Facebook API – How do I get a Facebook user’s profile image through the Facebook API (without requiring the user to “Allow” the application)

I’m working on a CMS that fetches a user’s profile image from their Facebook URL (that is, http://facebook.com/users_unique_url). How can I accomplish this? Is there a Faceboook API call that fetches a user’s profile image URL without the user needing to Allow the application?