18,767 research outputs found
An inexact Newton-Krylov algorithm for constrained diffeomorphic image registration
We propose numerical algorithms for solving large deformation diffeomorphic
image registration problems. We formulate the nonrigid image registration
problem as a problem of optimal control. This leads to an infinite-dimensional
partial differential equation (PDE) constrained optimization problem.
The PDE constraint consists, in its simplest form, of a hyperbolic transport
equation for the evolution of the image intensity. The control variable is the
velocity field. Tikhonov regularization on the control ensures well-posedness.
We consider standard smoothness regularization based on - or
-seminorms. We augment this regularization scheme with a constraint on the
divergence of the velocity field rendering the deformation incompressible and
thus ensuring that the determinant of the deformation gradient is equal to one,
up to the numerical error.
We use a Fourier pseudospectral discretization in space and a Chebyshev
pseudospectral discretization in time. We use a preconditioned, globalized,
matrix-free, inexact Newton-Krylov method for numerical optimization. A
parameter continuation is designed to estimate an optimal regularization
parameter. Regularity is ensured by controlling the geometric properties of the
deformation field. Overall, we arrive at a black-box solver. We study spectral
properties of the Hessian, grid convergence, numerical accuracy, computational
efficiency, and deformation regularity of our scheme. We compare the designed
Newton-Krylov methods with a globalized preconditioned gradient descent. We
study the influence of a varying number of unknowns in time.
The reported results demonstrate excellent numerical accuracy, guaranteed
local deformation regularity, and computational efficiency with an optional
control on local mass conservation. The Newton-Krylov methods clearly
outperform the Picard method if high accuracy of the inversion is required.Comment: 32 pages; 10 figures; 9 table
Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems
Diffeomorphic Iterative Centroid Methods for Template Estimation on Large Datasets
International audienceA common approach for analysis of anatomical variability relies on the stimation of a template representative of the population. The Large Deformation Diffeomorphic Metric Mapping is an attractive framework for that purpose. However, template estimation using LDDMM is computationally expensive, which is a limitation for the study of large datasets. This paper presents an iterative method which quickly provides a centroid of the population in the shape space. This centroid can be used as a rough template estimate or as initialization of a template estimation method. The approach is evaluated on datasets of real and synthetic hippocampi segmented from brain MRI. The results show that the centroid is correctly centered within the population and is stable for different orderings of subjects. When used as an initialization, the approach allows to substantially reduce the computation time of template estimation
Inter-individual deep image reconstruction via hierarchical neural code conversion
The sensory cortex is characterized by general organizational principles such as topography and hierarchy. However, measured brain activity given identical input exhibits substantially different patterns across individuals. Although anatomical and functional alignment methods have been proposed in functional magnetic resonance imaging (fMRI) studies, it remains unclear whether and how hierarchical and fine-grained representations can be converted between individuals while preserving the encoded perceptual content. In this study, we trained a method of functional alignment called neural code converter that predicts a target subject’s brain activity pattern from a source subject given the same stimulus, and analyzed the converted patterns by decoding hierarchical visual features and reconstructing perceived images. The converters were trained on fMRI responses to identical sets of natural images presented to pairs of individuals, using the voxels on the visual cortex that covers from V1 through the ventral object areas without explicit labels of the visual areas. We decoded the converted brain activity patterns into the hierarchical visual features of a deep neural network using decoders pre-trained on the target subject and then reconstructed images via the decoded features. Without explicit information about the visual cortical hierarchy, the converters automatically learned the correspondence between visual areas of the same levels. Deep neural network feature decoding at each layer showed higher decoding accuracies from corresponding levels of visual areas, indicating that hierarchical representations were preserved after conversion. The visual images were reconstructed with recognizable silhouettes of objects even with relatively small numbers of data for converter training. The decoders trained on pooled data from multiple individuals through conversions led to a slight improvement over those trained on a single individual. These results demonstrate that the hierarchical and fine-grained representation can be converted by functional alignment, while preserving sufficient visual information to enable inter-individual visual image reconstruction
Distributed-memory large deformation diffeomorphic 3D image registration
We present a parallel distributed-memory algorithm for large deformation
diffeomorphic registration of volumetric images that produces large isochoric
deformations (locally volume preserving). Image registration is a key
technology in medical image analysis. Our algorithm uses a partial differential
equation constrained optimal control formulation. Finding the optimal
deformation map requires the solution of a highly nonlinear problem that
involves pseudo-differential operators, biharmonic operators, and pure
advection operators both forward and back- ward in time. A key issue is the
time to solution, which poses the demand for efficient optimization methods as
well as an effective utilization of high performance computing resources. To
address this problem we use a preconditioned, inexact, Gauss-Newton- Krylov
solver. Our algorithm integrates several components: a spectral discretization
in space, a semi-Lagrangian formulation in time, analytic adjoints, different
regularization functionals (including volume-preserving ones), a spectral
preconditioner, a highly optimized distributed Fast Fourier Transform, and a
cubic interpolation scheme for the semi-Lagrangian time-stepping. We
demonstrate the scalability of our algorithm on images with resolution of up to
on the "Maverick" and "Stampede" systems at the Texas Advanced
Computing Center (TACC). The critical problem in the medical imaging
application domain is strong scaling, that is, solving registration problems of
a moderate size of ---a typical resolution for medical images. We are
able to solve the registration problem for images of this size in less than
five seconds on 64 x86 nodes of TACC's "Maverick" system.Comment: accepted for publication at SC16 in Salt Lake City, Utah, USA;
November 201
Aligning individual brains with Fused Unbalanced Gromov-Wasserstein
Individual brains vary in both anatomy and functional organization, even
within a given species. Inter-individual variability is a major impediment when
trying to draw generalizable conclusions from neuroimaging data collected on
groups of subjects. Current co-registration procedures rely on limited data,
and thus lead to very coarse inter-subject alignments. In this work, we present
a novel method for inter-subject alignment based on Optimal Transport, denoted
as Fused Unbalanced Gromov Wasserstein (FUGW). The method aligns cortical
surfaces based on the similarity of their functional signatures in response to
a variety of stimulation settings, while penalizing large deformations of
individual topographic organization. We demonstrate that FUGW is well-suited
for whole-brain landmark-free alignment. The unbalanced feature allows to deal
with the fact that functional areas vary in size across subjects. Our results
show that FUGW alignment significantly increases between-subject correlation of
activity for independent functional data, and leads to more precise mapping at
the group level
- …