Root mean square error of two images

What is the function to calculate RSME of two images in matlab? i use:

 I = imread('C:\Users\teymo\Desktop\New folder\CPU\rgray8.bmp');
 J = imread('C:\Users\teymo\Desktop\New folder\CPU\blur.bmp'); 
 result = sqrt(mean((J-I).^2));
 message = sprintf('The Root mean square error is %.3f.', result); 
 msgbox(message);

but i get a error string error computing that, but the message box variable does show the root square but there are more than 1 number ?

"'The Root mean square error is 0.000.The Root mean square error is 2.848.The Root mean square error is 3.040.The Root mean square error is 3.056.The Root mean square error is 3.183.The Root mean square error is 3.350." It goes on forever so im not sure how to do it correctly

Answer 1

[Rik]

Imagen in Matlab are either 2D or 3D. Assuming your images are already 2D, the subtraction will be element-wise, after which you have an element-wise square, followed by mean. The mean function only reduces by 1 dimension, so you end up with a vector. That means sqrt will be an element-wise operation, so pog is a vector.

If you want a single number, you need to convert your images to a vector:

I = imread('C:\Users\teymo\Desktop\New folder\CPU\rgray8.bmp');
J = imread('C:\Users\teymo\Desktop\New folder\CPU\blur.bmp');
pog = sqrt(mean((J(:)-I(:)).^2));
%                 ^^^  ^^^ add this
message = sprintf('The Root mean square error is %.3f.', pog);
msgbox(message);

[Tey]

Thank you, it works!

[DGM]

Calculating RMSE (or MSE or MAD) directly on imported image data will likely be incorrect unless precautions are taken.

Most images are going to be integer-class, so the limited range of the numeric class will result in truncation when taking the difference and when squaring.

A = imread('peppers.png'); % these are both uint8
B = imnoise(A);

rmse1 = sqrt(mean((A(:)-B(:)).^2)) % direct calculation with integers

rmse1 = 9.1003

rmse2 = sqrt(mean((double(A(:))-double(B(:))).^2)) % convert to floats

rmse2 = 24.2077

rmse3 = sqrt(immse(A,B)) % or if you have IPT, you can just use immse()

rmse3 = 24.2077

[Tey]

Thanks for the updates, that is correct. SSIM or IMMSE are good alternatives