536 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
A new method for aspherical surface fitting with large-volume datasets
In the framework of form characterization of aspherical surfaces, European National Metrology Institutes (NMIs) have been developing ultra-high precision machines having the ability to measure aspherical lenses with an uncertainty of few tens of nanometers. The fitting of the acquired aspherical datasets onto their corresponding theoretical model should be achieved at the same level of precision. In this article, three fitting algorithms are investigated: the Limited memory-Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), the Levenberg–Marquardt (LM) and one variant of the Iterative Closest Point (ICP). They are assessed based on their capacities to converge relatively fast to achieve a nanometric level of accuracy, to manage a large volume of data and to be robust to the position of the data with respect to the model. Nev-ertheless, the algorithms are first evaluated on simulated datasets and their performances are studied. The comparison of these algorithms is extended on measured datasets of an aspherical lens. The results validate the newly used method for the fitting of aspherical surfaces and reveal that it is well adapted, faster and less complex than the LM or ICP methods.EMR
A first-order multigrid method for bound-constrained convex optimization
The aim of this paper is to design an efficient multigrid method for
constrained convex optimization problems arising from discretization of some
underlying infinite dimensional problems. Due to problem dependency of this
approach, we only consider bound constraints with (possibly) a single equality
constraint. As our aim is to target large-scale problems, we want to avoid
computation of second derivatives of the objective function, thus excluding
Newton like methods. We propose a smoothing operator that only uses first-order
information and study the computational efficiency of the resulting method
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