What does a low RMSE value of an image determine?

Hi,

I am comparing two images and wanted to calculate the error.

Does a lower RMSE value show a small error?

Thanks

Answer 1

[Image Analyst]

It means that the "test" image is close to the "reference" image on a pixel-by-pixel basis, if that's the RMSE method you used.

[Image Analyst]

I assume b and N are images, then it's almost correct. You need to square the (a-b) before you take the mean. You can use mean2() instead of mean(mean()) if they are gray scale images. See this snippet from my attached demo

%------ 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(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);

Note that there are now built in functions for mse called immse() and PSNR caleld psnr().