Not sure what features of the image are important, so I'll just throw this simple approach out there.
A = imread('https://www.mathworks.com/matlabcentral/answers/uploaded_files/966550/test.png');
Depending on the needs, you might want to clamp Amn to only represent cases where the vertical mean exceeds the global mean.
Amn = imclamp(Amn-mean(Amn,2));
You could also restrict your sample region to the lower half of the image:
Amn = mean(A(120:end,:),1);
Amn = imclamp(Amn-mean(Amn,2));
You could also look at the relative column averages in the upper and lower halves and interpolate. That might help, as the variations aren't uniform over the height of the image.
Amnu = mean(A(1:120,:),1);
Amnu = Amnu-mean(Amnu,2);
Amnl = mean(A(120:end,:),1);
Amnl = Amnl-mean(Amnl,2);
Amn = imresize([Amnu; Amnl],size(A),'bilinear');
Similarly, with intermediate clamping:
Amnu = mean(A(1:120,:),1);
Amnu = imclamp(Amnu-mean(Amnu,2));
Amnl = mean(A(120:end,:),1);
Amnl = imclamp(Amnl-mean(Amnl,2));
Amn = imresize([Amnu; Amnl],size(A),'bilinear');
... but if we're going to try to get local with the averaging, what about a local average filter? We can just do something similar to what imflatfield() does and divide by the local mean.
blurred = imfilter(A,fk/sum(fk(:)),'replicate');
bmn = mean(blurred(~isnan(blurred)));
I have no idea if any of these are technically appropriate, so I'm just going to throw out a bunch of stuff and let you pick and choose what parts you think are suited for the task.
