Orientation of the sum of displaced 2d gaussians

36 Views Asked by At

I'm interested in finding the orientation of the sum of 2d gaussians.

If one gaussian is placed at the origin, and another displaced along the x axis, the sum of the two is going to have an orientation along the x axis.

How can I show this analytically?

My initial thought was to take the Fourier Transform of the sum of the two gaussians, and analyse the magnitude of the transform to deduce the orientation - by taking the derivative and calculating the maxima, for instance.

I'm wondering whether there is some better method that I'm unaware of for such an analysis.

Any thoughts?

Thanks!