What is the arbitrary scaling factor s in camera calibration?

[crackwitz]

@blauertee

So this stackexchange answer is definetly completely wrong?

that answer is fine.

what gave you the impression that it weren’t, or that I would think so? that’s not a rhetorical question. I’d like to know what made you think that. if you were just using some rhetorical device to goad me into responding, I don’t appreciate that.

@blauertee

What you’re saying is that even though i have a calibrated camera and a z coordinate to my object it is impossible to figure out the size of that object because the camera matrix can not provide that mapping?

I’m not saying that. that’s an entirely new situation, at least as I understood what you wrote so far.

@blauertee

I’m trying to figure out what size an object at distance d from the camera would have in pixels. In my understanding this is exactly what the camera matrix should do.

yes.

@blauertee

Given a 3d Point (x,y, d) it should project that point onto a UV Image plane (u, v).

yes.

@blauertee

But in the documentation an “arbitrary scaling factor” s is introduced which seems to throw away all the useful information that I put into the calibration.

no. the projection of the 3D point is the screen-space point (x, y, 1) or (x, y).

you misunderstand the point of s.

@blauertee

To my understanding, mathematically, […] all the relavant information would fall out of the calibration process, including the physical sensor size etc

sensor size cannot be determined from intrinsic calibration, no matter “if opencv didn’t normalize by that factor s” or did.