The permissions to enable the "Picture" feature of the User Profile Editor can be granted to an existing Access Template, or a new one can be created. The key is adding the two attributes below:
1) In the Access Templates available within ARS MMC, browse to the User Self-management folder, and either select or copy the "Self-Account Management' template. (If there is an existing one in use, then Right Click on it, choose Properties, then go to the Permissions tab.)
2) On the Permissions tab, select "Add" button
3) Select "Only the following classes" and then scroll down and select "User".
4) Select the "Object property access" button, and then check off both "Read Properties" and "Write Properties", then select "Next" button.
5) Select "The following properties" button and then check off "Show all possible properties".
6) Look for the following two attributes and check them off: photo, thumbnailPhoto.
7) Select "Finish" and "Apply"
The user may have to login again to the Self Service again to be able to see and Browse for a photo to select.