There may be image libraries (or self-written code) that are capable to accomplish this. However, the image libraries Coppermine can be used with (GD and ImageMagick) are not capable to do so.
As far as I can see, momentshare is not an app that you can download and use on your webserver, but a service offering picture hosting, so they may have a special server setup (that's even most likely). Think of it as a service similar to youtube: although you can upload your video files in many different formats, they convert your video on the server (embedding it into flash afaik) and then host the converted video for you. They are only capable to do so because the server is theirs and they are allowed and capable to run a custom piece of code created by them.
Bottom line: just because momentshare is capable to accomplish this doesn't mean that it's possible to integrate this feature into coppermine.