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.

 

[CellCoree]

!

The equation for the half-max contour of a 2D Gaussian can be expressed as follows:

(x-x0)^2/a + (y-y0)^2/b = ln(2*h)

This equation represents the elliptical contour line where the Gaussian function has a value that is half of its maximum value (h). The parameters x0 and y0 represent the center of the Gaussian, while a and b control the spread of the Gaussian in the x and y directions, respectively. This equation can be used to plot the half-max contour of the Gaussian and visualize its shape. I hope this helps to clarify any confusion.