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Dr. Ariel Shamir's Home Page will give you a detailed description on how it's done. The technique is impressive and comes at a time when most of us thought of image editing as a plain vanilla service. On a related note, it's interesting to imagine how this may change things in the future. For one, it'll give copyrighting a whole new definition as pictures can be easily altered to remove content (and thereby creating totally new images).
Comments on TechCrunch also talk about editing music files, videos and even text to fit the browser in your desktop or handheld device.
All in all, it will be interesting to see how this service gets integrated into some of the more well-known photo editing softwares (like Photoshop) and whether the technology can be borrowed into resizing our videos.