Dunno what it is called, but I do know how it is done.
It's quite easy to do if your camera has burst mode and you have a tripod. If you don't have a tripod then something like the align_image_stack program that comes with hugin might be enough to line the images up and let you do it hand held.
Simply load each image as a layer in your favourite photo editor and selectively erase/merge down to uncover the dogs.
It's just a type of time lapse. They're not complicated to make, you just take the shots in a burst then lay them over the top of one another. Realistically, unless you're extremely lucky at least two of the frames will overlap and you'll need to cut out and reposition them.
I do them manually, but panorama / image stacking programs will probably work quite well until you have the dynamic parts overlapping. Doing them manually you can decide which frame takes precedence and try to get a tidy join.
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