ssim

Structural similarity (SSIM) index 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 (SSIM) index for grayscale image or volume 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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Calculate Structural Similarity Index (SSIM)

Open Live Script

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

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

Display both images as a montage. The images differ most along sharp high-contrast regions, such as the edges of the trellis.

montage({ref,A})
title('Reference Image (Left) vs. Blurred Image (Right)')

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

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

Display the local SSIM map. Include the global SSIM value in the figure title. Small values of local SSIM appear as dark pixels in the local SSIM map. Regions with small local SSIM value correspond to areas where the blurred image noticeably differs from the reference image. Large values of local SSIM value appear as bright pixels. Regions with large local SSIM correspond to uniform regions of the reference image, where blurring has less of an impact on the image.

imshow(ssimmap,[])
title(['Local SSIM Map with Global SSIM Value: ',num2str(ssimval)])

Input Arguments

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`A` — Image whose quality is to be measured
2-D grayscale image | 3-D grayscale volume

Image whose quality is to be measured, specified as a 2-D grayscale image or 3-D grayscale volume.

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

`ref` — Reference image
2-D grayscale image | 3-D grayscale volume

Reference image against which quality is measured, specified as a 2-D grayscale image or 3-D grayscale volume of the same size and data type 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)

`'DynamicRange'` — Dynamic range of the input image
`diff(getrangefromclass(A))` (default) | positive scalar

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].

`'Exponents'` — Exponents for luminance, contrast, and structural terms
`[1 1 1]` (default) | 3-element vector of nonnegative numbers

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

`'Radius'` — Standard deviation of isotropic Gaussian function
`1.5` (default) | positive number

Standard deviation of isotropic Gaussian function, specified as a positive number. 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.

`'RegularizationConstants'` — Regularization constants for luminance, contrast, and structural terms
3-element vector of nonnegative numbers

Regularization constants for the luminance, contrast, and structural terms, specified as a 3-element vector of nonnegative 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

Output Arguments

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`ssimval` — SSIM index
nonnegative number

SSIM index, returned as a nonnegative number. The data type of ssimval is double except when A is data type single, in which case ssimval is of class single.

`ssimmap` — Local values of SSIM index
numeric array

Local values of SSIM index, returned as a numeric array of nonnegative numbers of the same size as the input image, A. The data type of ssimmap is double except when A is data type single, in which case ssimmap is of class single.

More About

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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 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.

$S S I M (x, y) = {[l (x, y)]}^{α} \cdot {[c (x, y)]}^{β} \cdot {[s (x, y)]}^{γ}$

where

$\begin{array}{l} l (x, y) = \frac{2 μ_{x} μ_{y} + C_{1}}{μ_{x}^{2} + μ_{y}^{2} + C_{1}}, \\ c (x, y) = \frac{2 σ_{x} σ_{y} + C_{2}}{σ_{x}^{2} + σ_{y}^{2} + C_{2}}, \\ s (x, y) = \frac{σ_{x y} + C_{3}}{σ_{x} σ_{y} + C_{3}} \end{array}$

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 C₃ = C₂/2 (default selection of C₃) the index simplifies to:

$S S I M (x, y) = \frac{(2 μ_{x} μ_{y} + C_{1}) (2 σ_{x y} + C_{2})}{(μ_{x}^{2} + μ_{y}^{2} + C_{1}) (σ_{x}^{2} + σ_{y}^{2} + C_{2})}$

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.

Documentation

ssim

Syntax

Description

Examples

Calculate Structural Similarity Index (SSIM)

Input Arguments

`A` — Image whose quality is to be measured
2-D grayscale image | 3-D grayscale volume

`ref` — Reference image
2-D grayscale image | 3-D grayscale volume

Name-Value Pair Arguments

`'DynamicRange'` — Dynamic range of the input image
`diff(getrangefromclass(A))` (default) | positive scalar

`'Exponents'` — Exponents for luminance, contrast, and structural terms
`[1 1 1]` (default) | 3-element vector of nonnegative numbers

`'Radius'` — Standard deviation of isotropic Gaussian function
`1.5` (default) | positive number

`'RegularizationConstants'` — Regularization constants for luminance, contrast, and structural terms
3-element vector of nonnegative numbers

Output Arguments

`ssimval` — SSIM index
nonnegative number

`ssimmap` — Local values of SSIM index
numeric array

More About

Structural Similarity Index

Algorithms

References

See Also

Topics

Introduced in R2014a

Image Processing Toolbox Documentation

Support

Documentation

ssim

Syntax

Description

Examples

Calculate Structural Similarity Index (SSIM)

Input Arguments

A — Image whose quality is to be measured 2-D grayscale image | 3-D grayscale volume

ref — Reference image 2-D grayscale image | 3-D grayscale volume

Name-Value Pair Arguments

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

'Exponents' — Exponents for luminance, contrast, and structural terms [1 1 1] (default) | 3-element vector of nonnegative numbers

'Radius' — Standard deviation of isotropic Gaussian function 1.5 (default) | positive number

'RegularizationConstants' — Regularization constants for luminance, contrast, and structural terms 3-element vector of nonnegative numbers

Output Arguments

ssimval — SSIM index nonnegative number

ssimmap — Local values of SSIM index numeric array

More About

Structural Similarity Index

Algorithms

References

See Also

Topics

Introduced in R2014a

Image Processing Toolbox Documentation

Support

`A` — Image whose quality is to be measured
2-D grayscale image | 3-D grayscale volume

`ref` — Reference image
2-D grayscale image | 3-D grayscale volume

`'DynamicRange'` — Dynamic range of the input image
`diff(getrangefromclass(A))` (default) | positive scalar

`'Exponents'` — Exponents for luminance, contrast, and structural terms
`[1 1 1]` (default) | 3-element vector of nonnegative numbers

`'Radius'` — Standard deviation of isotropic Gaussian function
`1.5` (default) | positive number

`'RegularizationConstants'` — Regularization constants for luminance, contrast, and structural terms
3-element vector of nonnegative numbers

`ssimval` — SSIM index
nonnegative number

`ssimmap` — Local values of SSIM index
numeric array