Resolution and camera calibration

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Yes if you scale down the calibration images and the final images in the same way then everything cancels out.

You can also do the calibration at full resolution and then scale down the images - you just have to scale some of the calibration factors, fx,fy,cx,cy and the distortion values by the same factor.

Trickier is using a sub region of the calibrated image, the undistort is based on radial terms from the center so you need a little more 'finesse'