Confused about 1D log Gabor
You're misunderstanding:


Wikipedia describes $G(f)$, the frequency response of the Log-Gabor filter. So you don't "find" $f$, it's your free variable.
$f_0$ and $\sigma$ are parameters of your filter, which you chose to maximize the "distinguishability" of "different" pictures. You need to come up with what "different" and "similar" means for you, and then you can optimize these parameters to make the Gabor transform of picture reflect these definitions. Notice that this is totally dependent on the image content and application you're doing.