Why do I have different results?

Hello.

I tried to estimate MSE and RMSE error between orignal image and my reconstructed images using the two codes below. I do observe I have different results of MSE and RMSE values for both codes when run separately. I don't know why. Both codes uses the same Original and reconstructed images (Gray scale images). Can anyone explain this to me ?? Also find attached function file used with code 1. Thanks

%%  Code 1 (Obtained MSE = 4.635 and RMSE = 2.153 )

% Read original and reconstructed image

data = imread('baby_GT[1-Original].bmp');
subplot(2, 2, 1);
imshow(data, []);
title('Original Gray Image');

estimate = imread('baby_GT[8-Our Method].bmp');
subplot(2, 2, 2);
imshow(estimate, []);
title('Reconstructed Gray Image');

% To compute MSE and RMSE
[mse, rmse] = RMSE(data,estimate);

% Alert user of the answer.
message = sprintf('The MSE = %.3f.\nThe RMSE = %.3f.', mse, rmse);
msgbox(message);% 


%% Code 2 (Obtained MSE = 10.03 and RMSE = 3.17 )

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('baby_GT[1-Original].bmp');
[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.

% Read in a reconstructed gray scale demo image.
reconImage = imread('baby_GT[8-Our Method].bmp');
[rows columns] = size(reconImage);
% Display the second image.
subplot(2, 2, 2);
imshow(reconImage, []);
title('Reconstructed 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(reconImage)) .^ 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);
% To get the Root Mean Squared Error.  It will be a floating numbers.
rmse = sqrt(mse);
% 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 MSE = %.2f.\nThe RMSE = %.2f.\nThe PSNR = %.2f', mse, rmse, PSNR);
msgbox(message);

Answer 1

[Miriam]

You should convert data and estimate using double() as well. The RMSE function also contains a squared error calculation where any negative differences will be clipped to zero. Try:

[mse, rmse] = RMSE(double(data),double(estimate));

for code 1.

Answer 2

[Image Analyst]

The R in RMSE means root, or square root. Check out this line of code

rmse = sqrt(mse);

so, now, you say "I do observe I have different results in MSE and RMSE values. I don't know why." Did you overlook the line of code above?

Attach 'baby_GT[1-Original].bmp' and 'baby_GT[8-Our Method].bmp' and the RMSE() function, if you want more help so we can run your code.

[Chidiebere Ike]

@ Image Analyst.

What I meant by "I do observe I have different results in MSE and RMSE values" is that I have different results of MSE and RMSE values for both codes when run separately (code 1 and code 2) despite having the same images. I should obtain same values for MSE and RMSE for both codes. Thats my point. Find attached file. Thanks

[Image Analyst]

If you use code 1 (someone else's) you have a line that subtracts the images

data - estimate

and that will clip to zero and not give negative numbers if the arrays are uint8. You should use code 2 (code I wrote) which casts the arrays to double and avoids the clipping problem.

[Chidiebere Ike]

Noted, Thanks. But does the same code (code you wrote) applicable to color image as well ? I used the code only on Grayscale images

[Image Analyst]

It looks like you'd need to change this

mse = sum(sum(squaredErrorImage)) / (rows * columns);

to this

mse = sum(sum(squaredErrorImage)) / numel(squaredErrorImage);

but I'd really recommend you use the built-in functions psnr() and immse().