How to reconstruct screen from an image?

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Hi all, OpenCV beginner here.

I have an image containing a projector screen somewhere in it. The screen is a rectangle, but is distorted by the projection (so not a rectangle in the image). What I need to do is

1. detect where the projector screen is in the image
2. cut everything but the screen
3. warp the screen back into a rectangle

So basically: find the projector screen + reconstruct it as a 2d image, ignoring everything else.

I can control what appears on the projector screen, so I was thinking of displaying red dots at the corners, to make the detection easier. Not sure what to do after that, though.

I googled around how to do this with OpenCV and I'm not any wiser for what I found. Stereo projections and calibration matrices... does anyone have code examples or human-friendly instructions?

I need help both with basic terminology (=what to google for) and how things click together in practice.