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We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20$times$ speedup for a two dimensional, real world multi-subject medical image registration problem.
With this work, we release CLAIRE, a distributed-memory implementation of an effective solver for constrained large deformation diffeomorphic image registration problems in three dimensions. We consider an optimal control formulation. We invert for a
We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its velocity. Tikho
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 o
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 a
3D image registration is one of the most fundamental and computationally expensive operations in medical image analysis. Here, we present a mixed-precision, Gauss--Newton--Krylov solver for diffeomorphic registration of two images. Our work extends t