If you enable frontend editing to uploaders ( See Table VII-D2: Uploader edit ) he gets an Edit link in the photo description box under the slide. The pop-up page that appears after clicking the link is a ( limited ) version of the edit photo information admin screen, with the one photo and it has also the delete link in it.
You must be either administrator or the uploader of the photo to see the link.
Actually the rule is:
IF ( user is NOT on the blacklist )
AND ( ( user can admin albums ) OR ( user is owner of the photo AND user can upload AND the upload edit switch is on ) )
Right now only administrator can use the edit-function, not the user. I have tested with both a user and admin. I cannot find a button to let user edit their album
Table VII-A under Upload Photos: tick the box for the appropriate userrole