1,803 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
Diffeomorphic density registration
In this book chapter we study the Riemannian Geometry of the density
registration problem: Given two densities (not necessarily probability
densities) defined on a smooth finite dimensional manifold find a
diffeomorphism which transforms one to the other. This problem is motivated by
the medical imaging application of tracking organ motion due to respiration in
Thoracic CT imaging where the fundamental physical property of conservation of
mass naturally leads to modeling CT attenuation as a density. We will study the
intimate link between the Riemannian metrics on the space of diffeomorphisms
and those on the space of densities. We finally develop novel computationally
efficient algorithms and demonstrate there applicability for registering RCCT
thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi
Indirect Image Registration with Large Diffeomorphic Deformations
The paper adapts the large deformation diffeomorphic metric mapping framework
for image registration to the indirect setting where a template is registered
against a target that is given through indirect noisy observations. The
registration uses diffeomorphisms that transform the template through a (group)
action. These diffeomorphisms are generated by solving a flow equation that is
defined by a velocity field with certain regularity. The theoretical analysis
includes a proof that indirect image registration has solutions (existence)
that are stable and that converge as the data error tends so zero, so it
becomes a well-defined regularization method. The paper concludes with examples
of indirect image registration in 2D tomography with very sparse and/or highly
noisy data.Comment: 43 pages, 4 figures, 1 table; revise
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