Equation for half-max contour of 2D Gaussian?

[mikeph]

Hi all,

If I have a Gaussian with the equation:

G(x,y) = h*exp(-(x-x0)^2/a -(y-y0)^2/b)

where x0, y0, a, b and h are the parameters which may vary, what's the equation for the elliptical contour line at the half-max of G?

I'm getting myself confused!

Thanks for help

 

[haruspex]

G(x,y) = h*exp(-(x-x0)^2/a -(y-y0)^2/b)
what's the equation for the elliptical contour line at the half-max of G?

How far did you get? Did you find the max value? Did you plug half that into the equation to see what resulted?

 

[mikeph]

I was wondering if there is some standard result that meant I didn't have to do all that.

 

[mathman]

Hi all,

If I have a Gaussian with the equation:

G(x,y) = h*exp(-(x-x0)^2/a -(y-y0)^2/b)

where x0, y0, a, b and h are the parameters which may vary, what's the equation for the elliptical contour line at the half-max of G?

I'm getting myself confused!

Thanks for help

G(x,y) = h/2 is what you want.

(x-x0)²/a + (y-y0)²/b = ln2.