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# measerr

Quality metrics of signal or image approximation

## Description

example

[PSNR,MSE,MAXERR,L2RAT] = measerr(X,XAPP) returns the peak signal-to-noise ratio, PSNR, mean square error, MSE, maximum squared error, MAXERR, and ratio of squared norms, L2RAT, for an input signal or image, X, and its approximation, XAPP.

example

[PSNR,MSE,MAXERR,L2RAT] = measerr(X,XAPP,BPS) uses the bits per sample, BPS, to determine the peak signal-to-noise ratio.

## Examples

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Approximate an RGB image and compute the quality metrics.

Load an RGB image. Return the image dimensions and minimum and maximum values.

X = imread('africasculpt.jpg');
size(X)
ans = 1×3

512   512     3

[min(X(:)) max(X(:))]
ans = 1x2 uint8 row vector

0   236

Define the image approximation by setting equal to 1 all RGB values less than or equal to 100.

Xapp = X;
Xapp(X<=100) = 1;

Display the image and its approximation.

subplot(1,2,1)
image(X)
title('Original Image')
subplot(1,2,2)
image(Xapp)
title('Approximation')

Compute the quality metrics of the image approximation.

[psnr,mse,maxerr,L2rat] = measerr(X,Xapp)
psnr = 17.5287
mse = 1.1487e+03
maxerr = 99
L2rat = 0.9398

Approximate a grayscale image and calculate approximation quality metrics.

Create a 256-by-256 grayscale image with intensities between $0$ and ${2}^{16}-1$.

val = 0:2^16-1;
X = reshape(val,256,256);

There are 16 bits per sample. Define the image approximation by setting equal to 1 all grayscale values less than or equal to 1000. Display the image and its approximation.

Xapp = X;
Xapp(X<=1000) = 1;
colormap(gray(2^16))
subplot(1,2,1)
image(X)
title('Original Image')
subplot(1,2,2)
image(Xapp)
title('Approximation')

There are 16 bits per sample. Compute the quality metrics of the grayscale approximation.

bps = 16;
[psnr,mse,maxerr,L2rat] = measerr(X,Xapp)
psnr = 11.0733
mse = 5.0786e+03
maxerr = 999
L2rat = 1.0000

## Input Arguments

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Input signal or image, specified as a real-valued array.

Approximation of signal or image X, specified as a real-valued array. XAPP is the same size as X.

Bits per sample of the input data, specified as a positive integer. The default value is 8, so the maximum possible pixel value of an image (MAXI) is 255. More generally, when samples are represented using linear Pulse Code Modulation with B bits per sample, MAXI is 2B−1.

## Output Arguments

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Peak signal-to-noise ratio (PSNR) in decibels, returned as a positive real number. The PSNR is only meaningful for data encoded in terms of bits per sample or bits per pixel. For example, an image with 8 bits per pixel contains integers from 0 to 255.

Mean square error, returned as a positive real number. MSE is the squared norm of the difference between X and XAPP divided by the number of elements.

Maximum absolute squared deviation of the data X from the approximation XAPP, returned as a positive real number.

Energy ratio between the approximation XAPP and input data X, returned as a positive real number. L2RAT is the ratio of the squared norm of XAPP to X.

## More About

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### Peak Signal to Noise Ratio

The peak signal-to-noise ratio (PSNR) in decibels between a signal and its approximation is

$20{\mathrm{log}}_{10}\left(\frac{{2}^{B}-1}{\sqrt{MSE}}\right)$

where MSE represents the mean square error, and B represents the bits per sample.

### Mean Square Error

The mean square error (MSE) between a signal or image, X, and an approximation, Y, is

$\frac{||X-Y|{|}^{2}}{N}$

where N is the number of elements in the signal.

## References

[1] Huynh-Thu, Q. and M. Ghanbari. "Scope of Validity of PSNR in Image/Video Quality Assessment." Electronics Letters. Vol. 44, Issue 13, 2008, pp. 800–801.

## See Also

### Topics

Introduced in R2010b

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