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# ssim

Structural Similarity Index (SSIM) for measuring image quality

## Syntax

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

___ = ssim(__,Name,Value,...) computes the SSIM, using name-value pairs to control aspects of the computation. Parameter names can be abbreviated.

## Examples

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### Calculate Structural Similarity Index (SSIM)

This example shows how to compute the SSIM value for a blurred image given the original image as a reference image.

Read an image and blur it. Display both images.

```ref = imread('pout.tif');
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);

figure, imshow(ssimmap,[]);
title(sprintf('ssim Index Map - Mean ssim Value is %0.4f',ssimval));```
`The SSIM value is 0.9407.`

## Input Arguments

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### A — Image whose quality is to be measured2-D grayscale image | 3-D volume image

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

### ref — Reference image against which quality is measured2-D grayscale image | 3-D volume image

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 single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example:

### 'DynamicRange' — Dynamic range of the input imagediff(getrangefromclass(A)) (default) | positive scalar

Dynamic range of the input image, specified as a positive scalar. By default, this value is chosen based on the class of the input image A, as diff(getrangefromclass(A)). When class of A is single or double, this value is 1, by default.

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

### 'Exponents' — Exponents for the luminance, contrast, and structural terms respectively[1 1 1] (default) | three-element vector of nonnegative real numbers, [alpha beta gamma]

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

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

### 'Radius' — Standard deviation of isotropic Gaussian function1.5 (default) | positive scalar

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

### 'RegularizationConstants' — Regularization constants for the luminance, contrast, and structural termsthree-element vector of nonnegative real numbers,[C1 C2 C3]

Regularization constants for the luminance, contrast, and structural terms, specified as a three-element vector of nonnegative real numbers. ssim 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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### ssimval — Structural Similarity (SSIM) Index scalar

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.

### ssimmap — Local values of Structural Similarity (SSIM) Index numeric array

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] Wang Zhou, Bovik, Alan C., Sheikh, Hamid R., and Simoncelli, Eero P.Image Qualifty Assessment: From Error Visibility to Structural Similarity. IEEE Transactions on Image Processing, Volume 13, Issue 4, pp. 600–612, April 2004