Calculating mean square difference (MSD) of two matrices

I would like to calculate the MSD of two matrices, but I cannot figure what MSD actually is. From my understanding, it is like this:

Im = [0 252 204;
    221 135 58;
    156 122 127]

Im2 = [169 250 237;
    186 196 148;
    227 148 4]

F2 = sum(sum(mean(Im2-Im).^2))

Answer 1

[Chunru]

Im = [0 252 204;
    221 135 58;
    156 122 127]

Im = 3×3

0 252 204 221 135 58 156 122 127

Im2 = [169 250 237;
    186 196 148;
    227 148 4]

Im2 = 3×3

169 250 237 186 196 148 227 148 4

F2 = sum(sum(mean(Im2-Im).^2))

F2 = 5.4722e+03

% Mean Squared Difference
%   mean   diff     squared    all elements
F = mean((Im - Im2).^2,        'all')

F = 7.0607e+03

[Jimmy Neutron]

What does the 'all' do?

and why is there a difference when just summing all the values?

[Chunru]

'all' means to sum all elements of the array. sum(sum(mean(Im2-Im).^2)) is to compute the difference (Im2-Im), then find its mean, then square, then sum up all elements.

[DGM]

If you have IPT, why not just use immse()?

Im = [0 252 204;
    221 135 58;
    156 122 127];

Im2 = [169 250 237;
    186 196 148;
    227 148 4];

% you could do all this
F = mean((Im - Im2).^2,'all')

F = 7.0607e+03

% or you could just do this
F = immse(Im,Im2)

F = 7.0607e+03