Time Discrete Extrapolation in a Riemannian Space of Images

  • Alexander EfflandEmail author
  • Martin Rumpf
  • Florian Schäfer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


The Riemannian metamorphosis model introduced and analyzed in [7, 12] is taken into account to develop an image extrapolation tool in the space of images. To this end, the variational time discretization for the geodesic interpolation proposed in [2] is picked up to define a discrete exponential map. For a given weakly differentiable initial image and a sufficiently small initial image variation it is shown how to compute a discrete geodesic extrapolation path in the space of images. The resulting discrete paths are indeed local minimizers of the corresponding discrete path energy. A spatial Galerkin discretization with cubic splines on coarse meshes for image deformations and piecewise bilinear finite elements on fine meshes for image intensity functions is used to derive a fully practical algorithm. The method is applied to real images and image variations recorded with a digital camera.


Image extrapolation Shape space Elastic registration Exponential map 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Alexander Effland
    • 1
    Email author
  • Martin Rumpf
    • 1
  • Florian Schäfer
    • 2
  1. 1.Institute for Numerical SimulationUniversität BonnBonnGermany
  2. 2.California Institute of TechnologyPasadenaUSA

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