How can I create a binary mask?

I want to create a binary mask, where there will be random white dots in the area. But it will be more dense in the middle. For the reference please check the image.

row = 320;
col = 320;
trnMask = zeros(row,col)
trnMask = rand(320);
figure,imshow(trnMask);

I tried this code. But it doesn't work.

Answer 1

[DGM]

Without having clear technical goals, I'm just going to assume that no technical requirements exist for shape or density. I'm going to treat this as a rudimentary dithering operation.

% image size
s = 320;

% generate some gaussian profile or something?
sg = s*0.15; % gaussian shape parameter
os = 0.05; % background noise
R = linspace(-s/2,s/2,s);
prof = exp(-(R.^2 + R.'.^2)/(2*sg^2));
prof = prof*(1-os) + os;

% create random mask
mask = rand(s);

% binarize profile by comparing gray levels to mask
out = mask <= prof;

imshow(out)