Direct LDDMM of Discrete Currents with Adaptive Finite Elements

Please always quote using this URN: urn:nbn:de:0297-zib-13090
  • We consider Large Deformation Diffeomorphic Metric Mapping of general $m$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete $m$-current attributes.

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Author:Andreas Günther, Hans Lamecker, Martin Weiser
Document Type:ZIB-Report
Tag:Adaptive Finite Elements; Currents; Diffeomorphic Registration; Large Deformation; Matching
MSC-Classification:37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Exx Low-dimensional dynamical systems / 37E30 Homeomorphisms and diffeomorphisms of planes and surfaces
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J20 Optimal control problems involving partial differential equations
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Axx General theory of differentiable manifolds [See also 32Cxx] / 58A25 Currents [See also 32C30, 53C65]
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J72 Correspondences and other transformation methods (e.g. Lie- Bäcklund) [See also 35A22]
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Date of first Publication:2011/06/14
Series (Serial Number):ZIB-Report (11-22)
Published in:An extended version appeared under the title "Flexible Shape Matching with Finite Element Based LDDMM" in: International Journal of Computer Vision November 2013, Volume 105, Issue 2, pp 128-143
DOI:https://doi.org/10.1007/s11263-012-0599-3