multissim

Multiscale structural similarity (MS-SSIM) index for image quality

Syntax

score = multissim(I,Iref)

score = multissim(I,Iref,Name,Value)

[score,qualityMaps] = multissim(___)

Description

score = multissim(I,Iref) calculates the multi-scale structural similarity (MS-SSIM) index, score, for image I, using Iref as the reference image. A value closer to 1 indicates better image quality and a value closer to 0 indicates poorer quality.

MS-SSIM is only defined for grayscale images. For inputs with more than two dimensions, multissim treats each element of higher dimensions as a separate 2-D grayscale image.

score = multissim(I,Iref,Name,Value) controls aspects of the computation using one or more name-value arguments. For example, specify the number of scales using the 'NumScales' argument.

[score,qualityMaps] = multissim(___) also returns the local MS-SSIM index value for each pixel in each scaled version of I. The qualitymap output is a cell array containing maps for each of the scaled versions of I. Each quality map is the same size as the corresponding scaled version of I.

Examples

Calculate MS-SSIM

Load an image into the workspace.

Iref = imread('pout.tif');

Create a noisy version of the image for comparison purposes.

I = imnoise(Iref,'salt & pepper',0.05);

Display the original image and noisy image.

figure; 
montage({Iref,I}); 

Calculate the MS-SSIM index that measures the quality of the input image compared to the reference image.

score = multissim(I,Iref)

score = single

0.6732

Calculate MS-SSIM and Get Local MS-SSIM Maps

Load an image into the workspace.

Iref = imread('pout.tif');
I = Iref;

Add noise to a localized part of the image.

I(1:100,1:100) = imnoise(Iref(1:100,1:100),'salt & pepper',0.05);

Display the original image and the noisy image.

figure; 
montage({Iref,I});

Calculate the local MS-SSIM index maps for the noisy image, qualitymaps, using the original image as the reference. The return value, qualitymaps, is a cell array containing a quality map for each of the scaled versions of the image. Each map is the same size as the corresponding scaled version of the image.

[~, qualitymaps] = multissim(I,Iref);
figure
montage(qualitymaps,'Size',[1 5])

Calculate MS-SSIM Specifying Scale Weights

Load an image into the workspace.

Iref = imread('pout.tif');

Create a noisy version of the image for comparison purposes.

I = imnoise(Iref,'salt & pepper',0.05);

Display the original image and the noisy version of the image.

figure; 
montage({Iref,I});

Calculate the MS-SSIM index for the noisy image, using the original image as the reference. Specify how much to weigh the local MS-SSIM index calculations for each scaled image, using the 'ScaleWeights' argument. The example uses the weight values defined in the article by Wang, Simoncelli, and Bovik.

score = multissim(I,Iref,'ScaleWeights',[0.0448,0.2856,0.3001,0.2363,0.1333])

score = single

0.6773

Calculate MS-SSIM of Color Image

Read a color image into the workspace.

RGB = imread("kobi.png");

Create a version of the image with added salt and pepper noise.

RGBNoisy = imnoise(RGB,"salt & pepper");

Display the two images in a montage.

montage({RGB,RGBNoisy})

Calculate the MS-SSIM of each color channel of the noisy image.

score = multissim(RGBNoisy,RGB);
score = squeeze(score)

score = 3×1 single column vector

    0.7084
    0.7135
    0.7066

Calculate MS-SSIM for dlarray Input

Read a color image into the workspace.

ref = imread("strawberries.jpg");
ref = im2single(ref);

Simulate a batch of six images by replicating the image along the fourth dimension.

refBatch = repmat(ref,[1 1 1 6]);

Create a copy of the batch of images, adding salt and pepper noise.

noisyBatch = imnoise(refBatch,"salt & pepper");

Create a formatted dlarray object for the original and noisy batch of images. The format is "SSCB" for spatial-spatial-channel-batch.

dlrefBatch = dlarray(refBatch,"SSCB");
dlnoisyBatch = dlarray(noisyBatch,"SSCB");

Calculate the MS-SSIM score of the noisy data with respect to the original data.

scores = multissim(dlnoisyBatch,dlrefBatch);

Remove the singleton dimensions corresponding to the spatial dimensions and display the scores. Each element is the MS-SSIM score for one color channel of one image of the batch.

squeeze(scores)

ans = 
  3(C) × 6(B) single dlarray

    0.8334    0.8335    0.8348    0.8335    0.8340    0.8349
    0.8325    0.8316    0.8309    0.8310    0.8317    0.8326
    0.8140    0.8123    0.8166    0.8129    0.8136    0.8123

Input Arguments

I — Input image

numeric array | dlarray object

Input image, specified as a numeric array of any dimension or a dlarray (Deep Learning Toolbox) object. Formatted dlarray objects cannot include more than one channel label, more than one batch label, and more than two spatial labels.

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

Iref — Reference image

numeric array | dlarray object

Reference image, specified as a numeric array of any dimension or a dlarray (Deep Learning Toolbox) object. Formatted dlarray objects cannot include more than one channel label, more than one batch label, and more than two spatial labels.

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

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: score = multissim(I,Iref,"NumScales",3);

NumScales — Number of scales

5 (default) | positive integer

Number of scales used to calculate the MS-SSIM index, specified as a positive integer. Setting NumScales to 1 is equivalent to using the ssim function with its Exponents name-value argument set to [1 1 1]. The size of the input image limits the number of scales. The multissim function scales the image (NumScales - 1) times, downsampling the image by a factor of 2 with each scaling.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

ScaleWeights — Relative values across scales

vector of positive numbers

Relative values across the scales, specified as a vector of positive elements. The length of the vector is equal to the number of scales, because each element corresponds to one of the scaled versions of the original image. The multissim function normalizes the values to 1. By default, the scale weights equal fspecial("gaussian",[1,numScales],1). The multissim function uses a Gaussian distribution as the default because the human visual sensitivity peaks at middle frequencies and decreases in both directions. For an example of setting ScaleWeights, see Calculate MS-SSIM Specifying Scale Weights.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Sigma — Standard deviation

1.5 (default) | positive number

Standard deviation of the isotropic Gaussian function, specified as a positive number. This value specifies the weighting of the neighborhood pixels around a pixel for estimating local statistics. The multissim function uses weighting to avoid blocking artifacts when estimating local statistics.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

DynamicRange — Dynamic range of input image

positive number

Dynamic range of the input image, specified as a positive number. The default value of DynamicRange depends on the data type of image I, and is calculated as diff(getrangefromclass(I)). 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

Output Arguments

score — MS-SSIM index

numeric scalar | numeric array | dlarray object

MS-SSIM index for image quality, returned as a numeric scalar, numeric array, or dlarray (Deep Learning Toolbox) object as indicated in the table. The value of score is typically in the range [0, 1]. The value 1 indicates the highest quality and occurs when I and Iref are equivalent. Smaller values correspond to poorer quality. For some combinations of inputs and name-value pair arguments, score can be negative.

Input Image Type	MS-SSIM Value
2-D numeric matrices	Numeric scalar with a single MS-SSIM measurement.
2-D dlarray objects	1-by-1 dlarray object with a single MS-SSIM measurement.
N-D numeric arrays with N>2	Numeric array of the same dimensionality as the input images. The first two dimensions of score are singleton dimensions. There is one MS-SSIM measurement for each element along the higher dimensions.
Unformatted N-D dlarray objects with N>2	dlarray object of the same dimensionality as the input images. The first two dimensions of score are singleton dimensions. There is one MS-SSIM measurement for each element along the higher dimensions.
Formatted N-D dlarray objects with N>2	dlarray object of the same dimensionality as the input images. The spatial dimensions of score are singleton dimensions. There is one MS-SSIM measurement for each element along any channel or batch dimension.

qualityMaps — Local MS-SSIM index values

cell array of numeric arrays | cell array of dlarray objects

Local MS-SSIM index values for each pixel in each scaled version, returned as a cell array of numeric arrays or a cell array of dlarray (Deep Learning Toolbox) objects. The size of the cell array is 1-by-NumScales. Each element in qualityMaps indicates the quality of the corresponding pixel at the corresponding scale factor. The format of each element uses the formatting of the scores argument, based on the format of the input images.

Algorithms

The structural similarity (SSIM) index measures perceived quality by quantifying the SSIM between an image and a reference image (see ssim). The multissim function calculates the MS-SSIM index by combining the SSIM index of several versions of the image at various scales. The MS-SSIM index can be more robust when compared to the SSIM index with regard to variations in viewing conditions.

The multissim function uses double-precision arithmetic for input images of class double. All other types of input images use single-precision arithmetic.

References

[1] Wang, Z., Simoncelli, E.P., Bovik, A.C. Multiscale Structural Similarity for Image Quality Assessment. In: The Thirty-Seventh Asilomar Conference on Signals, Systems & Computers, 2003, 1398–1402. Pacific Grove, CA, USA: IEEE, 2003. https://doi.org/10.1109/ACSSC.2003.1292216.

Extended Capabilities

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Image Processing on a GPU.

Version History

Introduced in R2020a

R2022b: Support for thread-based environments

multissim now supports thread-based environments.

R2021a: Calculate metrics of deep learning arrays and specify dimensions of computation

The multissim function now accepts dlarray input for deep learning applications.

This function also supports formatted data with dimension labels of 'S' (spatial), 'C' (channel), and 'B' (batch). For data with a batch dimension, the function returns a separate result for each index along the batch dimension.

R2021a: Support for GPU acceleration

multissim now supports GPU acceleration (requires Parallel Computing Toolbox™).