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 $H^1$- or $H^2$-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

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 $1024^3$ 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 $256^3$---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

Gemeindetransformationsprozesse Gestalten: eine empirisch-theologische Untersuchung der Wahrnehmung von Gemeindetransformationsprozessen am Beispiel der Freien evangelischen Gemeinde Darmstadt

Text in German with German and English summariesDie vorliegende Forschungsarbeit erforscht Transformationsprozesse von etablierten Gemeinden, die auf eine missionale Neuausrichtung zielen. Den Kern der Arbeit bildet die empirische Untersuchung des eränderungsprozesses der Freien evangelischen Gemeinde Darmstadt. Es wird untersucht, wie die Mitglieder diesen Prozess erlebt und wahrgenommen haben, um herauszufinden, wodurch dieser Prozess gefördert und gehemmt wurde. Die Arbeit beschäftigt sich außerdem mit der von Luhmann entwickelten systemischen Organisationstheorie, die dabei hilft zu verstehen, wie Gemeinde als Organisation funktioniert und was dies für deren Veränderung bedeutet. Es wird versucht die Ergebnisse der empirischen Forschung mithilfe dieser Theorie zu deuten und einzuordnen, um aufzuzeigen, inwiefern diese Theorie bei Veränderungsprozessen helfen kann, den Fokus auf die Aspekte zu lenken, die für eine erfolgreiche Umsetzung relevant sind. Ziel der Arbeit ist es, Hilfestellung für zukünftige Transformationsprozesse zu geben, indem sie fragt, was aus dem Prozess der Freien evangelischen Gemeinde Darmstadt und der systemischen Organisationstheorie gelernt werden kann.This MTh dissertation explores transformational processes of established churches, that aim towards missional renewal. Core of this thesis is the empirical study of the transformation-process of the Freie evangelische Gemeinde Darmstadt. The study explores the perception of the church members of this process, to find out ways it was supported and blocked. The thesis also deals with the theory of organized social systems by Luhmann, that helps to understand how local church works as an organization and what this means regarding change. The Thesis interprets the results of the empirical study based on this theory to show, how it can help depict those aspects, that are relevant to successfully implement transformational processes. Aim of this thesis is to give assistance to shape future transformational processes by asking what can be learned from the developments of the Freie evangelische Gemeinde Darmstadt and the theory of organized social systems.Christian Spirituality, Church History and MissiologyM.Th. (Missiology