How to calculate MSE and PSNR in two different size image (block matching)?

% This code is for template matching
clc; clear all; close all;

[filename, pathname, filterindex] = uigetfile( ...
{  '*.jpg','JPEG (*.jpg)'; ...
   '*.bmp','Windows Bitmap (*.bmp)'; ...
   '*.tif','TIFF (*.tif)';...
   '*.fig','Figures (*.fig)'; ...
   '*.*',  'All Files (*.*)'}, ...
   'Choose image(s) to be processed', ...
   'MultiSelect', 'off');
if filterindex==0, end

filename=cellstr(filename);

J= imread(horzcat(pathname,char(filename)));   % read complete image
I= rgb2gray(J); % colour to gray conversion/ 3D to 2D
imshow(I)
[Ir Ic]=size(I); %size check

subplot(2, 2, 1);
imshow(I)
title('Complete Grayscale Image', 'FontSize', 10);

T= imread('Template1.jpg'); % read template of the image
[Tr Tc]= size(T);
subplot(2, 2, 2);
imshow(T)
title('Template Image', 'FontSize', 10);

R= normxcorr2(T,I)   % Find normalize cross correlation
S = xcorr(T)
U=imcrop(R,[Tc Tr Ic Ir]);  % crop the extra pixels
[r c y]= find(U==(max(max(R))))   %find the coordinates where maximum correlation exists
RGB = insertShape(I, 'rectangle', [c r Tc Tr], 'LineWidth', 3); % create a box around maximum match

subplot(2, 2, 3);
imshow(RGB)
title('Matching Image', 'FontSize', 10);
subplot(2, 2, 4);
surf(U), shading flat
title('Cross correlation in surface', 'FontSize', 10); % graphics processing unit (GPU)'

[row col] = size(I);
err = 0;
for i = 1:row
    for j = 1:col
        err = err + (I(i,j) - T(i,j))^2;
    end
end
mse = err / (row*col);
psnr = 10*log10(n*n/mse);

I GOT THIS ERROR

Index in position 2 exceeds array bounds (must not exceed 112).
Error in Template_matching (line 75)
        err = err + (I(i,j) - T(i,j))^2;

[madhan ravi]

size(T) % ?

[LFM]

114x112 uint8

[madhan ravi]

size(I) % ?

[LFM]

600x800 uint8

Answer 1

[Image Analyst]

You don't want to do it that way since your template does not have as many rows as your larger image. What you want to do is to use your template as a kernel in a 2-D convolution. Untested code:

[rowsI, columnsI, numColorsI] = size(I);
[rowsT, columnsT, numColorsT] = size(T);
err = 0;
for j = 1 : (columnsI - columnsT)
    for i = 1 : (rowsI - rowsT)
        for c = 1 : columnsT
            for r = 1 : rowsT
                err = err + (I(i + r, j + c) - T(r, c))^2;
            end
        end
    end
end

If you want, you could handle the bottom and right edge effects where you have a shrinking window. I just went up until the template bumped up against the edge of the window and quit.

[LFM]

Thank you so much for your help, although i'm still running the code. It does really takes some time (lterally 3-4 hour). Plus, i'd make some mistakes on the MSE code.

I am not really sure what you mean by (If you want, you could handle the bottom and right edge effects where you have a shrinking window.).

If you wouldn't mind, may I ask if this is correct?

 mse = err / (rowsI*columnsI);

[Image Analyst]

No it's definitely not. If you used my loop, that's not even the number of elements (pixels) that were compared. Anyway, that's not the MSE since you're scanning a window and some pixels in the input image will be "covered" several times as the window moves across them. So you'd be over-counting.

I think you need to rethink what you're trying to do. I'm not sure it makes sense to compute the MSE of a large window and a smaller window. Explain why you think it does.

[LFM]

Thank you for responding. So, as you can see i'm doing a template matching and find the match position of the template in the image by normalized cross correlation. In template matching, the template will move pixel to pixel to find the match position. In this case, the match area will produce the value approximately to 1 means it is match. Now what i'm trying to do is the opposite of it. I'm trying to find the error between the template and the image. In my understanding, the smaller the MSE the closer the data fit. So, is this impossible to achieve or do you have sugesstion how I can accomplish this.

[Image Analyst]

I wish you had just said that in the first place because I have a demo already made up for that. See Attached.

[LFM]

Thank you but i see the demo is about normalized cross correlation. Now what i need to find is the error between the the template and the image when the template goes around to find the perfect match. In this case i thought MSE could be use. Am I wrong?