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Statistical estimation of the structural similarity index for image quality assessment

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Abstract

The structural similarity (SSIM) index has been studied from different perspectives in the last decade. Most of the developments consider its parameters fixed. Because each of these parameters corresponds to the weight of a factor in the final SSIM coefficient, the usual assumption that all parameters are equal to one is questionable. In this article, a new estimation method is proposed from a statistical perspective. The approach we develop is a model-based estimation method so that the usual assumption that all parameters are equal to one can be handled via approximate hypothesis-testing techniques that are properly developed in the context of regression. The method considers nonlinear models with multiplicative noise to explain the root mean square error as a function of the SSIM index. A numerical experiment based on a Monte Carlo simulation is carried out to test whether the parameters are all equal to one and to gain more insight into the performance of the estimates in practice. Our analysis showed that the assumption that the parameters are equal to one is not supported by the data and may lead to a misconception of the closeness between two images.

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Notes

  1. https://www.mathworks.com/matlabcentral/answers/9217-need-ssim-m-code.

  2. https://gist.github.com/Bibimaw/8873663.

  3. URL: https://github.com/faosorios/SSIM.

  4. URL: https://www.iceye.com/downloads/datasets.

  5. URL:  http://sipi.usc.edu/database.

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Acknowledgements

The authors acknowledge the suggestions and comments from the Associate Editor and anonymous referees that led to a significant improvement of the manuscript. Felipe Osorio and Ronny Vallejos acknowledge financial support from CONICYT through the MATH-AMSUD program, Grant 20-MATH-03, from UTFSM, Grants PI_LI_19_11 and P_LIR_2020_20. Ronny Vallejos was also partially funded by the Advanced Center for Electrical and Electronic Engineering (AC3E), Grant FB-0008. Silvia M. Ojeda and Marcos Landi were supported by Secretaría de Ciencia y Tecnología (SeCyT) from Universidad Nacional de Córdoba. Proyecto Consolidar 2018-2121 (P.I.D. No. 33620180100055CB) y CIEM (Córdoba), CONICET.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile

    Felipe Osorio & Ronny Vallejos

  2. U-Planner, Avenida Tupungato 3850, Curauma, Valparaíso, Chile

    Wilson Barraza

  3. Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Medina Allende s/n, Ciudad Universitaria (X5000HUA), Córdoba, Argentina

    Silvia María Ojeda

  4. Instituto de Diversidad y Ecología Animal, CONICET y Facultad de Ciencias Exactas Físicas y Naturales, Universidad Nacional de Córdoba, 5016, Córdoba, Argentina

    Marcos Alejandro Landi

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  1. Felipe Osorio
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  2. Ronny Vallejos
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  3. Wilson Barraza
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  4. Silvia María Ojeda
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  5. Marcos Alejandro Landi
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Correspondence to Felipe Osorio.

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Osorio, F., Vallejos, R., Barraza, W. et al. Statistical estimation of the structural similarity index for image quality assessment. SIViP 16, 1035–1042 (2022). https://doi.org/10.1007/s11760-021-02051-9

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  • DOI: https://doi.org/10.1007/s11760-021-02051-9

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