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# ssim

Structural Similarity Index (SSIM) for measuring image quality

## Syntax

ssimval = ssim(A,ref)
[ssimval,ssimmap] = ssim(A,ref)
___ = ssim(A,ref,Name,Value)

## Description

ssimval = ssim(A,ref) computes the Structural Similarity Index (SSIM) value for image A using ref as the reference image.

example

[ssimval,ssimmap] = ssim(A,ref) also returns the local SSIM value for each pixel in A.

___ = ssim(A,ref,Name,Value) computes the SSIM, using name-value pairs to control aspects of the computation.

## Examples

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Read an image into the workspace. Create another version of the image, applying a blurring filter. Display both images.

H = fspecial('Gaussian',[11 11],1.5);
A = imfilter(ref,H,'replicate');

subplot(1,2,1); imshow(ref); title('Reference Image');
subplot(1,2,2); imshow(A);   title('Blurred Image');

Calculate the global SSIM value for the image and local SSIM values for each pixel. Return the global SSIM value and display the local SSIM value map.

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

fprintf('The SSIM value is %0.4f.\n',ssimval);
The SSIM value is 0.9407.

figure, imshow(ssimmap,[]);
title(sprintf('ssim Index Map - Mean ssim Value is %0.4f',ssimval));

## Input Arguments

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Image whose quality is to be measured, specified as a 2-D grayscale image or 3-D volume image. Must be the same size and class as ref

Data Types: single | double | int16 | uint8 | uint16

Reference image against which quality if measured, specified as a 2-D grayscale image or 3-D volume image. Must be the same size and class as A

Data Types: single | double | int16 | uint8 | uint16

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: ssim(A,ref,'DynamicRange',100)

Dynamic range of the input image, specified as a positive scalar. The default value of DynamicRange depends on the data type of image A, and is calculated as diff(getrangefromclass(A)). For example, the default dynamic range is 255 for images of data type uint8, and the default is 1 for images of data type double or single with pixel values in the range [0, 1].

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32

Exponents for the luminance, contrast, and structural terms, specified as a 3-element vector of nonnegative real numbers, [alpha beta gamma].

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32

Standard deviation of isotropic Gaussian function, specified as a positive scalar. This value is used for weighting the neighborhood pixels around a pixel for estimating local statistics. This weighting is used to avoid blocking artifacts in estimating local statistics.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32

Regularization constants for the luminance, contrast, and structural terms, specified as a 3-element vector of nonnegative real numbers of the form [c1 c2 c3]. The ssim function uses these regularization constants to avoid instability for image regions where the local mean or standard deviation is close to zero. Therefore, small non-zero values should be used for these constants.

By default,

• C1 = (0.01*L).^2, where L is the specified DynamicRange value.

• C2 = (0.03*L).^2, where L is the specified DynamicRange value.

• C3 = C2/2

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32

## Output Arguments

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Structural Similarity (SSIM) Index, returned as a scalar double, except when A and ref are of class single, in which case ssimval is of class single.

Local values of Structural Similarity (SSIM) Index, returned as a numeric array of class double except when A and ref are of class single, in which case ssimmap is of class single. ssimmap is an array of the same size as input image A.

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### Structural Similarity Index

An image quality metric that assesses the visual impact of three characteristics of an image: luminance, contrast and structure.

## Algorithms

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.

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

where

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

where μx, μy, σxy, and σxy are the local means, standard deviations, and cross-covariance for images x, y. If α = β = γ = 1 (the default for Exponents), and C3 = C2/2 (default selection of C3) the index simplifies to:

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

## References

[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.