Enhancement of the structural similarity index SSIM
Abstract
Properties of a popular measure of comparing a digital image with a reference – the index of structural similarity, called SSIM in the literature – are explored. It is proved that the SSIM and its derivative functions are not metrics. Variants of the index modification are described. It is shown that measures similar to this index evaluate not quality of images, but their similarity by fragments. Additionally, it is shown that the averaged expert assessments called MOS are very subjective and cannot exact correlate with numerical estimates of similarity of the compared images. To get the SSIM index, a matrix of local estimates is calculated. Each evaluation determines similarity of two analyzed pixels with the same coordinates taking into account neighboring pixels. Usually, the average arithmetic value of the obtained matrix is used as the SSIM index. Instead, to improve the SSIM index, it is proposed to use the scale parameter of the Weibull distribution, which approximates the histogram of the local index estimates. On a set of images from the public database TID2013, it is shown that the proposed parameter is a more accurate characteristic of image similarity than the mean of local estimates.
About the Author
V. V. Starovoitov
The United Institute of Informatics Problems of the National Academy of Sciences of Belarus
Belarus
Belarus
Valery V. Starovoitov – D. Sc. (Engineering), Chief Researcher.
6, Surganova Str., 220012, MinskReferences
1. Wang Z., Bovik A. C., Sheikh H. R., Simoncelli E. P. Image quality assessment: from error visibility to structural similarity. IEEE Transactions on Image Processing, 2004, vol. 13, no. 4, рр. 600–612.
2. Ponomarenko N., Jin L., Ieremeiev O., Lukin V., Egiazarian K., Kuo C. Image database TID2013: peculiarities, results and perspectives. Signal Processing: Image Communication, 2015, vol. 30, рр. 57–77.
3. Geusebroek J., Smeulders A. W. M. A six-stimulus theory for stochastic texture. International Journal of Computer Vision, 2005, vol. 62, no. 1–2, рр. 7–16.
4. Xue W., Mou X. Reduced reference image quality assessment based on Weibull statistics. Proceedings of the 2nd International Workshop on Quality of Multimedia Experience. N.Y., 2010, рр. 11–16.
5. Brunet D., Vrscay E. R., Wang Z. On the mathematical properties of the structural similarity index. IEEE Transactions on Image Processing, 2012, vol. 21, no. 4, рр. 1488–1499.
6. Hore A., Ziou D. Image quality metrics: PSNR vs. SSIM. Proceedings of the 20th International Conference on Pattern Recognition. Washington, 2010, рр. 2366–2369.
7. Starovoitov V. V. Lokal'nye geometricheskie metody cifrovoj obrabotki i analiza izobrazhenij. Local Geometric Methods of Digital Image Processing and Analysis. Minsk, In-t tehn. kibernetiki NAN Belarusi Publ., 1997, 284 р. (in Russian).
8. Sidorov D. V. Modifikacija algoritma SSIM [SSIM algorithm modification]. Prikladnaja informatika [Applied Informatics], 2010, no. 4, рр. 123–125 (in Russian).
9. Wang Z., Simoncelli E. P., Bovik A. C. Multiscale structural similarity for image quality assessment. Proceedings of the 37th Asilomar Conference on Signals, Systems and Computers. USA, CA, 2004, vol. 2. рр. 1398–1402.
10. Eremeev O. I. Integrirovannaja metrika vizual'nogo kachestva izobrazhenij pri nalichii jetalona [Integrated metric of visual quality of images in the presence of a standard]. Sistemi obrobki іnformacіi [Information Processing Systems], 2014, no. 5, рр. 35–42 (in Russian).
11. Scholte H. S., Ghebreab S., Waldorp L., Smeulders A. W., Lamme V. A. Brain responses strongly correlate with Weibull image statistics when processing natural images. Journal of Vision, 2009, vol. 29, no. 4, рp. 11–25.
12. Statisticheskie metody. Raspredelenie Vejbulla. Analiz dannyh. State Standart R 50779.27–2017. Statistical methods. Weibull distribution. Data analysis. Moscow, Gosstandart Rossii, Izd-vo standartov Publ., 2017, 62 р. (in Russian).
13. Shewhart W. A. Statistical Method from the Viewpoint of Quality Control. Washington, Courier Corporation, 1939, 155 p.
14. Wheeler D. J. Problems with Skewness and Kurtosis. Part II. What do the shape parameters do? Quality Digest Daily, 2011. Available at: https://www.spcpress.com/pdf/DJW231.pdf (accessed 20.05.2018).
Review
For citations:
Starovoitov V.V. Enhancement of the structural similarity index SSIM. Informatics. 2018;15(3):41-55. (In Russ.)
Views: 971
Email this article 