How to mathematically obtain camera trace path from video

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Dan
Dan 2016-7-12
I have an aerial video of some (approximately flat) view (no depth maps required).
I want to obtain the shape of the ground path the camera center passed upon.
The path does not have to be correct with correspondence to the worl'd north, or have any world coordinates. just have approximately the same shape, even if affine transformed.
I have already for each frame, the matrix that represents the affine transformation between that frame and the previous frame, at a good accuracy, meaning i have a matrix that for each pixel in a frame, gives the location of that pixel in the consecutive frame.
Given that the camera is moving, how can I obtain the SHAPE (over time) of the ground path of the spot on the ground that is in the center of the frames (=the trace)?
More generally, the question is actually only about knowing the relative center of the frame, for each frame, with correspondence to the first frame.
Any leads, as well as answers would benefit me a great deal.

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