1. A method for stabilizing a digital video, the method comprising: receiving a reference video frame depicting a scene, the reference video frame depicting a reference point represented by one or more pixels at a reference pixel location; receiving a second frame depicting at least a portion of the scene, wherein movement of the reference point between the first and second frame results in the reference point being depicted at a different pixel location in the second frame; generating a stabilized second frame by non-uniformly shifting at least some points depicted in the second frame by an amount based on distances of the points from an edge of the second frame such that a greater shift is applied to non-edge points than edge points; and generating a stabilized video comprising a sequence of frames including the reference frame and the stabilized second frame, wherein depicted motion of the reference point between the first frame and the stabilized second frame is reduced relative to depicted motion of the reference point between the first frame and the second frame.