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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.

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Author information

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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