There's I think 3 ways to do this.
1) You uncover as much as you can then use Photoshop (or a similar image editor) to fake reveal the rest of the black. Filling in the blanks so-to-speak.
2) You can make another UI object load the current zone's map image. The fog is layer over the image, so by loading the current zone's image directly, you get a fog free picture. Then take a screenshot and you have a clean version.
3) There's a way to displace the fog on the main map, essentially shoving it off to the side so it doesn't obscure the map. This is what's been done in the above screenshot.
The second way is the easiest and best.