Skip to main content
Springer Nature Link
Log in

Expert Regularizers for Task Specific Processing

  • Conference paper
Scale Space and Variational Methods in Computer Vision (SSVM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7893))

  • 3716 Accesses

Abstract

This study is concerned with constructing expert regularizers for specific tasks. We discuss the general problem of what is desired from a regularizer, when one knows the type of images to be processed. The aim is to improve the processing quality and to reduce artifacts created by standard, general-purpose, regularizers, such as total-variation or nonlocal functionals.

Fundamental requirements for the theoretic expert regularizer are formulated. A simplistic regularizer is then presented, which approximates in some sense the ideal requirements.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. Arias, P., Caselles, V., Facciolo, G.: Analysis of a variational framework for exemplar-based image inpainting. Multiscale Model. & Simul. 10(2), 473–514 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing. Applied Mathematical Sciences, vol. 147. Springer (2002)

    Google Scholar 

  3. Aujol, J.F., Chambolle, A.: Dual norms and image decomposition models. IJCV 63(1), 85–104 (2005)

    Article  MathSciNet  Google Scholar 

  4. Bayram, I., Kamasak, M.E.: A Directional Total Variation. In: Proceedings of 20th European Signal Processing Conference, EUSIPCO 2012 (2012)

    Google Scholar 

  5. Berkels, B., Burger, M., Droske, M., Nemitz, O., Rumpf, M.: Cartoon extraction based on anisotropic image classification. In: Vision, Modeling, and Visualization Proceedings, pp. 293–300 (2006)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Brox, T., Bruhn, A., Papenberg, N., Weickert, J.: High accuracy optical flow estimation based on a theory for warping. In: Pajdla, T., Matas, J(G.) (eds.) ECCV 2004. LNCS, vol. 3024, pp. 25–36. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Brox, T., Kleinschmidt, O., Cremers, D.: Efficient nonlocal means for denoising of textural patterns. IEEE Trans. Image Processing 17(7), 1083–1092 (2008)

    Article  MathSciNet  Google Scholar 

  9. Buades, A., Coll, B., Morel, J.-M.: A review of image denoising algorithms, with a new one. SIAM Multiscale Modeling and Simulation 4(2), 490–530 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Burger, M., Gilboa, G., Osher, S., Xu, J.: Nonlinear inverse scale space methods. Comm. in Math. Sci. 4(1), 179–212 (2006)

    MathSciNet  MATH  Google Scholar 

  11. Chan, T.F., Esedoglu, S., Park, F.E.: A fourth order dual method for staircase reduction in texture extraction and image restoration problems. In: ICIP, pp. 4137–4140 (2010)

    Google Scholar 

  12. Coupé, P., Manjón, J.V., Fonov, V., Pruessner, J., Robles, M., Louis Collins, D.: Patch-based segmentation using expert priors: Application to hippocampus and ventricle segmentation. Neuroimage 54(2), 940–954 (2011)

    Article  Google Scholar 

  13. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans. Image Processing 16(8), 2080–2095 (2007)

    Article  MathSciNet  Google Scholar 

  14. Droske, M., Rumpf, M.: A variational approach to non-rigid morphological registration. SIAM Appl. Math. 64(2), 668–687 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Processing 15(12), 3736–3745 (2006)

    Article  MathSciNet  Google Scholar 

  16. Gilboa, G., Osher, S.: Nonlocal linear image regularization and supervised segmentation. SIAM Multiscale Modeling and Simulation 6(2), 595–630 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Modeling & Simulation, 1005–1028 (2008)

    Google Scholar 

  18. Hu, Y., Jacob, M.: Higher degree total variation (hdtv) regularization for image recovery. IEEE Transactions on Image Processing 21(5), 2559–2571 (2012)

    Article  MathSciNet  Google Scholar 

  19. Hutter, J., Grimm, R., Forman, C., Hornegger, J., Schmitt, P.: Vessel Adapted Regularization for Iterative Reconstruction in MR Angiography. In: Proceedings, 20th Annual Meeting, Int. Soc. Magnetic Resonance in Medicine (ISMRM) (2012)

    Google Scholar 

  20. Kindermann, S., Osher, S., Jones, P.: Deblurring and denoising of images by nonlocal functionals. SIAM Multiscale Modeling & Simul. 4(4), 1091–1115 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  21. Lou, Y., Zhang, X., Osher, S., Bertozzi, A.: Image recovery via nonlocal operators. Journal of Scientific Computing 42(2), 185–197 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  22. Meyer, Y.: Oscillating patterns in image processing and in some nonlinear evolution equations. The 15th Dean Jacquelines B. Lewis Memorial Lectures (March 2001)

    Google Scholar 

  23. Osher, S., Burger, M., Goldfarb, D., Xu, J., Yin, W.: An iterative regularization method for total variation based image restoration. SIAM Journal on Multiscale Modeling and Simulation 4, 460–489 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  24. Osher, S., Esedoglu, S.: Decomposition of images by the anisotropic rudin-osher-fatemi model. Comm. Pure Appl. Math 57, 1609–1626 (2003)

    MathSciNet  Google Scholar 

  25. Osher, S., Sole, A., Vese, L.: Image decomposition and restoration using total variation minimization and the H− 1 norm. SIAM Multiscale Modeling and Simulation 1(3), 349–370 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  26. Roth, S., Black, M.J.: Fields of experts: A framework for learning image priors. In: IEEE Computer Society Conference on CVPR 2005, pp. 860–867 (2005)

    Google Scholar 

  27. Rubinstein, R., Zibulevsky, M., Elad, M.: Double sparsity: Learning sparse dictionaries for sparse signal approximation. IEEE Transactions on Image Processing 58(3), 1553–1564 (2010)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  29. Tschumperlé, D., Brun, L.: Non-local regularization and registration of multi-valued images by pdes and variational methods on higher dimensional spaces. In: Mathematical Image Processing, pp. 181–197 (2011)

    Google Scholar 

  30. Weickert, J.: Anisotropic Diffusion in Image Processing. Teubner-Verlag, Stuttgart (1998)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Technion, Israel Institute of Technology, Haifa, 32000, Israel

    Guy Gilboa

Authors
  1. Guy Gilboa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Fraunhofer Gesellschaft, Institut für Graphische Datenverarbeitung, Fraunhoferstraße 5, 64283, Darmstadt, Germany

    Arjan Kuijper

  2. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010, Graz, Austria

    Kristian Bredies

  3. Institute for Computer Graphics and Vision, Graz University of Technology, Inffeldgasse 16, 8010, Graz, Austria

    Thomas Pock  & Horst Bischof  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gilboa, G. (2013). Expert Regularizers for Task Specific Processing. In: Kuijper, A., Bredies, K., Pock, T., Bischof, H. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2013. Lecture Notes in Computer Science, vol 7893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38267-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38267-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38266-6

  • Online ISBN: 978-3-642-38267-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation