How do people store images on the back end and only allow certain people have access to it?

Ex: a user login to a website and uploads a profile pic. I want to restrict the access to only allow the user that uploads the pic gets to have access.

So, if a second person somehow gets the URL to the pic, he or she still can not access it because she or he doesn't have the right permission(http://ift.tt/1Txo5LW). Right now i have it so that the user can upload a profile pic but then anyone that has the URL are able to type in the browser and see the pic. I dont want that.

This is a project for fun so all suggestions are welcome.