You would pick a random white cell that is considered "outside" the black area, then you flood to the surrounding tiles until you have no more white cells to flood. Then you find all the white cells that didnt get flooded and turn them black.

If you [s]want[/s] need ugly optimizations, you could make the pic in a quadtree with all bottom level nodes existing, and have the not-top-level nodes be either black white or both, so you can flood at a higher level if the high nodes are only of single color, and then go deeper in the tree to flood smaller areas when you get to an node with both black and white.

Something like that.

Edit: Though im not sure if that would be even faster...