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The approaches are completely different.

Microsoft:

"Our algorithm first reconstructs the 3D input camera path as well as dense, per-frame proxy geometries. We then optimize a novel camera path for the output video (shown in red) that is smooth and passes near the input cameras while ensuring that the virtual camera looks in directions that can be rendered well from the input."

Instagram:

"... Smartphones didn’t have nearly enough power to replicate video-editing software, but they did have built-in gyroscopes. On a smartphone, instead of using power-hungry algorithms to model the camera’s movement, he could measure it directly. And he could funnel those measurements through a simpler algorithm that could map one frame to the next, giving the illusion that the camera was being held steady"



Wow. I would never have guessed that this would be possible to do by analyzing the gyroscope data. It must be sensitive enough to detect small / tiny jerks in your phone as those seemingly tiny jerks can often translate into enormous motion in your camera lens especially if a subject is far away.


Well, you can do stabilization as well for those, I guess.




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