I think the email with the picture and the invitation is a perfect thank you.
As a 50-something fuddy-duddy I think the important thing is to express your thanks. Handwritten note, typed letter, email, phone call, Face Time--it's all good. Where I draw the line is a texted thank you, because texts are so short that it's hard to say much, and text speak is just a tad too informal.
Now, the problem with an email is that you might send it to someone who insists on the handwritten note. While I think this will eventually change, to some extent, it's a know your audience type of thing. I think we're going to have a few years of affronted recipients of emailed thank-yous holding the smelling salts and exclaiming, "My dear, he sent an email instead of writing. No more birthday presents for him!"
But I hope that as time renders the new technologies more familiar, people will just appreciate getting thanked, no matter how those thanks are sent.