Black And White To Colour Game Environment?

I'm no shader guy so I don't know how you would implement this, but I think it could work something like this:
You create a black texture like a depth texture you fill with white from the center. The overall black and white effect could be a postprocessing effect that takes the character's offset from the center into account while looking into that texture and desaturates all but the white pixels. The NPCs would need a shader that reads the same texture and decide on what to show depending on the white.
The texture of course would need to be large enough to accommodate for the character being farthest off center in any direction and still overlapping the while screen.