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Measuring application

I would like to develop a system to capture images of a machine table and transform this image to a top-down view with correct measurements.

On the machine table, sheets with different thickness can be placed and we need to do real world measurements on the top plane of these sheets. The thickness is known.

The camera is fixed and can be placed either straight above the table but also on the side/corner of the table.

I have done camera calibration using a chessboard pattern and I have done perspective correction. So, at the moment I can make correct measurements on images in the same plane as the calibration (i.e Z=0)

So the question is how can I manage to measure an image at another plane/thickness (i.e Z>0) without doing a new calibration on that height.

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