301 research outputs found
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
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
Partial Differential Equation-Constrained Diffeomorphic Registration from Sum of Squared Differences to Normalized Cross-Correlation, Normalized Gradient Fields, and Mutual Information: A Unifying Framework; 35632143
This work proposes a unifying framework for extending PDE-constrained Large Deformation Diffeomorphic Metric Mapping (PDE-LDDMM) with the sum of squared differences (SSD) to PDE-LDDMM with different image similarity metrics. We focused on the two best-performing variants of PDE-LDDMM with the spatial and band-limited parameterizations of diffeomorphisms. We derived the equations for gradient-descent and Gauss-Newton-Krylov (GNK) optimization with Normalized Cross-Correlation (NCC), its local version (lNCC), Normalized Gradient Fields (NGFs), and Mutual Information (MI). PDE-LDDMM with GNK was successfully implemented for NCC and lNCC, substantially improving the registration results of SSD. For these metrics, GNK optimization outperformed gradient-descent. However, for NGFs, GNK optimization was not able to overpass the performance of gradient-descent. For MI, GNK optimization involved the product of huge dense matrices, requesting an unaffordable memory load. The extensive evaluation reported the band-limited version of PDE-LDDMM based on the deformation state equation with NCC and lNCC image similarities among the best performing PDE-LDDMM methods. In comparison with benchmark deep learning-based methods, our proposal reached or surpassed the accuracy of the best-performing models. In NIREP16, several configurations of PDE-LDDMM outperformed ANTS-lNCC, the best benchmark method. Although NGFs and MI usually underperformed the other metrics in our evaluation, these metrics showed potentially competitive results in a multimodal deformable experiment. We believe that our proposed image similarity extension over PDE-LDDMM will promote the use of physically meaningful diffeomorphisms in a wide variety of clinical applications depending on deformable image registration
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
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