- #1
TheCanadian
- 367
- 13
Case 1: I have a 2D Gaussian: ## Ae^{-[\frac { (x-x_o)^2 }{2 \sigma_x ^2} + \frac { (y-y_o)^2 }{2 \sigma_y ^2}]} ## where ## \sigma_x \neq \sigma_y ## (at least not necessarily). Using this as my 2D Gaussian, would the normalization constant be ## A = \frac {1}{2\pi (\sigma_x ^2 + \sigma_y ^2)} ##? In this context, what does ## \sigma = \sqrt{ \sigma_x ^2 + \sigma_y ^2} ## even mean?
Case 2: if ## \sigma_x = \sigma_y = \sigma ## in all cases, then I have: ## Ae^{-[\frac { (x-x_o)^2 + (y-y_o)^2 }{2 \sigma^2}]} ##. Would the normalization constant be ## A = \frac {1}{2\pi \sigma^2} ## in that case?
Also, in terms of physical significance, what is the difference between sigma in the first case and the second case (if any)?
Any help would be great!
Case 2: if ## \sigma_x = \sigma_y = \sigma ## in all cases, then I have: ## Ae^{-[\frac { (x-x_o)^2 + (y-y_o)^2 }{2 \sigma^2}]} ##. Would the normalization constant be ## A = \frac {1}{2\pi \sigma^2} ## in that case?
Also, in terms of physical significance, what is the difference between sigma in the first case and the second case (if any)?
Any help would be great!
Last edited: