Skip to main content
SpringerLink
Log in

Unconstrained Structural Similarity-Based Optimization

  • Conference paper
  • First Online:
Image Analysis and Recognition (ICIAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8814))

Included in the following conference series:

Abstract

We establish a general framework, along with a set of algorithms, for the incorporation of the Structural Similarity (SSIM) quality index measure as the fidelity, or “data fitting,” term in objective functions for optimization problems in image processing. The motivation for this approach is to replace the widely used Euclidean distance, known as a poor measure of visual quality, by the SSIM, which has been recognized as one of the best measures of visual closeness. Some experimental results are also presented.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albuquerque, G., Eisemann, M., Magnor, M.A.: Perception-based visual quality measures. In: 2011 IEEE Conference on Visual Analytics Science and Technology (VAST), pp. 13–20 (2011)

    Google Scholar 

  2. Brunet, D.: A Study of the Structural Similarity Image Quality Measure with Applications to Image Processing. Ph.D. Thesis, Department of Applied Mathematics, University of Waterloo (2012)

    Google Scholar 

  3. Brunet, D., Vrscay, E.R., Wang, Z.: Structural similarity-based approximation of signals and images using orthogonal bases. In: Campilho, A., Kamel, M. (eds.) ICIAR 2010. LNCS, vol. 6111, pp. 11–22. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Brunet, D., Vrscay, E.R., Wang, Z.: On the mathematical properties of the structural similarity index. Proc. IEEE Trans. Image Processing 21(4), 1488–1499 (2012)

    Article  MathSciNet  Google Scholar 

  5. Amir Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM Journal on Imaging Sciences Archive 2(1), 183–202 (2009)

    Article  MATH  Google Scholar 

  6. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press (2004)

    Google Scholar 

  7. Channappayya, S.S., Bovik, A.C., Caramanis, C., Heath Jr, R.W.: Design of linear equalizers optimized for the structural similarity index. IEEE Transactions on Image Processing 17(6), 857–872 (2008)

    Article  MathSciNet  Google Scholar 

  8. Donoho, D.: Denoising by Soft-Thresholding. IEEE Transactions on Information Theory 41(3), 613–627 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  9. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least Angle Regression. The Annals of Statistics 32, 407–451 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. Mairal, J., Bach, F., Jenatton, R., Obozinski, G.: Convex Optimization with Sparsity-Inducing Norms. Optimization for Machine Learning. MIT Press (2011)

    Google Scholar 

  12. Ortega, J.M.: The Newton-Kantorovich Theorem. The American Mathematical Monthly 75(6), 658–660 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rehman, A., Rostami, M., Wang, Z., Brunet, D., Vrscay, E.R.: SSIM-inspired image restoration using sparse representation. EURASIP J. Adv. Sig. Proc. (2012). doi:10.1186/1687-6180-2012-16

    Google Scholar 

  14. Rehman, A., Gao, Y., Wang, J., Wang, Z.: Image classification based on complex wavelet structural similarity. Sig. Proc. Image Comm. 28(8), 984–992 (2013)

    Article  Google Scholar 

  15. Tseng, P., Yun, S.: A Coordinate Gradient Descent Method for Non-smooth Separable Minimization. Journal of Mathematical Programming 117(1–2), 387–423 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Turlach, B.A.: On algorithms for solving least squares problems under an \(\ell _1\) penalty or an \(\ell _1\) constraint. In: Proceedings of the American Statistical Association, Statistical Computing Section, pp. 2572–2577 (2005)

    Google Scholar 

  17. Wang, Z., Bovik, A.C.: A universal image quality index. IEEE Signal Processing Letters 9(3), 81–84 (2002)

    Article  Google Scholar 

  18. Wang, Z., Bovik, A.C., Sheikh, H.-R., Simoncelli, E.S.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Processing 13(4), 600–612 (2004)

    Article  Google Scholar 

  19. Wang, S., Rehman, A., Wang, Z., Ma, S., Gao, W.: SSIM-motivated rate-distortion optimization for video coding. IEEE Trans. Circuits Syst. Video Techn. 22(4), 516–529 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo, Waterloo, ON, N2L3G1, Canada

    Daniel Otero & Edward R. Vrscay

Authors
  1. Daniel Otero
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edward R. Vrscay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Otero .

Editor information

Editors and Affiliations

  1. Faculty of Engineering, University of Porto, Porto, Portugal

    Aurélio Campilho

  2. Dept. of Electrical and Computer Eng., University of Waterloo, Waterloo, Ontario, Canada

    Mohamed Kamel

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Otero, D., Vrscay, E.R. (2014). Unconstrained Structural Similarity-Based Optimization. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2014. Lecture Notes in Computer Science(), vol 8814. Springer, Cham. https://doi.org/10.1007/978-3-319-11758-4_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11758-4_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11757-7

  • Online ISBN: 978-3-319-11758-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation