How to rewrite 2D Gaussian eqn in terms of x?

[ireland01]

http://upload.wikimedia.org/math/1/9/8/1983171154842b0b061fc42aa5eb7642.png"

How to rewrite this 2D Gaussian eqn in terms of x?
i need to calculate the x and y values.
let x0=0 and y0=0.

is it complex?

 

[HallsofIvy]

What do you mean by "write in terms of x"? It is already written in terms of x and y and cannot be written in terms of x only.

Do you mean "solve for x"? Again, because it is a function of both x and y, you cannot solve it for x alone. You can assume a specific value for y and then solve for x.

But to "solve for x" you would also have to have a specific value of f(x,y).

I simply don't understand what you mean by "calculate the x and y values". In general, x and y can have any real values. What conditions are you placing on f(x,y) to give specific x and y values that you could calculate?

 

[ireland01]

yes sorry i mean solve for x

let f(x,y) = y = 2. say

 

[Mentallic]

I've never seen $\sigma$ so assuming it's to be treated as a constant, yes you certainly can solve for x given y and f(x,y). It's relatively simple too.

$$-ln\left(\frac{f(x,y)}{A}\right)=\frac{(x-x_0)^2}{2\sigma_x^2}+\frac{(y-y_0)^2}{2\sigma_y^2}$$

It should be obvious from here how to solve for x.