I googled his version, which I'm not as fond of. I'm not for sure on if his version would be copyrighted. My version however is not his version, and I did not consult his version when making this (actually did not know of its existence).
As for copyrights--I found this from a sight on copyrights.
"Consider the Mona Lisa. It is in the public domain; copyright ownership is held by the public. If a graphic artist modifies the original for a Web site, the modified Mona Lisa is then copyrighted, even though the original is in the public domain." Also when the owner of a work has been dead over 200 years, it is public domain (ie: any Shakespearean work).
There needs to be a slight twist, I think, like having a character drawing the beard on the painting like graffiti or adding something in the background to amp the joke. I'm not sure that this alone would be enough.