It seems like every api that Google has to get profile pictures requires the owner of the profile picture to be authenticated.
I did find an endpoint from this stackoverflow question :
http://picasaweb.google.com/data/entry/api/user/${emailAddress}?alt=json
It does work without authentication, but it seems to only work for older email accounts, and I can't find any documentation for it in Google's docs.
Is there any other way to do this?