you can deform yourself enough to delay recognizing yourself in the mirror. you recognize yourself immediately now because you remember how you look like, but you had to learn how you look like first. humans (and few other animals) can recognize themselves because we can correlate what that other monkey looking at us is doing with what we are doing. the mirror-challenged will always think it's someone else and will often attack mirrors.
i think the ability to see yourself in what is not directly your body is why we are awesome at tool usage and identifying with that set of pixels called a cursor