reconstruction Error of 2 colored images

I have an original image of dimension 300x300x3 (RGB)

after removing some entries, I apply an algorithm to reconstuct the original image.

Now i want to find the relative error between the 2 images.

....
 % I call my function norm_fro to calcuate the error
Erec(i)= norm_fro( X_origin , X_r ecovered);
....
    
%  here is my norm_fro function
function f = norm_fro( X , Xhat )

f = norm(X -Xhat,'fro')^2/norm(X,'fro')^2;

end

I get this error

Error using norm
Input must be 2-D.

Error in norm_fro (line 11)
f = norm(X -Xhat,'fro')^2/norm(X,'fro')^2;

Answer 1

[sanidhyak]

Hi fadmas18,

I understand that you are trying to find the relative error between 2 images using MATLAB’s “norm” function inside your custom-made function “norm_fro”.

When running the provided code, I too faced a similar error. This error occurs because the input images provided, “X” and “Xhat” are 3D arrays (300×300×3 for RGB), while the norm function with the “fro” option expects a 2D matrix. To resolve this, you need to reshape the images into 2D matrices before applying the Frobenius norm.

Kindly refer to the following corrected code:

function f = norm_fro(X, Xhat) 
% Reshape 3D image into 2D matrix 
X = reshape(X, [], size(X, 3)); 
Xhat = reshape(Xhat, [], size(Xhat, 3)); 

% Compute Frobenius norm 
f = norm(X - Xhat, 'fro')^2 / norm(X, 'fro')^2; 
end 

The command “reshape(X, [], size(X, 3))” changes the 300×300×3 image into a 90000×3 matrix, making it compatible with the “norm” function. This method enables the correct computation of the Frobenius norm for the 2D representation. With this adjustment, the "Input must be 2-D" error is fixed, allowing for an accurate calculation of the relative error.

For further reference on the “norm” function in MATLAB, kindly refer to the below documentation:

• https://www.mathworks.com/help/matlab/ref/norm.html

Cheers & Happy Coding!