteristics, but
is flexible enough to explain shapes that cannot be represented by the SSM. We
introduce a simple algorithm for fitting a GPMM to a surface or image. This
results in a non-rigid registration approach, whose regularization properties
are defined by a GPMM. We show how we can obtain different registration
schemes,including methods for multi-scale, spatially-varying or hybrid
registration, by constructing an appropriate GPMM. As our approach strictly
separates modelling from the fitting process, this is all achieved without
changes to the fitting algorithm. We show the applicability and versatility of
GPMMs on a clinical use case, where the goal is the model-based segmentation of
3D forearm images
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