Given these two images from twitter.
http://a3.twimg.com/profile_images/130500759/lowres_profilepic.jpg
http://a1.twimg.com/profile_images/58079916/lowres_pr
A very simple approach:
f( "http://a3.twimg.com/profile_images/130500759/" ) = a3_130500759.jpg
f( "http://a1.twimg.com/profile_images/58079916/" ) = a1_58079916.jpg
As the other parts of this URL are constant, you can use the subdomain, the last part of the query path as a unique filename.
Don't know what could be a problem with this solution