I have a question as follows:
Suppose I have an image(size=360x640(row by col)), and I have a center coordinate that's say is (20, 100). What I want is to generate a probability distribution that has the highest value in that center (20,100), and lower probability value in the neighbor and much more lower value farer than the center.
All I figure out is to put a multivariate gaussian (since the dimension is 2D) and set mean to the center(20,100). But is that correct and how do I design the covariance matrix?
Thanks!!
You could do it in 2D by generating radial and polar coordinates
Along the line:
Pi = 3.1415926
cx = 20
cy = 100
r = sqrt( -2*log(1-U(0,1)) )
a = 2*Pi*U(0,1)
x = scale*r*cos(a)
y = scale*r*sin(a)
return (x + cx, y + cy)
where scale is a parameter to make it from unitless gaussian to some unit applicable to your problem. U(0,1) is uniform in [0...1) random value.
Reference: Box-Muller sampling.
If you want generic 2D gaussian, meaning ellipse in 2D, then you'll have to use different scales for X and Y, and rotate (x,y) vector by predefined angle using well-known rotation matrix
