MSE Mean Square Error

I De-noise some images and I want to evaluate them so I calculate SNR but I want to use another like Mean Square Error (MSE) I saw some people use it but I don't know what is express in my case I have a noisy image like input and De-noised one in the out put Or maybe PSNR please help me

Answer 1

[Image Analyst]

See my demo:

% Demo to calculate PSNR of a gray scale image.
% http://en.wikipedia.org/wiki/PSNR
% Clean up.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;

%------ GET DEMO IMAGES ----------------------------------------------------------
% Read in a standard MATLAB gray scale demo image.
grayImage = imread('cameraman.tif');
[rows columns] = size(grayImage);

% Display the first image.
subplot(2, 2, 1);
imshow(grayImage, []);
title('Original Gray Scale Image', 'FontSize', fontSize);
set(gcf, 'Position', get(0,'Screensize')); % Maximize figure.

% Get a second image by adding noise to the first image.
noisyImage = imnoise(grayImage, 'gaussian', 0, 0.003);

% Display the second image.
subplot(2, 2, 2);
imshow(noisyImage, []);
title('Noisy Image', 'FontSize', fontSize);

%------ PSNR CALCULATION ----------------------------------------------------------
% Now we have our two images and we can calculate the PSNR.
% First, calculate the "square error" image.
% Make sure they're cast to floating point so that we can get negative differences.
% Otherwise two uint8's that should subtract to give a negative number
% would get clipped to zero and not be negative.
squaredErrorImage = (double(grayImage) - double(noisyImage)) .^ 2;
% Display the squared error image.
subplot(2, 2, 3);
imshow(squaredErrorImage, []);
title('Squared Error Image', 'FontSize', fontSize);
% Sum the Squared Image and divide by the number of elements
% to get the Mean Squared Error.  It will be a scalar (a single number).
mse = sum(sum(squaredErrorImage)) / (rows * columns);
% Calculate PSNR (Peak Signal to Noise Ratio) from the MSE according to the formula.
PSNR = 10 * log10( 256^2 / mse);
% Alert user of the answer.
message = sprintf('The mean square error is %.2f.\nThe PSNR = %.2f', mse, PSNR);
msgbox(message);

[Soum]

Thanks Image Analyst for your answer

Just a question in my case I've a noisy Image 'already noisy' without adding noise like in input and in the out put I've a De-noised image not like your case Image---->Noisy Image

anyway my Question is :if I calculate the SNR and PSNR between the noisy image and De-noised image

squaredErrorImage = (double(NoisyImage) - double(De-noisedImage)) .^ 2;

Thanks in advanced :)

[rashed]

Sir, Please see the attached image. I copy and paste the code and found the result. I do not know what they are meaning. I am developing a steganography apps and for this analysis part i have to calculate the MSE and PSNR of the stego image and original image. Please help me out of this confussion sir. Thanks

[Image Analyst]

That message box could not have been generated by my code if you look at my code. I only state the values once, not 3 times. Why don't you start a new discussion and post both your m-file and your image and we'll see how we can fix this?

[rashed]

Sir I have told you that i only copy and paste this code but my result shows me like this. That's why i upload the message box why it show 3 times. Thanks

[Image Analyst]

Somehow your cameraman.tif must have turned into a color image. The version of it that ships with MATLAB is definitely a grayscale image. What does this say:

[rows, columns, numberOfColorChannels] = size(grayImage)

It should say 256, 256, 1. If the third number is 3 then either you changed my demo to use a color image (most likely) or else somehow your cameraman.tif image is not the original one.

[Rasheed Khankan]

I think that the maximum value is 255 not 256.

[JDC]

That may well be. But he's referring to the dimensions of the image, not the pixel value.

[hayat ali]

@Image Analyst

thank yuo for your cooperation. but I have question

what are the range values that can be used in D, M,and V in both salt & pepper and gaussian

I = imread('eight.tif');
J = imnoise(I,'salt & pepper',D);
K = imnoise(I,'gaussian ',M,V);

[DGM]

@hayat ali

From the imnoise() synopsis:

J = imnoise(I,'salt & pepper',D) adds "salt and pepper" noise to the

image I, where D is the noise density. This affects approximately

D*numel(I) pixels. The default for D is 0.05.

So D can obviously be anything from 0 to 1. Values outside that range will result in an error message.

Also from the synopsis:

The mean and variance parameters for 'gaussian', 'localvar', and

'speckle' noise types are always specified as if for a double image

in the range [0, 1].

So M can be anything real, and V can be anything real and positive. Given the fact that we're working in unit-scale though, it wouldn't make sense for V to be very large or for the magnitude of M to be far from zero.

Answer 2

[ashkan abbasi]

    % MSE & PSNR for a grayscale image (cameraman.tif) & its filtered
    % version
    clear
    clc
    im=imread('cameraman.tif');
    im=im2double(im);
    h1=1/9*ones(3,3);
    imf1=imfilter(im,h1,'replicate');
    h2=1/25*ones(5,5);
    imf2=imfilter(im,h2,'replicate');
    %
    MSE1=mean(mean((im-imf1).^2));
    MSE2=mean(mean((im-imf2).^2));
    MaxI=1;% the maximum possible pixel value of the images.
    PSNR1=10*log10((MaxI^2)/MSE1);
    PSNR2=10*log10((MaxI^2)/MSE2);

[ameena begam]

hai,,ashkan my question is why u r using mean in MSE ,,why not using SUM function,,,thankyou,,please tell me

[Image Analyst]

The M in MSE means "Mean". He should use immse() and psnr(), the built in functions, though, if he has a recent enough version of MATLAB.

[Rasheed Khankan]

Great, concise, and operative code... Thanks a lot.

Answer 3

[Desmond Michael]

Hello everyone, I've found a website regarding the above and its very helpful. http://vaaiibhav.me/calculating-the-psnr-and-mse-code-matlab/

Edit @Rik:

The link seems to have gone down. Here is a capture of that page from 2019.

[Image Analyst]

I don't see anything there at that web site - no zip file or download link like it says. Anyway, since my answer above, MATLAB has added built-in functions immse() and psnr() to make it easy for you.

[Shaveta Arora]

Why is my Matlab is displaying

immse not found

and also psnr() is not there. Which versions support these built in functions?

[Image Analyst]

immse() was introduced in R2014b and psnr() was introduced in R2014a. See my attached demo where I do it without toolbox functions, and as given in my Answer way up at the top.

[indrani dalui]

This code are also calculate the PSNR for color image ?

[Image Analyst]

You have to decide what you want when you think of PSNR for a color image. Maybe you want the average PSNR of each color channel.

[DGM]

Note that if you have a version newer than R2014x and you don't have psnr() or immse(), bear in mind that both are still part of the Image Processing Toolbox, so you'll also need that.