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Structural Similarity Index (SSIM) for measuring image quality

`ssimval = ssim(A,ref)`

```
[ssimval,ssimmap]
= ssim(A,ref)
```

`___ = ssim(__,Name,Value,...)`

`___ = ssim(__,`

computes
the SSIM, using name-value pairs to control aspects of the computation.
Parameter names can be abbreviated.`Name,Value`

,...)

The Structural Similarity (SSIM) Index quality assessment index is based on the computation of three terms, namely the luminance term, the contrast term and the structural term. The overall index is a multiplicative combination of the three terms.

$$SSIM(x,y)={[l(x,y)]}^{\alpha}\cdot {[c(x,y)]}^{\beta}\cdot {[s(x,y)]}^{\gamma}$$

where

$$\begin{array}{l}l(x,y)=\frac{2{\mu}_{x}{\mu}_{y}+{C}_{1}}{{\mu}_{x}^{2}+{\mu}_{y}^{2}+{C}_{1}},\\ c(x,y)=\frac{2{\sigma}_{x}{\sigma}_{y}+{C}_{2}}{{\sigma}_{x}^{2}+{\sigma}_{y}^{2}+{C}_{2}},\\ s(x,y)=\frac{{\sigma}_{xy}+{C}_{3}}{{\sigma}_{x}{\sigma}_{y}+{C}_{3}}\end{array}$$

where μ_{x}, μ_{y},
σ_{x},σ_{y}, and
σ_{xy} are the local means, standard deviations,
and cross-covariance for images *x, y*. If α
= β = γ = 1 (the default for Exponents), and C_{3} =
C_{2}/2 (default selection of C_{3})
the index simplifies to:

$$SSIM(x,y)=\frac{(2{\mu}_{x}{\mu}_{y}+{C}_{1})(2{\sigma}_{xy}+{C}_{2})}{({\mu}_{x}^{2}+{\mu}_{y}^{2}+{C}_{1})({\sigma}_{x}^{2}+{\sigma}_{y}^{2}+{C}_{2})}$$

[1] Zhou, W., A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli. "Image
Qualifty Assessment: From Error Visibility to Structural Similarity." *IEEE
Transactions on Image Processing*. Vol. 13, Issue 4, April 2004, pp.
600–612.

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