Abstract
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.
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Acknowledgements
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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Bergmann, R., Fitschen, J.H., Persch, J., Steidl, G. (2017). Infimal Convolution Coupling of First and Second Order Differences on Manifold-Valued Images. In: Lauze, F., Dong, Y., Dahl, A. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2017. Lecture Notes in Computer Science(), vol 10302. Springer, Cham. https://doi.org/10.1007/978-3-319-58771-4_36
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