If you have it set in admin edit usergroups users can edit their photos and then in admin options you elect for users to move delete their images when they edit their photos they will be able to move or delete it.
I have just cheacked, both moving and deleting are set to yes in the admin options and the registered users are still set to what they are as standard but have just looked and cant seem to find the move/delete icon when logged in as a Registered User viewing one of my own photos?