Skip to main content
SpringerLink
Log in
Book cover

Image Processing Based on Partial Differential Equations pp 35–55Cite as

Image Dejittering Based on Slicing Moments

  • Conference paper

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

This is a preview of subscription content, 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   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Acar and C. R. Vogel. Analysis of total variation penalty methods for ill-posed problems. Inverse Prob., 10:1217–1229, 1994.

    Article  MathSciNet  Google Scholar 

  2. J.-F. Aujol and S.-H. Kang. Color image decomposition and restoration. Journal of Visual Communication and Image Representation (in press), 2005.

    Google Scholar 

  3. A. Chambolle and P. L. Lions. Image recovery via Total Variational minimization and related problems. Numer. Math., 76:167–188, 1997.

    Article  MathSciNet  Google Scholar 

  4. T. F. Chan, G. H. Golub, and P. Mulet. A nonlinear primal-dual method for total variation-based image restoration. SIAM Journal on Scientific Computing, 20:1964–1977, 1999.

    Article  MathSciNet  Google Scholar 

  5. T. F. Chan, S.-H. Kang, and J. Shen. Total variation denoising and enhancement of color images based on the CB and HSV color models. J. Visual Comm. Image Rep., 12(4):422–435, 2001.

    Article  Google Scholar 

  6. T. F. Chan, S. Osher, and J. Shen. The digital TV filter and non-linear denoising. IEEE Trans. Image Process., 10(2):231–241, 2001.

    Article  Google Scholar 

  7. T. F. Chan and J. Shen. Image Processing and Analysis: variational, PDE, wavelets, and stochastic methods. SIAM Publisher, Philadelphia, 2005.

    Google Scholar 

  8. T. F. Chan and J. Shen. Variational image inpainting. Comm. Pure Applied Math., 58:579–619, 2005.

    Article  MathSciNet  Google Scholar 

  9. T. F. Chan, J. Shen, and L. Vese. Variational PDE models in image processing. Notices Amer. Math. Soc., 50:14–26, 2003.

    MathSciNet  Google Scholar 

  10. I. Daubechies. Ten lectures on wavelets. SIAM, Philadelphia, 1992.

    Google Scholar 

  11. G. B. Folland. Real Analysis - Modern Techniques and Their Applications. John Wiley & Sons, Inc., second edition, 1999.

    Google Scholar 

  12. S. Geman and D. Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intell., 6:721–741, 1984.

    Article  Google Scholar 

  13. E. Giusti. Minimal Surfaces and Functions of Bounded Variation. Birkhäuser, Boston, 1984.

    Google Scholar 

  14. S.-H. Kang and J. Shen. Video dejittering by bake and shake. Image Vis. Comput., 24(2):143–152, 2006.

    Article  Google Scholar 

  15. A. Kokaram and P. Rayner. An algorithm for line registration of TV images based on a 2-D AR model. Signal Processing VI, Theories and Applications, pages 1283–1286, 1992.

    Google Scholar 

  16. A. Kokaram, P. M. B. Roosmalen, P. Rayner, and J. Biemond. Line registration of jittered video. IEEE Int’l Conference on Acoustics, Speech, and Signal Processing, pages 2553–2556, 1997.

    Google Scholar 

  17. Y. Meyer. Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, volume 22 of University Lecture Series. AMS, Providence, 2001.

    Google Scholar 

  18. D. Mumford. Geometry Driven Diffusion in Computer Vision, chapter “The Bayesian rationale for energy functionals”, pages 141-153. Kluwer Academic, 1994.

    Google Scholar 

  19. D. Mumford. Pattern theory: The mathematics of perception. Int’l Congress Mathematicians (ICM), III, Beijing, 2002.

    Google Scholar 

  20. D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Applied. Math., 42:577–685,1989.

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  22. J. Shen. On the foundations of vision modeling I. Weber’s law and Weberized TV restoration. Physica D: Nonlinear Phenomena, 175:241–251, 2003.

    Article  MathSciNet  Google Scholar 

  23. J. Shen. Bayesian video dejittering by BV image model. SIAM J. Appl. Math., 64 (5):1691–1708, 2004.

    Article  MathSciNet  Google Scholar 

  24. L. A. Vese. A study in the BV space of a denoising-deblurring variational problem. Appl. Math. Optim., 44(2):131–161, 2001.

    Article  MathSciNet  Google Scholar 

  25. L. A. Vese and S. J. Osher. Modeling textures with Total Variation minimization and oscillating patterns in image processing. J. Sci. Comput., 19(1-3):553–572, 2003.

    Article  MathSciNet  Google Scholar 

  26. C. Vogel. Computational Methods for Inverse Problems. SIAM, Philadelphia, 2002.

    Google Scholar 

  27. J. Weickert. Anisotropic Diffusion in Image Processing. Teubner-Verlag, Stuttgart, Germany, 1998.

    Google Scholar 

  28. S. C. Zhu, Y. N. Wu, and D. Mumford. Minimax entropy principle and its applications to texture modeling. Neural Comput., 9:1627–1660, 1997.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, KY 40515, Lexington, USA

    Sung Ha Kang

  2. School of Mathematics, University of Minnesota, MN 55455, Minneapolis

    Jackie Shen

Authors
  1. Sung Ha Kang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jackie Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, Johannes Brunsgate 12, N-5008, Bergen, Norway

    Xue-Cheng Tai

  2. Dept. Applied Math., SINTEF ICT, Blindern, 124, N-0314, Oslo, Norway

    Knut-Andreas Lie

  3. Assistant Director for Math & Physical Sciences Directorate, The National Science Foundation, 4201, Arlington, Virginia, USA

    Tony F. Chan

  4. Department of Mathematics, University of California at Los Angeles, Portola Plaza, 520, CA 90095, Los Angeles, USA

    Stanley Osher

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kang, S.H., Shen, J. (2007). Image Dejittering Based on Slicing Moments. In: Tai, XC., Lie, KA., Chan, T.F., Osher, S. (eds) Image Processing Based on Partial Differential Equations. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-33267-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-33267-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33266-4

  • Online ISBN: 978-3-540-33267-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation