Journal of Mathematical Imaging and Vision

, Volume 57, Issue 3, pp 293–323 | Cite as

Mapping-Based Image Diffusion

  • Freddie Åström
  • Michael Felsberg
  • George Baravdish
Article

Abstract

In this work, we introduce a novel tensor-based functional for targeted image enhancement and denoising. Via explicit regularization, our formulation incorporates application-dependent and contextual information using first principles. Few works in literature treat variational models that describe both application-dependent information and contextual knowledge of the denoising problem. We prove the existence of a minimizer and present results on tensor symmetry constraints, convexity, and geometric interpretation of the proposed functional. We show that our framework excels in applications where nonlinear functions are present such as in gamma correction and targeted value range filtering. We also study general denoising performance where we show comparable results to dedicated PDE-based state-of-the-art methods.

Keywords

Image enhancement Denoising PDE Diffusion Gradient energy tensor Structure tensor 

Notes

Acknowledgments

We thank the reviewers for their helpful comments and suggestions which have improved this work. This research has received funding from the Swedish Foundation for Strategic Research through the grant VPS and from Swedish Research Council through grants for the projects energy models for computational cameras \((\hbox {EMC}^2)\) and Visualization adaptive Iterative Denoising of Images (VIDI), all within the Linnaeus environment CADICS and the excellence network ELLIIT. Support by the German Science Foundation and the Research Training Group (GRK 1653) is gratefully acknowledged by the first author.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Freddie Åström
    • 1
  • Michael Felsberg
    • 2
  • George Baravdish
    • 3
  1. 1.Heidelberg Collaboratory for Image Processing (HCI)Heidelberg UniversityHeidelbergGermany
  2. 2.Department of Electrical EngineeringLinköping UniversityLinköpingSweden
  3. 3.Department of Science and TechnologyLinköping UniversityLinköpingSweden

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