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| {{redirect|SSIM|the medical school in Davanagere, Karnataka, India|S. S. Institute of Medical Sciences|the South Sudan Independence Movement|South Sudan Liberation Movement}}
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| The '''structural similarity''' (SSIM) index is a method for measuring the similarity between two images. The SSIM index is a [[full reference metric]]; in other words, the measuring of image quality based on an initial uncompressed or distortion-free image as reference. SSIM is designed to improve on traditional methods like [[peak signal-to-noise ratio]] (PSNR) and [[mean squared error]] (MSE), which have proven to be inconsistent with human eye perception. | |
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| The difference with respect to other techniques mentioned previously such as MSE or PSNR is that these approaches estimate ''perceived errors''; on the other hand, SSIM considers image degradation as ''perceived change in structural information''. Structural information is the idea that the pixels have strong inter-dependencies especially when they are spatially close. These dependencies carry important information about the structure of the objects in the visual scene. | |
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| The SSIM metric is calculated on various windows of an image. The measure between two windows <math>x</math> and <math>y</math> of common size ''N''×''N'' is:
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| :<math>\hbox{SSIM}(x,y) = \frac{(2\mu_x\mu_y + c_1)(2\sigma_{xy} + c_2)}{(\mu_x^2 + \mu_y^2 + c_1)(\sigma_x^2 + \sigma_y^2 + c_2)}</math>
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| with
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| * <math>\scriptstyle\mu_x</math> the [[average]] of <math>\scriptstyle x</math>;
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| * <math>\scriptstyle\mu_y</math> the [[average]] of <math>\scriptstyle y</math>;
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| * <math>\scriptstyle\sigma_x^2</math> the [[variance]] of <math>\scriptstyle x</math>;
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| * <math>\scriptstyle\sigma_y^2</math> the [[variance]] of <math>\scriptstyle y</math>;
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| * <math>\scriptstyle \sigma_{xy}</math> the [[covariance]] of <math>\scriptstyle x</math> and <math>\scriptstyle y</math>;
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| * <math>\scriptstyle c_1 = (k_1L)^2</math>, <math>\scriptstyle c_2 = (k_2L)^2</math> two variables to stabilize the division with weak denominator;
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| * <math>\scriptstyle L</math> the [[dynamic range]] of the pixel-values (typically this is <math>\scriptstyle 2^{\#bits\ per\ pixel}-1</math>);
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| * <math>\scriptstyle k_1 = 0.01</math> and <math>\scriptstyle k_2 = 0.03</math> by default.
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| In order to evaluate the image quality this formula is applied only on [[Luma (video)|luma]]. The resultant SSIM index is a decimal value between -1 and 1, and value 1 is only reachable in the case of two identical sets of data. Typically it is calculated on window sizes of 8×8. The window can be displaced pixel-by-pixel on the image but the authors propose to use only a subgroup of the possible windows to reduce the complexity of the calculation.
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| Structural dissimilarity (DSSIM) is a distance metric derived from SSIM (though the triangle inequality is not necessarily satisfied).
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| :<math>\hbox{DSSIM}(x,y) = \frac{1 - \hbox{SSIM}(x, y)}{2}</math>
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| ==See also==
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| * [[PSNR]]
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| * [[Video quality]]
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| ==References==
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| * Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, "[http://www.cns.nyu.edu/~zwang/files/papers/ssim.html Image quality assessment: From error visibility to structural similarity]," [[IEEE Transactions on Image Processing]], vol. 13, no. 4, pp. 600-612, Apr. 2004.
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| * Loza et al., "Structural Similarity-Based Object Tracking in Video Sequences", Proc. of the 9th International Conf. on Information Fusion, 2006.
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| ==External links==
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| * [http://www.ece.uwaterloo.ca/~z70wang/research/ssim/ Home page]
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| * [https://github.com/pornel/dssim C Implementation]
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| * [http://mehdi.rabah.free.fr/SSIM/ C/C++ Implementation]
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| * [http://pholia.tdi.informatik.uni-frankfurt.de/~philipp/software/dssim.shtml DSSIM C++ Implementation]
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| * [http://www.lomont.org/Software/Misc/SSIM/SSIM.html Chris Lomont's C# Implementation]
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| * [http://qpsnr.youlink.org/ qpsnr implementation (multi threaded C++)]
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| [[Category:Image processing]]
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