Infimal Convolution Coupling of First and Second Order Differences on Manifold-Valued Images

  • Ronny Bergmann
  • Jan Henrik FitschenEmail author
  • Johannes Persch
  • Gabriele Steidl
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


Recently infimal convolution type functions were used in regularization terms of variational models for restoring and decomposing images. This is the first attempt to generalize the infimal convolution of first and second order differences to manifold-valued images. We propose both an extrinsic and an intrinsic approach. Our focus is on the second one since the summands arising in the infimal convolution lie on the manifold themselves and not in the higher dimensional embedding space. We demonstrate by numerical examples that the approach works well on the circle, the 2-sphere, the rotation group, and the manifold of positive definite matrices with the affine invariant metric.


Infimal convolution TGV Higher order differences Restoration of manifold-valued images Decomposition of manifold-valued images 



Funding by the German Research Foundation (DFG) within the project STE 571/13-1 & BE 5888/2-1 and within the Research Training Group 1932, project area P3, is gratefully acknowledged. Furthermore, G. Steidl acknowledges the support by the German Federal Ministry of Education and Research (BMBF) through grant 05M13UKA (AniS).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Ronny Bergmann
    • 1
  • Jan Henrik Fitschen
    • 1
    Email author
  • Johannes Persch
    • 1
  • Gabriele Steidl
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Fraunhofer ITWMKaiserslauternGermany

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