Skip to main content
SpringerLink
Log in

Total Directional Variation for Video Denoising

  • Conference paper
  • First Online:
Scale Space and Variational Methods in Computer Vision (SSVM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 11603))

Abstract

In this paper we propose a variational approach for video denoising, based on a total directional variation (TDV) regulariser proposed in [20, 21] for image denoising and interpolation. In the TDV regulariser, the underlying image structure is encoded by means of weighted derivatives so as to enhance the anisotropic structures in images, e.g. stripes or curves with a dominant local directionality. For the extension of TDV to video denoising, the space-time structure is captured by the volumetric structure tensor guiding the smoothing process. We discuss this and present our whole video denoising workflow. The numerical results are compared with some state-of-the-art video denoising methods.

SP acknowledges UK EPSRC grant EP/L016516/1 for the CCA DTC. CBS acknowledges support from Leverhulme Trust project on Breaking the non-convexity barrier, EPSRC grant Nr. EP/M00483X/1, the EPSRC Centre EP/N014588/1, the RISE projects CHiPS and NoMADS, the CCIMI and the Alan Turing Institute.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Videos are freely available: Salesman and Miss America at www.cs.tut.fi/~foi/GCF-BM3D Xylophone in MATLAB; Water (re-scaled, grey-scaled and clipped, Jay Miller, CC 3.0) at www.videvo.net/video/water-drop/477; Franke’s function (a synthetic surface moving on fixed trajectories: the coloured one changes with the parula colormap).

  2. 2.

    Results are available at http://www.simoneparisotto.com/TDV4videodenoising.

References

  1. Arias, P., Morel, J.M.: Video denoising via empirical Bayesian estimation of space-time patches. J. Math. Imaging Vis. 60(1), 70–93 (2018)

    Article  MathSciNet  Google Scholar 

  2. Brailean, J.C., et al.: Noise reduction filters for dynamic image sequences: a review. Proc. IEEE 83(9), 1272–1292 (1995)

    Article  Google Scholar 

  3. Bredies, K., Kunisch, K., Pock, T.: Total generalized variation. SIAM J. Imaging Sci. 3(3), 492–526 (2010)

    Article  MathSciNet  Google Scholar 

  4. Buades, A., Coll, B., Morel, J.: A non-local algorithm for image denoising. In: IEEE CVPR 2005, vol. 2, pp. 60–65 (2005)

    Google Scholar 

  5. Buades, A., Lisani, J., Miladinović, M.: Patch-based video denoising with optical flow estimation. IEEE Trans. Image Process. 25(6), 2573–2586 (2016)

    Article  MathSciNet  Google Scholar 

  6. Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. SIAM J. Multiscale Model. Simul. 4(2), 490–530 (2005)

    Article  MathSciNet  Google Scholar 

  7. Burger, M., Dirks, H., Schönlieb, C.: A variational model for joint motion estimation and image reconstruction. SIAM J. Imaging Sci. 11(1), 94–128 (2018)

    Article  MathSciNet  Google Scholar 

  8. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40(1), 120–145 (2011)

    Article  MathSciNet  Google Scholar 

  9. Chambolle, A., Pock, T.: An introduction to continuous optimization for imaging. Acta Numerica 25, 161–319 (2016)

    Article  MathSciNet  Google Scholar 

  10. Dabov, K., Foi, A., Egiazarian, K.: Video denoising by sparse 3D transform-domain collaborative filtering. In: 15th European Signal Process, pp. 145–149 (2007)

    Google Scholar 

  11. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: BM3D image denoising with shape-adaptive principal component analysis. In: SPARS 2009 (2009)

    Google Scholar 

  12. Dalgas Kongskov, R., Dong, Y., Knudsen, K.: Directional total generalized variation regularization. ArXiv e-prints (2017)

    Google Scholar 

  13. Davy, A., Ehret, T., Facciolo, G., Morel, J., Arias, P.: Non-local video denoising by CNN. ArXiv e-prints (2018)

    Google Scholar 

  14. Horn, B.K., Schunck, B.: “determining optical flow”: a retrospective. Artif. Intell. 59(1), 81–87 (1993)

    Article  Google Scholar 

  15. Lebrun, M., Buades, A., Morel, J.: A nonlocal Bayesian image denoising algorithm. SIAM J. Imaging Sci. 6(3), 1665–1688 (2013)

    Article  MathSciNet  Google Scholar 

  16. Lucas, B.D., Kanade, T.: An iterative image registration technique with an application to stereo vision. In: IJCAI 1981, pp. 674–679. Morgan Kaufmann (1981)

    Google Scholar 

  17. Maggioni, M., Boracchi, G., Foi, A., Egiazarian, K.: Video denoising using separable 4D nonlocal spatiotemporal transforms. In: Proceedings of SPIE, vol. 7870 (2011)

    Google Scholar 

  18. Ozkan, M.K., Sezan, M.I., Tekalp, A.M.: Adaptive motion-compensated filtering of noisy image sequences. IEEE Trans. Circuits Syst. Video Technol. 3(4), 277–290 (1993)

    Article  Google Scholar 

  19. Papafitsoros, K., Schönlieb, C.B.: A combined first and second order variational approach for image reconstruction. J. Math. Imaging Vis. 48(2), 308–338 (2014)

    Article  MathSciNet  Google Scholar 

  20. Parisotto, S., Masnou, S., Schönlieb, C.B.: Higher order total directional variation. Part II: analysis. ArXiv e-prints (2018)

    Google Scholar 

  21. Parisotto, S., Masnou, S., Schönlieb, C.B., Lellmann, J.: Higher order total directional variation. Part I: imaging applications. ArXiv e-prints (2018)

    Google Scholar 

  22. Parisotto, S.: Anisotropic variational models and PDEs for inverse imaging problems. Ph.D. thesis, University of Cambridge (2019)

    Google Scholar 

  23. Portilla, J., et al.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Process. 12(11), 1338–1351 (2003)

    Article  MathSciNet  Google Scholar 

  24. Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60(1), 259–268 (1992)

    Article  MathSciNet  Google Scholar 

  25. Sánchez Prez, J., Meinhardt-Llopis, E., Facciolo, G.: TV-L1 optical flow estimation. IPOL 3, 137–150 (2013)

    Article  Google Scholar 

  26. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proceedings of IEEE International Conference on Computer Vision, pp. 839–846 (1998)

    Google Scholar 

  27. Weickert, J.: Anisotropic diffusion in image processing (1998)

    Google Scholar 

  28. Zach, C., Pock, T., Bischof, H.: A duality based approach for realtime TV-L1 optical flow. In: Hamprecht, F.A., Schnörr, C., Jähne, B. (eds.) DAGM 2007. LNCS, vol. 4713, pp. 214–223. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74936-3_22

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CCA, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

    Simone Parisotto

  2. DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

    Carola-Bibiane Schönlieb

Authors
  1. Simone Parisotto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carola-Bibiane Schönlieb
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Simone Parisotto .

Editor information

Editors and Affiliations

  1. University of LĂĽbeck, LĂĽbeck, Germany

    Jan Lellmann

  2. University of Erlangen-Nuremberg (FAU), Erlangen, Germany

    Martin Burger

  3. University of LĂĽbeck, LĂĽbeck, Germany

    Jan Modersitzki

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Parisotto, S., Schönlieb, CB. (2019). Total Directional Variation for Video Denoising. In: Lellmann, J., Burger, M., Modersitzki, J. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2019. Lecture Notes in Computer Science(), vol 11603. Springer, Cham. https://doi.org/10.1007/978-3-030-22368-7_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-22368-7_41

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22367-0

  • Online ISBN: 978-3-030-22368-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation