I will let you know two methods to find out Facebook profile and/or page to which the picture belongs. I cannot guarantee that this will work for all the pictures, but it does work for most of them. And Facebook keeps on updating the picture URL, so don't be surprised if it does not work. However, it does work as of the moment of making this post.
Let us suppose the picture link looks like this :
Now, all you need to do is copy the middle number from the above URL to make it seem like this :
Go to the above URL, and you'll get to the Facebook Page. It works for finding out Facebook Profiles as well.
Bottom line - just add the middle number on the URL after http://facebook.com/ and you'll get to the page/profile.
The method above works for pictures which have only 3 numbers on their URL. If the above method does not work, try this one.
Let's suppose the picture URL looks like this :
As you can see, there are 5 numbers on the URL. In this case, what you need to do is extract the middle number just like we did in the above method and put it beside http://www.facebook.com/profile.php?id= .
For example, for the above URL, your Facebook Profile link would look like this : www.facebook.com/profile.php?id=906175229