A WebmasterWorld thread has discussion on the basic topic of using absolute URLs versus relative URLs. I believe we covered the topic several times here, but not when it comes to image SEO.
Again, an absolute URL is using the full URL path, such as http://www.domain.com/filename. The relative URL is just using /filename in the source code.
Now when people rip off your content, sometimes they will forget to change the URLs and thus SEOs typically recommend using the absolute URL. Why? Because those rip off sites will then link to your content. The smarter spammers will strip out the domain anyway, so you don't win.
That being said, on the image SEO front, Tedster from the WebmasterWorldthread said there is some evidence that using an absolute URL in the image source code helps you "own" the image. Tedster said:
There is some evidence that using the absolute URL in the src attribute helps you "own" the image in the SERPs, rather than being ripped off by hotlinks. It's not a 100% sure thing, but as I said, there is "some" evidence.
I am not sure how true that is, I personally never looked into it.
Forum discussion at WebmasterWorld.