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A New Class of Wavelet-Based Metrics for Image Similarity Assessment

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An Erratum to this article was published on 25 July 2017

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Abstract

In this paper, we propose a new class of image similarity metrics based on a wavelet decomposition. By suitably combining weighted contributions of the different dyadic frequency bands, we define a class of similarity measures and we prove it is a metric. Moreover, we discuss the theoretical relationship between the novel class of metrics and the well-known structural similarity index (SSIM) and its multiscale versions (MSSSIM and CWSSIM). By using standard benchmark indexes over a reference database in the literature (the TID2013 database), we test the efficiency of the newly defined metrics in performing similarity assessment. We compare the performance of our metric with other well-known indexes in the literature, such as SSIM, FPH, MSSSIM, CWSSIM and PSNR, to demonstrate its improvement over the current state of the art, which becomes more evident when the query image is the one identified by the worst level of degradation which is perceived by the human visual system, as coded by the standard mean opinion score stored in the database.

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  • 25 July 2017

    An erratum to this article has been published.

Notes

  1. Average computed over 100 evaluations on images of size 512\(\times \)384 pixels.

  2. http://www.cns.nyu.edu/~lcv/ssim/.

  3. https://ece.uwaterloo.ca/~70wang/research/iwssim.

  4. https://it.mathworks.com/matlabcentral/fileexchange.

  5. http://users.ece.utexas.edu/bevans/projects/hashing/software.html.

References

  1. Amir, D.: Characterizations of Inner Product Spaces. Birkhauser Verlag, Basel (1986)

    Book  MATH  Google Scholar 

  2. Apostol, T.: Ptolemy inequality and the chordal metric. Math. Mag. 40, 233–235 (1967)

    Article  MathSciNet  MATH  Google Scholar 

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

    Chapter  Google Scholar 

  4. Brunet, D., Vrscay, E.R., Wang, Z.: On the mathematical properties of the structural similarity index. IEEE Trans. Image Process. 21(4), 1488–1499 (2012). doi:10.1109/TIP.2011.2173206

    Article  MathSciNet  MATH  Google Scholar 

  5. Chang, H., Zhang, J.: New metrics for clutter affecting human target acquisition. IEEE Trans. Aerosp. Electron. Syst. 1(42), 361–368 (2006). doi:10.1109/TAES.2006.1603429

    Article  Google Scholar 

  6. Daubechies, I., et al.: Ten Lectures on Wavelets, vol. 61. SIAM, Philadelphia (1992)

    Book  MATH  Google Scholar 

  7. Fawcett, T.: An introduction to ROC analysis. Pattern Recognit. Lett. 27(8), 861–874 (2006)

    Article  MathSciNet  Google Scholar 

  8. Hästö, P.A.: A new weighted metric: the relative metric I. Math. Anal. Appl. 274, 38–58 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hendee, W.R., Wells, P.N. (eds.): The Perception of Visual Information. Springer, Berlin (1997)

    MATH  Google Scholar 

  10. Horé, A., Ziou, D.: Image quality metrics: PSNR vs. SSIM. In: Proceedings of IEEE International Conference on Pattern Recognition, pp. 2366–2369. IEEE, Istanbul, Turkey (2010)

  11. Hsu, C.Y., Lu, C.S.: Geometric distortion-resilient image hashing system and its application scalability. In: Proceedings of the 2004 Workshop on Multimedia and Security, pp. 81–92. ACM, New York, NY, USA (2004). doi:10.1145/1022431.1022448

  12. Hubel, D.H., Wiesel, T.N.: Receptive fields and functional architecture in two non striate visual areas of the cat. J. Neurophysiol. 28, 229–289 (1965)

    Article  Google Scholar 

  13. Leach, M.: A complete distortion correction for MR images: Ii. rectification of static-field inhomogeneities by similarity-based profile mapping. PHYSICS IN MEDICINE AND BIOLOGY 50(11), 2651–2661 (2005). http://publications.icr.ac.uk/2089/

  14. Lissner, I., Preiss, J., Urban, P., Lichtenauer, M.S., Zolliker, P.: Image-difference prediction: from grayscale to color. IEEE Trans. Image Pocess. 22(2), 435–446 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mallat, S.: A Wavelet Tour of Signal Processing, Third Edition: The Sparse Way, 3rd edn. Academic Press, Cambridge (2008)

    Google Scholar 

  16. Monga, V., Evans, B.L.: Perceptual image hashing via feature points: performance evaluation and tradeoffs. IEEE Trans. Image Pocess. 15(11), 3452–3465 (2006)

    Article  Google Scholar 

  17. Nikvand, N., Wang, Z.: Image distortion analysis based on normalized perceptual information distance. Signal Image Video Process. 7(3), 403–410 (2013)

    Article  Google Scholar 

  18. Okarma, K.: Colour image quality assessment using structural similarity index and singular value decomposition. In: Computer Vision and Graphics, pp. 55–65. Springer (2009)

  19. Okarma, K.: Combined image similarity index. Opt. Rev. 19(5), 349–354 (2012)

    Article  Google Scholar 

  20. Pezoa, J., Torres, S., Cdova, J., Reeves, R.: An enhancement to the constant range method for nonuniformity correction of infrared image sequences. In: A. Sanfeliu, J. Martnez Trinidad, J. Carrasco Ochoa (eds.) Progress in Pattern Recognition, Image Analysis and Applications, Lecture Notes in Computer Science, vol. 3287, pp. 525–532. Springer Berlin Heidelberg (2004)

  21. Piella, G., Heijmans, H.: A new quality metric for image fusion. In: 2003 IEEE International Conference on Image Processing, vol. 2, pp. 173–176. IEEE (2003). doi:10.1109/ICIP.2003.1247209

  22. Ponomarenko, N., Battisti, F., Egiazarian, K., Astola, J., Lukin, V.: Metrics performance comparison for color image database. In: Fourth international workshop on video processing and quality metrics for consumer electronics, vol. 27 (2009)

  23. Ponomarenko, N., Ieremeiev, O., Lukin, V., Egiazarian, K., Jin, L., Astola, J., Vozel, B., Chehdi, K., Carli, M., Battisti, F., Jay Kuo, C.C.: Color image database TID2013: peculiarities and preliminary results. In: Proceedings of the 4th European Workshop on Visual Information Processing EUPIV2013

  24. Ponomarenko, N., Jin, L., Ieremeiev, O., Lukin, V., Egiazarian, K., Astola, J., Vozel, B., Chehdi, K., Carli, M., Battisti, F., Jay Kuo, C.C.: Image database TID2013: peculiarities, results and perspectives. Signal Process. Image Commun. 30, 57–77 (2015)

    Article  Google Scholar 

  25. Ponomarenko, N., Lukin, V., Zelensky, A., Egiazarian, K., Carli, M., Battisti, F.: TID2008-a database for evaluation of full-reference visual quality assessment metrics. Adv. Mod. Radioelectron. 10(4), 30–45 (2009)

    Google Scholar 

  26. Sampat, M.P., Wang, Z., Gupta, S., Bovik, A.C., Markey, M.K.: Complex wavelet structural similarity: a new image similarity index. IEEE Trans. Image Pocess. 18(11), 2385–2401 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Simoncelli, E.P., Freeman, W.T., Adelson, E.H., Heeger, D.J.: Shiftable multiscale transforms. IEEE Trans. Inform. Theory 38(2), 587–607 (1992)

    Article  MathSciNet  Google Scholar 

  28. Snidaro, L., Foresti, G.L.: A multi-camera approach to sensor evaluation in video surveillance. In: 2005 IEEE International Conference on Image Processing, pp. 1101–1104. IEEE (2005)

  29. Solomon, D.: A Guide to Data Compression Methods. Springer, Berlin (2002)

    Book  Google Scholar 

  30. Torres, L.H.: Modern Sampling Theory. Birkhäuser, Basel (2001)

    Google Scholar 

  31. Wang, Z., Bovik, A.C.: Mean squared error: Love it or leave it? A new look at signal fidelity measures. Signal Process. Mag. 26(1), 98–117 (2009)

    Article  Google Scholar 

  32. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Pocess. 13(4), 600–612 (2004). doi:10.1109/tip.2003.819861

    Article  Google Scholar 

  33. Wang, Z., Bovik, A.C., Simoncelli, E.P.: Structural approaches to image quality assessment. In: Bovik, A. (ed.) Handbook of Image and Video Processing, chap. 8.3, 2nd edn, pp. 961–974. Academic Press, Cambridge (2005)

    Chapter  Google Scholar 

  34. Wang, Z., Shang, X.: Spatial pooling strategies for perceptual image quality assessment. In: 2006 IEEE International Conference on Image Processing, pp. 2945–2948. IEEE (2006). doi:10.1109/ICIP.2006.313136

  35. Wang, Z., Simoncelli, E.P., Bovik, A.C.: Multiscale structural similarity for image quality assessment. In: Conference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers, 2004, vol. 2, pp. 1398–1402. IEEE (2003)

  36. Zujovic, J., Pappas, T.N., Neuhoff, D.L.: Structural texture similarity metrics for image analysis and retrieval. IEEE Trans. Image Pocess. 22(7), 2545–2558 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Via Ferrata 1, 27100, Pavia, Italy

    Maria Grazia Albanesi & Riccardo Amadeo

  2. CNR IMATI Enrico Magenes, via Ferrata 1, 27100, Pavia, Italy

    Silvia Bertoluzza

  3. ICH Humanitas, Milan, Italy

    Giulia Maggi

Authors
  1. Maria Grazia Albanesi
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  2. Riccardo Amadeo
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  3. Silvia Bertoluzza
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  4. Giulia Maggi
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Corresponding author

Correspondence to Silvia Bertoluzza.

Additional information

The original version of this article was revised: The double vertical bars are inserted instead of single vertical bars in Equation 9.

An erratum to this article is available at https://doi.org/10.1007/s10851-017-0751-3.

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Albanesi, M.G., Amadeo, R., Bertoluzza, S. et al. A New Class of Wavelet-Based Metrics for Image Similarity Assessment. J Math Imaging Vis 60, 109–127 (2018). https://doi.org/10.1007/s10851-017-0745-1

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  • DOI: https://doi.org/10.1007/s10851-017-0745-1

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