Skip to main content

Minimizing TGV-Based Variational Models with Non-convex Data Terms

  • Conference paper

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

Abstract

We introduce a method to approximately minimize variational models with Total Generalized Variation regularization (TGV) and non-convex data terms. Our approach is based on a decomposition of the functional into two subproblems, which can be both solved globally optimal. Based on this decomposition we derive an iterative algorithm for the approximate minimization of the original non-convex problem. We apply the proposed algorithm to a state-of-the-art stereo model that was previously solved using coarse-to-fine warping, where we are able to show significant improvements in terms of accuracy.

This work was supported by the Austrian Science Fund (project no. P22492).

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

Buying options

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 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bredies, K., Kunisch, K., Pock, T.: Total Generalized Variation. SIAM J. Img. Sci. 3(3), 492–526 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Werlberger, M.: Convex Approaches for High Performance Video Processing. PhD thesis, Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria (2012)

    Google Scholar 

  3. Ranftl, R., Gehrig, S., Pock, T., Bischof, H.: Pushing the Limits of Stereo Using Variational Stereo Estimation. In: Proc. Intelligent Vehicles Symposium (2012)

    Google Scholar 

  4. Pock, T., Zebedin, L., Bischof, H.: TGV-Fusion. In: Calude, C.S., Rozenberg, G., Salomaa, A. (eds.) Maurer Festschrift. LNCS, vol. 6570, pp. 245–258. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Woodford, O., Torr, P., Reid, I., Fitzgibbon, A.: Global stereo reconstruction under second order smoothness priors. In: Proc. CVPR, pp. 1–8 (2008)

    Google Scholar 

  6. Bleyer, M., Rhemann, C., Rother, C.: Patchmatch Stereo - Stereo Matching with Slanted Support Windows. In: Proc. BMVC, pp. 14.1–14.11 (2011)

    Google Scholar 

  7. Yamaguchi, K., Hazan, T., McAllester, D., Urtasun, R.: Continuous markov random fields for robust stereo estimation. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part V. LNCS, vol. 7576, pp. 45–58. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  8. Trobin, W., Pock, T., Cremers, D., Bischof, H.: An unbiased second-order prior for high-accuracy motion estimation. In: Rigoll, G. (ed.) DAGM 2008. LNCS, vol. 5096, pp. 396–405. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Pock, T., Schoenemann, T., Graber, G., Bischof, H., Cremers, D.: A convex formulation of continuous multi-label problems. In: Forsyth, D., Torr, P., Zisserman, A. (eds.) ECCV 2008, Part III. LNCS, vol. 5304, pp. 792–805. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Ishikawa, H.: Exact optimization for markov random fields with convex priors. PAMI 25, 1333–1336 (2003)

    Article  Google Scholar 

  11. Pock, T., Cremers, D., Bischof, H., Chambolle, A.: Global solutions of variational models with convex regularization. SIAM J. Img. Sci. 3(4), 1122–1145 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. 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 

  13. Gorski, J., Pfeuffer, F., Klamroth, K.: Biconvex sets and optimization with biconvex functions: a survey and extensions. Mathematical Methods of Operations Research 66, 373–407 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. de Leeuw, J.: Block-relaxation algorithms in statistics. Technical report, Dept. of Statistics, UCLA (1994)

    Google Scholar 

  15. Geiger, A., Lenz, P., Urtasun, R.: Are we ready for autonomous driving? the kitti vision benchmark suite. In: Proc. CVPR, pp. 3354–3361 (2012)

    Google Scholar 

  16. Scharstein, D., Szeliski, R., Zabih, R.: A taxonomy and evaluation of dense two-frame stereo correspondence algorithms. In: IEEE Workshop on Stereo and Multi-Baseline Vision (SMBV), pp. 131–140 (2001)

    Google Scholar 

  17. Nikolova, M.: A variational approach to remove outliers and impulse noise. JMIV 20(1-2), 99–120 (2004)

    Article  MathSciNet  Google Scholar 

  18. Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. JMIV 40, 120–145 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Img. Sci. 2(1), 183–202 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Boyle, J.P., Dykstra, R.L.: A method for finding projections onto the intersection of convex sets in Hilbert spaces. Lexture Notes in Statistics 37, 28–47 (1986)

    Article  MathSciNet  Google Scholar 

  21. Zabih, R., Ll, J.W.: Non-parametric local transforms for computing visual correspondence. In: Eklundh, J.-O. (ed.) ECCV 1994. LNCS, vol. 801, pp. 151–158. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  22. Hamming, R.W.: Error detecting and error correcting codes. Bell System Technical Journal 29(2), 147–160 (1950)

    MathSciNet  Google Scholar 

  23. Birchfield, S., Tomasi, C.: A pixel dissimilarity measure that is insensitive to image sampling. PAMI 20(4), 401–406 (1998)

    Article  Google Scholar 

  24. Hermann, S., Klette, R.: Iterative semi-global matching for robust driver assistance systems. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds.) ACCV 2012, Part III. LNCS, vol. 7726, pp. 465–478. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  25. Geiger, A., Roser, M., Urtasun, R.: Efficient large-scale stereo matching. In: Kimmel, R., Klette, R., Sugimoto, A. (eds.) ACCV 2010, Part I. LNCS, vol. 6492, pp. 25–38. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  26. Hirschmueller, H.: Accurate and efficient stereo processing by semi-global matching and mutual information. In: Proc. CVPR, pp. 807–814 (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ranftl, R., Pock, T., Bischof, H. (2013). Minimizing TGV-Based Variational Models with Non-convex Data Terms. 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_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38267-3_24

  • 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