The fft function can calculate the Fourier transform across any dimensions you choose. I do not understand the notation in that image, so this is something of a guess.
To calculate the Fourier transform of ‘x’ down the columns:
X1 = fft(x);
and across the rows:
X2 = fft(x,[],2);
Xc = mean(abs(X1));
Xr = mean(abs(X2),2);
That should do what you want.
MATLAB dimension conventions can be a bit confusing when first encountered.
